

s ! # Duration of 9192631770 periods of the radiation second s # corresponding to the transition between the two hyperfine # levels of the ground state of the cesium-133 atom

m ! # Length of the path traveled by light in a vacuum meter m # during 1|299792458 seconds. Originally meant to be # 1e-7 of the length along a meridian from the equator # to a pole.

A ! # The current which produces a force of 2e-7 N/m between two ampere A # infinitely long wires that are 1 meter apart amp ampere

cd ! # Luminous intensity in a given direction of a source which candela cd # emits monochromatic radiation at 540e12 Hz with radiant # intensity 1|683 W/steradian. (This differs from radiant # intensity (W/sr) in that it is adjusted for human # perceptual dependence on wavelength. The frequency of # 540e12 Hz (yellow) is where human perception is most # efficient.)

mol ! # The amount of substance of a system which contains as many mole mol # elementary entities as there are atoms in 0.012 kg of # carbon 12. The elementary entities must be specified and # may be atoms, molecules, ions, electrons, or other # particles or groups of particles. It is understood that # unbound atoms of carbon 12, at rest and in the ground # state, are referred to.

K ! # 1|273.16 of the thermodynamic temperature of the triple kelvin K # point of water



The radian and steradian are defined as dimensionless primitive units.

The radian is equal to m/m and the steradian to m^2/m^2 so these units are

dimensionless. Retaining them as named units is useful because it allows

clarity in expressions and makes the meaning of unit definitions more clear.

These units will reduce to 1 in conversions but not for sums of units or for

arguments to functions.



radian !dimensionless # The angle subtended at the center of a circle by # an arc equal in length to the radius of the # circle sr !dimensionless # Solid angle which cuts off an area of the surface steradian sr # of the sphere equal to that of a square with # sides of length equal to the radius of the # sphere



Some primitive non-SI units



US$ ! # The US dollar is chosen arbitrarily to be the primitive # unit of money.

bit ! # Basic unit of information (entropy). The entropy in bits # of a random variable over a finite alphabet is defined # to be the sum of -p(i)*log2(p(i)) over the alphabet where # p(i) is the probability that the random variable takes # on the value i.

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

Prefixes (longer names must come first)



###########################################################################

yotta- 1e24 # Greek or Latin octo, “eight” zetta- 1e21 # Latin septem, “seven” exa- 1e18 # Greek hex, “six” peta- 1e15 # Greek pente, “five” tera- 1e12 # Greek teras, “monster” giga- 1e9 # Greek gigas, “giant” mega- 1e6 # Greek megas, “large” myria- 1e4 # Not an official SI prefix kilo- 1e3 # Greek chilioi, “thousand” hecto- 1e2 # Greek hekaton, “hundred” deca- 1e1 # Greek deka, “ten” deka- deca deci- 1e-1 # Latin decimus, “tenth” centi- 1e-2 # Latin centum, “hundred” milli- 1e-3 # Latin mille, “thousand” micro- 1e-6 # Latin micro or Greek mikros, “small” nano- 1e-9 # Latin nanus or Greek nanos, “dwarf” pico- 1e-12 # Spanish pico, “a bit” femto- 1e-15 # Danish-Norwegian femten, “fifteen” atto- 1e-18 # Danish-Norwegian atten, “eighteen” zepto- 1e-21 # Latin septem, “seven” yocto- 1e-24 # Greek or Latin octo, “eight”

quarter- 1|4 semi- 0.5 demi- 0.5 hemi- 0.5 half- 0.5 double- 2 triple- 3 treble- 3

kibi- 2^10 # In response to the convention of illegally mebi- 2^20 # and confusingly using metric prefixes for gibi- 2^30 # powers of two, the International tebi- 2^40 # Electrotechnical Commission aproved these pebi- 2^50 # binary prefixes for use in 1998. If you exbi- 2^60 # want to refer to “megabytes” using the Ki- kibi # binary definition, use these prefixes. Mi- mebi Gi- gibi Ti- tebi Pi- pebi Ei- exbi

Y- yotta Z- zetta E- exa P- peta T- tera G- giga M- mega k- kilo h- hecto da- deka d- deci c- centi m- milli n- nano p- pico f- femto a- atto z- zepto y- yocto



Names of some numbers



one 1 two 2 double 2 couple 2 three 3 triple 3 four 4 quadruple 4 five 5 quintuple 5 six 6 seven 7 eight 8 nine 9 ten 10 twenty 20 thirty 30 forty 40 fifty 50 sixty 60 seventy 70 eighty 80 ninety 90 hundred 100 thousand 1000 million 1e6

These number terms were described by N. Chuquet and De la Roche in the 16th

century as being successive powers of a million. These definitions are still

used in most European countries. The current US definitions for these

numbers arose in the 17th century and don’t make nearly as much sense. These

numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric

W. Weisstein.

usbillion 1e9 ustrillion 1e12 usquadrillion 1e15 usquintillion 1e18 ussextillion 1e21 usseptillion 1e24 usoctillion 1e27 usnonillion 1e30 usnoventillion nonillion usdecillion 1e33 usundecillion 1e36 usduodecillion 1e39 ustredecillion 1e42 usquattuordecillion 1e45 usquindecillion 1e48 ussexdecillion 1e51 usseptendecillion 1e54 usoctodecillion 1e57 usnovemdecillion 1e60 usvigintillion 1e63

centillion 1e303 googol 1e100

brbillion million^2 brtrillion million^3 brquadrillion million^4 brquintillion million^5 brsextillion million^6 brseptillion million^7 broctillion million^8 brnonillion million^9 brnoventillion brnonillion brdecillion million^10 brundecillion million^11 brduodecillion million^12 brtredecillion million^13 brquattuordecillion million^14 brquindecillion million^15 brsexdecillion million^16 brseptdecillion million^17 broctodecillion million^18 brnovemdecillion million^19 brvigintillion million^20

These numbers fill the gaps left by the European system above.

milliard 1000 million billiard 1000 million^2 trilliard 1000 million^3 quadrilliard 1000 million^4 quintilliard 1000 million^5 sextilliard 1000 million^6 septilliard 1000 million^7 octilliard 1000 million^8 nonilliard 1000 million^9 noventilliard nonilliard decilliard 1000 million^10

For consistency

brmilliard milliard brbilliard billiard brtrilliard trilliard brquadrilliard quadrilliard brquintilliard quintilliard brsextilliard sextilliard brseptilliard septilliard broctilliard octilliard brnonilliard nonilliard brnoventilliard noventilliard brdecilliard decilliard

The British Centillion would be 1e600. The googolplex is another

familiar large number equal to 10^googol. These numbers give overflows.

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

Derived units which can be reduced to the primitive units



#############################################################################



Named SI derived units (officially accepted)



newton kg m / s^2 # force N newton pascal N/m^2 # pressure or stress Pa pascal joule N m # energy J joule watt J/s # power W watt coulomb A s # charge C coulomb volt W/A # potential difference V volt ohm V/A # electrical resistance siemens A/V # electrical conductance S siemens farad C/V # capacitance F farad weber V s # magnetic flux Wb weber henry Wb/A # inductance H henry tesla Wb/m^2 # magnetic flux density T tesla hertz /s # frequency Hz hertz



Dimensions. These are here to help with dimensional analysis and

because they will appear in the list produced by hitting ‘?’ at the

“You want:” prompt to tell the user the dimension of the unit.



LENGTH meter AREA LENGTH^2 VOLUME LENGTH^3 MASS kilogram CURRENT ampere AMOUNT mole ANGLE radian SOLID_ANGLE steradian MONEY US$ FORCE newton PRESSURE FORCE / AREA STRESS FORCE / AREA CHARGE coulomb CAPACITANCE farad RESISTANCE ohm CONDUCTANCE siemens INDUCTANCE henry FREQUENCY hertz VELOCITY LENGTH / TIME ACCELERATION VELOCITY / TIME DENSITY MASS / VOLUME LINEAR_DENSITY MASS / LENGTH VISCOSITY FORCE TIME / AREA KINEMATIC_VISCOSITY VISCOSITY / DENSITY



units derived easily from SI units



gram millikg gm gram g gram tonne 1000 kg t tonne metricton tonne sthene tonne m / s^2 funal sthene pieze sthene / m^2 quintal 100 kg bar 1e5 Pa # About 1 atm vac millibar micron micrometer # One millionth of a meter bicron picometer # One brbillionth of a meter cc cm^3 are 100 m^2 liter 1000 cc # The liter was defined in 1901 as the oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at l liter # the temperature of its maximum density # under a pressure of 1 atm. This was # supposed to be 1000 cubic cm, but it # was discovered that the original # measurement was off. In 1964, the # liter was redefined to be exactly 1000 # cubic centimeters. mho siemens # Inverse of ohm, hence ohm spelled backward galvat ampere # Named after Luigi Galvani angstrom 1e-10 m # Convenient for describing molecular sizes xunit 1.00202e-13 meter # Used for measuring wavelengths siegbahn xunit # of X-rays. It is defined to be # 1|3029.45 of the spacing of calcite # planes at 18 degC. It was intended # to be exactly 1e-13 m, but was # later found to be off slightly. fermi 1e-15 m # Convenient for describing nuclear sizes # Nuclear radius is from 1 to 10 fermis barn 1e-28 m^2 # Used to measure cross section for # particle physics collision, said to # have originated in the phrase “big as # a barn”. shed 1e-24 barn # Defined to be a smaller companion to the # barn, but it’s too small to be of # much use. brewster micron^2/N # measures stress-optical coef diopter /m # measures reciprocal of lens focal length fresnel 1e12 Hz # occasionally used in spectroscopy shake 1e-8 sec svedberg 1e-13 s # Used for measuring the sedimentation # coefficient for centrifuging. gamma microgram # Also used for 1e-9 tesla lambda microliter spat 1e12 m # Rarely used for astronomical measurements preece 1e13 ohm m # resistivity planck J s # action of one joule over one second sturgeon /henry # magnetic reluctance daraf 1/farad # elastance (farad spelled backwards) leo 10 m/s^2 poiseuille N s / m^2 # viscosity mayer J/g K # specific heat mired / microK # reciprocal color temperature. The name # abbreviates micro reciprocal degree. crocodile megavolt # used informally in UK physics labs metricounce 25 g mounce metricounce finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light # with wavelength 296.7 nm. fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure # the energy incident on the receiving # body across a specified frequency # bandwidth. [12] jansky fluxunit # K. G. Jansky identified radio waves coming Jy jansky # from outer space in 1931. pfu / cm^2 sr s # particle flux unit – Used to measure # rate at which particles are received by # a spacecraft as particles per solid # angle per detector area per second. [18] pyron cal_IT / cm^2 min # Measures heat flow from solar radiation, # from Greek work “pyr” for fire. katal mol/sec # Measure of the amount of a catalyst. One kat katal # katal of catalyst enables the reaction # to consume or produce on mol/sec.



time



sec s minute 60 s min minute hour 60 min hr hour day 24 hr d day da day week 7 day wk week sennight 7 day fortnight 14 day blink 1e-5 day # Actual human blink takes 1|3 second
ce 1e-2 day cron 1e6 years watch 4 hours # time a sentry stands watch or a ship’s # crew is on duty. bell 1|8 watch # Bell would be sounded every 30 minutes.



angular measure



sign 1|12 circle # Angular extent of one sign of the zodiac turn circle revolution turn rev turn pulsatance radian / sec gon 1|100 rightangle # measure of grade grade gon centesimalminute 1|100 grade centesimalsecond 1|100 centesimalminute milangle 1|6400 circle # Official NIST definition. # Another choice is 1e-3 radian. pointangle 1|32 circle # Used for reporting compass readings centrad 0.01 radian # Used for angular deviation of light # through a prism. mas milli arcsec # Used by astronomers seclongitude circle (seconds/day) # Astronomers measure longitude # (which they call right ascension) in # time units by dividing the equator into # 24 hours instead of 360 degrees.



Some geometric formulas



circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi) spherevolume(r) [m;m^3] 4|3 pi r^3 ; cuberoot(spherevolume/4|3 pi) spherevol(r) [m;m^3] spherevolume(r) ; ~spherevolume(spherevol) square(x) x^2 ; sqrt(square)



Solid angle measure



sphere 4 pi sr squaredegree 1|180^2 pi^2 sr squareminute 1|60^2 squaredegree squaresecond 1|60^2 squareminute squarearcmin squareminute squarearcsec squaresecond sphericalrightangle 0.5 pi sr octant 0.5 pi sr



Concentration measures



percent 0.01

mill 0.001 # Originally established by Congress in 1791 # as a unit of money equal to 0.001 dollars, # it has come to refer to 0.001 in general. # Used by some towns to set their property # tax rate, and written with a symbol similar # to the % symbol but with two 0’s in the # denominator. [18] proof 1|200 # Alcohol content measured by volume at # 60 degrees Fahrenheit. This is a USA # measure. In Europe proof=percent. ppm 1e-6 partspermillion ppm ppb 1e-9 partsperbillion ppb # USA billion ppt 1e-12 partspertrillion ppt # USA trillion karat 1|24 # measure of gold purity caratgold karat gammil mg/l basispoint 0.01 % # Used in finance fine 1|1000 # Measure of gold purity

The pH scale is used to measure the concentration of hydronium (H3O+) ions in

a solution. A neutral solution has a pH of 7 as a result of dissociated

water molecules.

pH(x) [;mol/liter] 10^(-x) mol/liter ; (-log(pH liters/mol))



Temperature



Two types of units are defined: units for converting temperature differences

and functions for converting absolute temperatures. Conversions for

differences start with “deg” and conversions for absolute temperature start

with “temp”.



TEMPERATURE kelvin TEMPERATURE_DIFFERENCE kelvin

tempC(x) [;K] x K + stdtemp ; (tempC +(-stdtemp))/K # In 1741 Anders Celsius tempcelsius(x) [;K] tempC(x); ~tempC(tempcelsius) # introduced a temperature degcelsius K # scale with water boiling at 0 degrees and degC K # freezing at 100 degrees at standard # pressure. After his death the fixed points # were reversed and the scale was called the # centigrade scale. Due to the difficulty of # accurately measuring the temperature of # melting ice at standard pressure, the # centigrade scale was replaced in 1954 by # the Celsius scale which is defined by # subtracting 273.15 from the temperature in # Kelvins. This definition differed slightly # from the old centigrade definition, but the # Kelvin scale depends on the triple point of # water rather than a melting point, so it # can be measured accurately.

tempF(x) [;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 tempfahrenheit(x) [;K] tempF(x) ; ~tempF(tempfahrenheit) degfahrenheit 5|9 degC # Fahrenheit defined his temperature scale degF 5|9 degC # by setting 0 to the coldest temperature # he could produce in his lab with a salt # water solution and by setting 96 degrees to # body heat. In Fahrenheit’s words: # # Placing the thermometer in a mixture of # sal ammoniac or sea salt, ice, and water # a point on the scale will be found which # is denoted as zero. A second point is # obtained if the same mixture is used # without salt. Denote this position as # 30. A third point, designated as 96, is # obtained if the thermometer is placed in # the mouth so as to acquire the heat of a # healthy man.” (D. G. Fahrenheit, # Phil. Trans. (London) 33, 78, 1724)

degreesrankine degF # The Rankine scale has the degrankine degreesrankine # Fahrenheit degree, but it’s zero degreerankine degF # is at absolute zero. degR degrankine tempR degrankine temprankine degrankine

tempreaumur(x) [;K] x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur degreaumur 10|8 degC # The Reaumur scale was used in Europe and # particularly in France. It is defined # to be 0 at the freezing point of water # and 80 at the boiling point. Reaumur # apparently selected 80 because it is # divisible by many numbers.

degK K # “Degrees Kelvin” is forbidden usage. tempK K # For consistency.

Units cannot handle wind chill or heat index because they are two variable

functions, but they are included here for your edification. Clearly these

equations are the result of a model fitting operation.



wind chill index (WCI) a measurement of the combined cooling effect of low

air temperature and wind on the human body. The index was first defined

by the American Antarctic explorer Paul Siple in 1939. As currently used

by U.S. meteorologists, the wind chill index is computed from the

temperature T (in ?F) and wind speed V (in mi/hr) using the formula:

WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.

For very low wind speeds, below 4 mi/hr, the WCI is actually higher than

the air temperature, but for higher wind speeds it is lower than the air

temperature.



heat index (HI or HX) a measure of the combined effect of heat and

humidity on the human body. U.S. meteorologists compute the index

from the temperature T (in ?F) and the relative humidity H (as a

value from 0 to 1).

HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH

- .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2

- 0.0199 T^2 H^2.



Physical constants



Basic constants

pi 3.14159265358979323846 c 2.99792458e8 m/s # speed of light in vacuum (exact) light c mu0 4 pi 1e-7 H/m # permeability of vacuum (exact) epsilon0 1/mu0 c^2 # permittivity of vacuum (exact) energy c^2 # convert mass to energy e 1.602176462e-19 C # electron charge h 6.62606876e-34 J s # Planck constant hbar h / 2 pi spin hbar G 6.673e-11 N m^2 / kg^2 # Newtonian gravitational constant coulombconst 1/4 pi epsilon0 # listed as “k” sometimes

Physico-chemical constants

atomicmassunit 1.66053873e-27 kg# atomic mass unit (defined to be u atomicmassunit # 1|12 of the mass of carbon 12) amu atomicmassunit amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of # the 3 naturally occuring neutral # isotopes of oxygen amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral # oxygen 16 atom dalton u # Maybe this should be amu_chem? avogadro grams/amu mol # size of a mole N_A avogadro gasconstant 8.314472 J / mol K # molar gas constant R gasconstant boltzmann R / N_A # Boltzmann constant k boltzmann molarvolume mol R stdtemp / atm # Volume occupied by one mole of an # ideal gas at STP.
loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an # ideal gas at STP. Loschmidt did # work similar to Avogadro.
stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a sigma stefanboltzmann # blackbody at temperature T is # given by sigma T^4. wiendisplacement 2.8977686e-3 m K # Wien’s Displacement Law gives the # frequency at which the the Planck # spectrum has maximum intensity. # The relation is lambda T = b where # lambda is wavelength, T is # temperature and b is the Wien # displacement. This relation is # used to determine the temperature # of stars.
K_J 483597.9 GHz/V # Direct measurement of the volt is difficult. Until # recently, laboratories kept Weston cadmium cells as # a reference, but they could drift. In 1987 the # CGPM officially recommended the use of the # Josephson effect as a laboratory representation of # the volt. The Josephson effect occurs when two # superconductors are separated by a thin insulating # layer. A “supercurrent” flows across the insulator # with a frequency that depends on the potential # applied across the superconductors. This frequency # can be very accurately measured. The Josephson # constant K_J, which is equal to 2e/h, relates the # measured frequency to the potential. The value # given here is the officially specified value for # use beginning in 1990. The 1998 recommended value # of the constant is 483597.898 GHz/V. R_K 25812.807 ohm # Measurement of the ohm also presents difficulties. # The old approach involved maintaining resistances # that were subject to drift. The new standard is # based on the Hall effect. When a current carrying # ribbon is placed in a magnetic field, a potential # difference develops across the ribbon. The ratio # of the potential difference to the current is # called the Hall resistance. Klaus von Klitzing # discovered in 1980 that the Hall resistance varies # in discrete jumps when the magnetic field is very # large and the temperature very low. This enables # accurate realization of the resistance h/e^2 in the # lab. The value given here is the officially # specified value for use beginning in 1990.

Various conventional values

gravity 9.80665 m/s^2 # std acceleration of gravity (exact) force gravity # use to turn masses into forces atm 101325 Pa # Standard atmospheric pressure atmosphere atm Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact) water gram force/cm^3 # Standard weight of water (exact) waterdensity gram / cm^3 # Density of water H2O water wc water # water column mach 331.46 m/s # speed of sound in dry air at STP standardtemp 273.15 K # standard temperature stdtemp standardtemp

Weight of mercury and water at different temperatures using the standard

force of gravity.

Hg10C 13.5708 force gram / cm^3 # These units, when used to form
Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate Hg23C 13.5386 force gram / cm^3 # because of considerations of the Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale. Hg40C 13.4973 force gram / cm^3 Hg60F 13.5574 force gram / cm^3
H2O0C 0.99987 force gram / cm^3 H2O5C 0.99999 force gram / cm^3 H2O10C 0.99973 force gram / cm^3 H2O15C 0.99913 force gram / cm^3 H2O18C 0.99862 force gram / cm^3 H2O20C 0.99823 force gram / cm^3 H2O25C 0.99707 force gram / cm^3 H2O50C 0.98807 force gram / cm^3 H2O100C 0.95838 force gram / cm^3

Atomic constants

Rinfinity 10973731.568 /m # The wavelengths of a spectral series R_H 10967760 /m # can be expressed as # 1/lambda = R (1/m^2 - 1/n^2). # where R is a number that various # slightly from element to element. # For hydrogen, R_H is the value, # and for heavy elements, the value # approaches Rinfinity, which can be # computed from # m_e c alpha^2 / 2 h # with a loss of 5 digits # of precision.
alpha 7.297352533e-3 # The fine structure constant was # introduced to explain fine # structure visible in spectral # lines. It can be computed from # mu0 c e^2 / 2 h
# with a loss of 3 digits precision # and loss of precision in derived # values which use alpha. bohrradius alpha / 4 pi Rinfinity prout 185.5 keV # nuclear binding energy equal to 1|12 # binding energy of the deuteron

Planck constants

planckmass 2.1767e-8 kg # sqrt(hbar c / G) m_P planckmass plancktime hbar / planckmass c^2 t_P plancktime plancklength plancktime c l_P plancklength

Masses of elementary particles

electronmass 5.485799110e-4 u m_e electronmass protonmass 1.00727646688 u m_p protonmass neutronmass 1.00866491578 u m_n neutronmass muonmass 0.1134289168 u m_mu muonmass deuteronmass 2.01355321271 u m_d deuteronmass alphaparticlemass 4.0015061747 u m_alpha alphaparticlemass

particle wavelengths: the compton wavelength of a particle is

defined as h / m c where m is the mass of the particle.

electronwavelength h / m_e c
lambda_C electronwavelength protonwavelength h / m_p c lambda_C,p protonwavelength neutronwavelength h / m_n c lambda_C,n neutronwavelength

Magnetic moments

bohrmagneton e hbar / 2 electronmass mu_B bohrmagneton nuclearmagneton e hbar / 2 protonmass mu_N nuclearmagneton mu_mu 4.49044813e-26 J/T # Muon magnetic moment mu_p 1.410606633e-26 J/T # Proton magnetic moment mu_e 928.476362e-26 J/T # Electron magnetic moment mu_n 0.96623640e-26 J/T # Neutron magnetic moment mu_d 0.433073457e-26 J/T # Deuteron magnetic moment



Units derived from physical constants



kgf kg force technicalatmosphere kgf / cm^2 at technicalatmosphere hyl kgf s^2 / m # Also gram-force s^2/m according to [15] mmHg mm Hg torr mmHg # These units, both named after Evangelista tor Pa # Torricelli, should not be confused.
# Acording to [15] the torr is actually # atm/760 which is slightly different. inHg inch Hg inH2O inch water mmH2O mm water eV e V # Energy acquired by a particle with charge e electronvolt eV # when it is accelerated through 1 V lightyear c julianyear # The 365.25 day year is specified in ly lightyear # NIST publication 811 lightsecond c s lightminute c min parsec au / tan(arcsec) # Unit of length equal to distance pc parsec # from the sun to a point having # heliocentric parallax of 1 # arcsec (derived from parallax # second). A distant object with # paralax theta will be about # (arcsec/theta) parsecs from the # sun (using the approximation # that tan(theta) = theta).
rydberg h c Rinfinity # Rydberg energy crith 0.089885 gram # The crith is the mass of one # liter of hydrogen at standard # temperature and pressure. amagatvolume molarvolume amagat mol/amagatvolume # Used to measure gas densities lorentz bohrmagneton / h c # Used to measure the extent # that the frequency of light # is shifted by a magnetic field. cminv h c / cm # Unit of energy used in infrared invcm cminv # spectroscopy.
wavenumber cminv kcal_mol kcal / mol N_A # kcal/mol is used as a unit of # energy by physical chemists.



CGS system based on centimeter, gram and second



dyne cm gram / s^2 # force dyn dyne erg cm dyne # energy poise gram / cm s # viscosity, honors Jean Poiseuille P poise rhe /poise # reciprocal viscosity stokes cm^2 / s # kinematic viscosity St stokes stoke stokes lentor stokes # old name Gal cm / s^2 # acceleration, used in geophysics galileo Gal # for earth’s gravitational field # (note that “gal” is for gallon # but “Gal” is the standard symbol # for the gal which is evidently a # shortened form of “galileo”.) barye dyne/cm^2 # pressure barad barye # old name kayser 1/cm # Proposed as a unit for wavenumber balmer kayser # Even less common name than “kayser” kine cm/s # velocity bole g cm / s # momentum pond gram force glug gram force s^2 / cm # Mass which is accelerated at # 1 cm/s^2 by 1 gram force darcy centipoise cm^2 / s atm # Measures permeability to fluid flow.

                                    #   One darcy is the permeability of a
                                    #   medium that allows a flow of cc/s
                                    #   of a liquid of centipoise viscosity
                                    #   under a pressure gradient of
                                    #   atm/cm.  Named for H. Darcy. 

mohm cm / dyn s # mobile ohm, measure of mechanical mobileohm mohm # mobility mechanicalohm dyn s / cm # mechanical resistance acousticalohm dyn s / cm^5 # ratio of the sound pressure of # 1 dyn/cm^2 to a source of strength # 1 cm^3/s ray acousticalohm rayl dyn s / cm^3 # Specific acoustical resistance eotvos 1e-9 Gal/cm # Change in gravitational acceleration # over horizontal distance

Electromagnetic units derived from the abampere

abampere 10 A # Current which produces a force of abamp abampere # 2 dyne/cm between two infinitely aA abampere # long wires that are 1 cm apart biot aA # alternative name for abamp Bi biot abcoulomb abamp sec abcoul abcoulomb abfarad abampere sec / abvolt abhenry abvolt sec / abamp abvolt dyne cm / abamp sec abohm abvolt / abamp abmho /abohm gauss abvolt sec / cm^2 Gs gauss maxwell abvolt sec # Also called the “line” Mx maxwell oersted gauss / mu0 Oe oersted gilbert gauss cm / mu0 Gb gilbert Gi gilbert unitpole 4 pi maxwell emu erg/gauss # “electro-magnetic unit”, a measure of # magnetic moment, often used as emu/cm^3 # to specify magnetic moment density.

Gaussian system: electromagnetic units derived from statampere.



Note that the Gaussian units are often used in such a way that Coulomb’s law

has the form F= q1 * q2 / r^2. The constant 1|4piepsilon0 is incorporated

into the units. From this, we can get the relation force=charge^2/dist^2.

This means that the simplification esu^2 = dyne cm^2 can be used to simplify

units in the Gaussian system, with the curious result that capacitance can be

measured in cm, resistance in sec/cm, and inductance in sec^2/cm. These

units are given the names statfarad, statohm and stathenry below.

statampere 10 A cm / s c statamp statampere statvolt dyne cm / statamp sec statcoulomb statamp s esu statcoulomb statcoul statcoulomb statfarad statamp sec / statvolt cmcapacitance statfarad stathenry statvolt sec / statamp statohm statvolt / statamp statmho /statohm statmaxwell statvolt sec franklin statcoulomb debye 1e-18 statcoul cm # unit of electrical dipole moment helmholtz debye/angstrom^2 # Dipole moment per area jar 1000 statfarad # approx capacitance of Leyden jar



Some historical eletromagnetic units



intampere 0.999835 A # Defined as the current which in one intamp intampere # second deposits .001118 gram of # silver from an aqueous solution of # silver nitrate. intfarad 0.999505 F intvolt 1.00033 V intohm 1.000495 ohm # Defined as the resistance of a # uniform column of mercury containing # 14.4521 gram in a column 1.063 m # long and maintained at 0 degC. daniell 1.042 V # Meant to be electromotive force of a # Daniell cell, but in error by .04 V faraday N_A e mol # Charge that must flow to deposit or faraday_phys 96521.9 C # liberate one gram equivalent of any faraday_chem 96495.7 C # element. (The chemical and physical # values are off slightly from what is # obtained by multiplying by amu_chem # or amu_phys. These values are from # a 1991 NIST publication.) Note that # there is a Faraday constant which is # equal to N_A e and hence has units of # C/mol.
kappline 6000 maxwell # Named by and for Gisbert Kapp siemensunit 0.9534 ohm # Resistance of a meter long column of # mercury with a 1 mm cross section.



Photometric units



LUMINOUS_INTENSITY candela LUMINOUS_FLUX lumen LUMINOUS_ENERGY talbot ILLUMINANCE lux EXITANCE lux

candle 1.02 candela # Standard unit for luminous intensity hefnerunit 0.9 candle # in use before candela hefnercandle hefnerunit # violle 20.17 cd # luminous intensity of 1 cm^2 of # platinum at its temperature of # solidification (2045 K)

lumen cd sr # Luminous flux (luminous energy per lm lumen # time unit)

talbot lumen s # Luminous energy lumberg talbot

lux lm/m^2 # Illuminance or exitance (luminous lx lux # flux incident on or coming from phot lumen / cm^2 # a surface) ph phot # footcandle lumen/ft^2 # Illuminance from a 1 candela source # at a distance of one foot metercandle lumen/m^2 # Illuminance from a 1 candela source # at a distance of one meter

mcs metercandle s # luminous energy per area, used to # measure photographic exposure

nox 1e-3 lux # These two units were proposed for skot 1e-3 apostilb # measurements relating to dark adapted # eyes.

Luminance measures

LUMINANCE nit

nit cd/m^2 # Luminance: the intensity per projected stilb cd / cm^2 # area of an extended luminous source. sb stilb # (nit is from latin nitere = to shine.)

apostilb cd/pi m^2 asb apostilb blondel apostilb # Named after a French scientist.

Equivalent luminance measures. These units are units which measure

the luminance of a surface with a specified exitance which obeys

Lambert’s law. (Lambert’s law specifies that luminous intensity of

a perfectly diffuse luminous surface is proportional to the cosine

of the angle at which you view the luminous surface.)

equivalentlux cd / pi m^2 # luminance of a 1 lux surface equivalentphot cd / pi cm^2 # luminance of a 1 phot surface lambert cd / pi cm^2 footlambert cd / pi ft^2

The bril is used to express “brilliance” of a source of light on a

logarithmic scale to correspond to subjective perception. An increase of 1

bril means doubling the luminance. A luminance of 1 lambert is defined to

have a brilliance of 1 bril.

bril(x) [;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100

Some luminance data from the IES Lighting Handbook, 8th ed, 1993

sunlum 1.6e9 cd/m^2 # at zenith sunillum 100e3 lux # clear sky sunillum_o 10e3 lux # overcast sky sunlum_h 6e6 cd/m^2 # value at horizon skylum 8000 cd/m^2 # average, clear sky skylum_o 2000 cd/m^2 # average, overcast sky moonlum 2500 cd/m^2

Photographic Exposure Value



The Additive Photographic EXposure (APEX) system developed in Germany in

the 1960s was an attempt to simplify exposure determination for people

who relied on exposure tables rather than exposure meters. Shortly

thereafter, nearly all cameras incorporated exposure meters, so the APEX

system never caught on, but the concept of Exposure Value (EV) given by



A^2 LS ES

2^EV = — = – = –

T K C



Where

A = Relative aperture (f-number)

T = Shutter time in seconds

L = Scene luminance in cd/m2

E = Scene illuminance in lux

S = Arithmetic ISO film speed

K = Reflected-light meter calibration constant

C = Incident-light meter calibration constant



remains in use. Strictly speaking, an Exposure Value is a combination

of aperture and shutter time, but it’s also commonly used to indicate

luminance (or illuminance). Conversion to luminance or illuminance

units depends on the ISO film speed and the meter calibration constant.

Common practice is to use an ISO film speed of 100 (because film speeds

are in even 1/3-step increments, the exact value is 64 * 2^(2|3)).

Calibration constants vary among camera and meter manufacturers: Canon,

Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while

Minolta and Pentax use a value of 14. Minolta and Sekonic use a value

of 250 for incident-light meters with flat receptors.

s100 64 * 2^(2|3) / lx s # exact speed for ISO 100 film

Reflected-light meter calibration constant with ISO 100 film

k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic k1400 14 (cd/m2) / lx s # For Minolta and Pentax

Incident-light meter calibration constant with ISO 100 film

c250 250 lx / lx s # flat-disc receptor

Exposure value to scene luminance with ISO 100 film

For Minolta or Pentax

#ev100(x) [;cd/m^2] 2^x k1400 / s100; log2(ev100 s100 / k1400)

For Canon, Nikon or Sekonic

ev100(x) [;cd/m^2] 2^x k1250 / s100; log2(ev100 s100 / k1250)

Exposure value to scene illuminance with ISO 100 film

iv100(x) [1;lx] 2^x c250 / s100; log2(iv100 s100 / c250)



Astronomical time measurements



Astronmical time measurement is a complicated matter. The length of the true

day at a given place can be 21 seconds less than 24 hours or 30 seconds over

24 hours. The two main reasons for this are the varying speed of the earth

in its elliptical orbit and the fact that the sun moves on the ecliptic

instead of along the celestial equator. To devise a workable system for time

measurement, Simon Newcomb (1835-1909) used a fictitious “mean sun”.

Consider a first fictitious sun traveling along the ecliptic at a constant

speed and coinciding with the true sun at perigee and apogee. Then

considering a second fictitious sun traveling along the celestial equator at

a constant speed and coninciding with the first fictitious sun at the

equinoxes. The second fictitious sun is the “mean sun”. From this equations

can be written out to determine the length of the mean day, and the tropical

year. The length of the second was determined based on the tropical year

from such a calculation and was officially used from 1960-1967 until atomic

clocks replaced astronomical measurements for a standard of time. All of the

values below give the mean time for the specified interval.



See “Mathematical Astronomy Morsels” by Jean Meeus for more details

an a description of how to compute the correction to mean time.



TIME second

anomalisticyear 365.2596 days # The time between successive # perihelion passages of the # earth. siderealyear 365.256360417 day # The time for the earth to make # one revolution around the sun # relative to the stars. tropicalyear 365.242198781 day # The time needed for the mean sun # as defined above to increase # its longitude by 360 degrees. # Most references defined the # tropical year as the interval # between vernal equinoxes, but # this is misleading. The length # of the season changes over time # because of the eccentricity of # the earth’s orbit. The time # between vernal equinoxes is # approximately 365.24237 days # around the year 2000. See # “Mathematical Astronomy # Morsels” for more details. eclipseyear 346.62 days # The line of nodes is the # intersection of the plane of # Earth’s orbit around the sun # with the plane of the moon’s # orbit around earth. Eclipses # can only occur when the moon # and sun are close to this # line. The line rotates and # appearances of the sun on the # line of nodes occur every # eclipse year.
saros 223 synodicmonth # The earth, moon and sun appear in # the same arrangement every # saros, so if an eclipse occurs, # then one saros later, a similar # eclipse will occur. (The saros # is close to 19 eclipse years.) # The eclipse will occur about # 120 degrees west of the # preceeding one because the # saros is not an even number of # days. After 3 saros, an # eclipse will occur at # approximately the same place. siderealday 86164.09054 s # The sidereal day is the interval siderealhour 1|24 siderealday # between two successive transits siderealminute 1|60 siderealhour # of a star over the meridian, siderealsecond 1|60 siderealminute # or the time required for the # earth to make one rotation # relative to the stars. The # more usual solar day is the # time required to make a # rotation relative to the sun. # Because the earth moves in its # orbit, it has to turn a bit # extra to face the sun again, # hence the solar day is slightly # longer. anomalisticmonth 27.55454977 day # Time for the moon to travel from # perigee to perigee nodicalmonth 27.2122199 day # The nodes are the points where draconicmonth nodicalmonth # an orbit crosses the ecliptic. draconiticmonth nodicalmonth # This is the time required to # travel from the ascending node # to the next ascending node. siderealmonth 27.321661 day # Time required for the moon to # orbit the earth lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds # Mean time between full moons. synodicmonth lunarmonth # Full moons occur when the sun lunation synodicmonth # and moon are on opposite sides lune 1|30 lunation # of the earth. Since the earth lunour 1|24 lune # moves around the sun, the moon # has to revolve a bit extra to # get into the full moon # configuration. year tropicalyear yr year month 1|12 year mo month lustrum 5 years # The Lustrum was a Roman # purification ceremony that took # place every five years. # Classically educated Englishmen # used this term. decade 10 years century 100 years millennium 1000 years millennia millennium solaryear year lunaryear 12 lunarmonth calendaryear 365 day commonyear 365 day leapyear 366 day julianyear 365.25 day gregorianyear 365.2425 day islamicyear 354 day # A year of 12 lunar months. They islamicleapyear 355 day # began counting on July 16, AD 622 # when Muhammad emigrated to Medina # (the year of the Hegira). They need # 11 leap days in 30 years to stay in # sync with the lunar year which is a # bit longer than the 29.5 days of the # average month. The months do not # keep to the same seasons, but # regress through the seasons every # 32.5 years.
islamicmonth 1|12 islamicyear # They have 29 day and 30 day months.

The Hewbrew year is also based on lunar months, but synchronized to the solar

calendar. The months vary irregularly between 29 and 30 days in length, and

the years likewise vary. The regular year is 353, 354, or 355 days long. To

keep up with the solar calendar, a leap month of 30 days is inserted every

3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This

gives leap years that last 383, 384, or 385 days.

Sidereal days

mercuryday 58.6462 day venusday 243.01 day # retrograde earthday siderealday marsday 1.02595675 day jupiterday 0.41354 day saturnday 0.4375 day uranusday 0.65 day # retrograde neptuneday 0.768 day plutoday 6.3867 day

Sidereal years from http://ssd.jpl.nsaa.gov/phys_props_planets.html. Data

was updated in May 2001 based on the 1992 Explanatory Supplement to the

Astronomical Almanac and the mean longitude rates. Apparently the table of

years in that reference is incorrect.

mercuryyear 0.2408467 julianyear venusyear 0.61519726 julianyear earthyear siderealyear marsyear 1.8808476 julianyear jupiteryear 11.862615 julianyear saturnyear 29.447498 julianyear uranusyear 84.016846 julianyear neptuneyear 164.79132 julianyear plutoyear 247.92065 julianyear

Objects on the earth are charted relative to a perfect ellipsoid whose

dimensions are specified by different organizations. The ellipsoid is

specified by an equatorial radius and a flattening value which defines the

polar radius. These values are the 1996 values given by the International

Earth Rotation Service (IERS) whose reference documents can be found at

http://maia.usno.navy.mil/

earthflattening 1|298.25642 earthradius_equatorial 6378136.49 m earthradius_polar (-earthflattening+1) earthradius_equatorial

landarea 148.847e6 km^2 oceanarea 361.254e6 km^2

moonradius 1738 km # mean value sunradius 6.96e8 m

Many astronomical values can be measured most accurately in a system of units

using the astronomical unit and the mass of the sun as base units. The

uncertainty in the gravitational constant makes conversion to SI units

significantly less accurate.

The astronomical unit was defined to be the length of the of the semimajor

axis of a massless object with the same year as the earth. With such a

definition in force, and with the mass of the sun set equal to one, Kepler’s

third law can be used to solve for the value of the gravitational constant.

Kepler’s third law says that (2 pi / T)^2 a^3 = G M where T is the orbital

period, a is the size of the semimajor axis, G is the gravitational constant

and M is the mass. The Gaussian gravitational constant is the sqrt(G) in

with M = 1 we find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called

the Gaussian gravitational constant, apparently because Gauss originally did

the calculations. However, when the original calculation was done, the value

for the length of the earth’s year was inaccurate. The value used is called

the Gaussian year. Changing the astronomical unit to bring it into agreement

with more accurate values for the year would have invalidated a lot of

previous work, so instead the astronomical unit has been kept equal to this

original value. This is accomplished by using a standard value for the

Gaussian gravitational constant. This constant is called k.

gauss_k 0.01720209895 # This beast has dimensions of # au^(3|2) / day and is exact. gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian # gravitational constant. This is a # fictional year, and doesn’t # correspond to any celestial event. astronomicalunit 499.004783806 light second # Value from the DE-405 au astronomicalunit # ephemeris for the above described # astronomical unit.
solarmass 1.9891e30 kg sunmass solarmass

sundist 1.0000010178 au # mean earth-sun distance moondist 3.844e8 m # mean earth-moon distance sundist_near 1.471e11 m # earth-sun distance at perihelion sundist_far 1.521e11 m # earth-sun distance at aphelion

The following are masses for planetary systems, not just the planet itself.

The comments give the uncertainty in the denominators. As noted above,

masses are given relative to the solarmass because this is more accurate.

The conversion to SI is uncertain because of uncertainty in G, the

gravitational constant.



Values are from http://ssd.jpl.nasa.gov/astro_constants.html

mercurymass solarmass / 6023600 # 250 venusmass solarmass / 408523.71 # 0.06 earthmoonmass solarmass / 328900.56 # 0.02 marsmass solarmass / 3098708 # 9 jupitermass solarmass / 1047.3486 # 0.0008 saturnmass solarmass / 3497.898 # 0.018 uranusmass solarmass / 22902.98 # 0.03 neptunemass solarmass / 19412.24 # 0.04 plutomass solarmass / 1.35e8 # 0.07e8

moonearthmassratio 0.012300034 # uncertainty 3 x 10-9 earthmass earthmoonmass / ( 1 + moonearthmassratio) moonmass moonearthmassratio earthmass

These are the old values for the planetary masses. They may give

the masses of the planets alone.

oldmercurymass 0.33022e24 kg oldvenusmass 4.8690e24 kg oldmarsmass 0.64191e24 kg oldjupitermass 1898.8e24 kg oldsaturnmass 568.5e24 kg olduranusmass 86.625e24 kg oldneptunemass 102.78e24 kg oldplutomass 0.015e24 kg

Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in

turn cites Global Earth Physics by CF Yoder, 1995.

mercuryradius 2440 km venusradius 6051.84 km earthradius 6371.01 km marsradius 3389.92 km jupiterradius 69911 km
saturnradius 58232 km uranusradius 25362 km neptuneradius 24624 km plutoradius 1151 km

moongravity 1.62 m/s^2



The Hartree system of atomic units, derived from fundamental units

of mass (of electron), action (planck’s constant), charge, and

the coulomb constant.

Fundamental units

atomicmass electronmass atomiccharge e atomicaction hbar

derived units (Warning: accuracy is lost from deriving them this way)

atomiclength bohrradius atomictime hbar^3/coulombconst^2 atomicmass e^4 # Period of first # bohr orbit atomicvelocity atomiclength / atomictime atomicenergy hbar / atomictime hartree atomicenergy Hartree hartree



These thermal units treat entropy as charge, from [5]



thermalcoulomb J/K # entropy thermalampere W/K # entropy flow thermalfarad J/K^2 thermalohm K^2/W # thermal resistance fourier thermalohm thermalhenry J K^2/W^2 # thermal inductance thermalvolt K # thermal potential difference



United States units



linear measure

The US Metric Law of 1866 legalized the metric system in the USA and defined

the meter in terms of the British system with the exact 1 meter = 39.37

inches. On April 5, 1893 Corwin Mendenhall decided, in what has become known

as the “Mendenhall Order” that the meter and kilogram would be the

fundamental standards in the USA. The definition from 1866 was turned around

to give an exact definition of the foot as 1200|3937 meters. This definition

was used until July of 1959 when the definition was changed to bring the US

into agreement with other countries. Since 1959, the foot has been exactly

0.3048 meters. At the same time it was decided that any data expressed in

feet derived from geodetic surveys within the US would continue to use the

old definition and call the old unit the “survey foot”.

US 1200|3937 m/ft # These four values will convert US- US # international measures to survey- US # US Survey measures geodetic- US int 3937|1200 ft/m # Convert US Survey measures to int- int # international measures

inch 2.54 cm in inch foot 12 inch feet foot ft foot yard 3 ft yd yard mile 5280 ft # The mile was enlarged from 5000 ft # to this number in order to make # it an even number of furlongs. # (The Roman mile is 5000 romanfeet.) line 1|12 inch # Also defined as ‘.1 in’ or as ‘1e-8 Wb’ rod 5.5 yard perch rod furlong 40 rod # From “furrow long” statutemile mile league 3 mile # Intended to be an an hour’s walk

surveyor’s measure

surveyorschain 66 surveyft surveychain surveyorschain surveyorspole 1|4 surveyorschain surveyorslink 1|100 surveyorschain chain 66 ft link 1|100 chain ch chain usacre 10 surveychain^2 intacre 10 chain^2 # Acre based on international ft intacrefoot acre surveyfoot usacrefoot usacre surveyfoot section mile^2 township 36 section homestead 160 acre # Area of land granted by the 1862 Homestead # Act of the United States Congress gunterschain surveyorschain

engineerschain 100 ft engineerslink 1|100 engineerschain ramsdenschain engineerschain ramsdenslink engineerslink

gurleychain 33 feet # Andrew Ellicott chain is the gurleylink 1|50 gurleychain # same length

wingchain 66 feet # Chain from 1664, introduced by winglink 1|80 wingchain # Vincent Wing, also found in a
# 33 foot length with 40 links.

nautical measure

fathom 6 ft # Originally defined as the distance from # fingertip to fingertip with arms fully # extended. nauticalmile 1852 m # Supposed to be one minute of latitude at # the equator. That value is about 1855 m. # Early estimates of the earth’s circumference # were a bit off. The value of 1852 m was # made the international standard in 1929. # The US did not accept this value until # 1954. The UK switched in 1970.

cable 1|10 nauticalmile intcable cable # international cable cablelength cable UScable 100 USfathom navycablelength 720 USft # used for depth in water marineleague 3 nauticalmile geographicalmile brnauticalmile knot nauticalmile / hr click km # US military slang klick click

Avoirdupois weight

pound 0.45359237 kg # The one normally used lb pound # From the latin libra grain 1|7000 pound # The grain is the same in all three # weight systems. It was originally # defined as the weight of a barley # corn taken from the middle of the # ear. ounce 1|16 pound oz ounce dram 1|16 ounce dr dram ushundredweight 100 pounds cwt hundredweight shorthundredweight ushundredweight uston shortton shortton 2000 lb quarterweight 1|4 uston shortquarterweight 1|4 shortton shortquarter shortquarterweight

Troy Weight. In 1828 the troy pound was made the first United States

standard weight. It was to be used to regulate coinage.

troypound 5760 grain troyounce 1|12 troypound ozt troyounce pennyweight 1|20 troyounce # Abbreviated “d” in reference to a dwt pennyweight # Frankish coin called the “denier” # minted in the late 700’s. There
# were 240 deniers to the pound. assayton mg ton / troyounce # mg / assayton = troyounce / ton usassayton mg uston / troyounce brassayton mg brton / troyounce fineounce troyounce # A troy ounce of 99.5% pure gold

Some other jewelers units

metriccarat 0.2 gram # Defined in 1907 metricgrain 50 mg carat metriccarat ct carat jewelerspoint 1|100 carat silversmithpoint 1|4000 inch momme 3.75 grams # Traditional Japanese unit based # on the chinese mace. It is used for # pearls in modern times and also for # silk density. The definition here # was adopted in 1891.

Apothecaries’ weight

appound troypound apounce troyounce apdram 1|8 apounce apscruple 1|3 apdram

Liquid measure

usgallon 231 in^3 # US liquid measure is derived from gal gallon # the British wine gallon of 1707.
quart 1|4 gallon # See the “winegallon” entry below pint 1|2 quart # more historical information.
gill 1|4 pint usquart 1|4 usgallon uspint 1|2 usquart usgill 1|4 uspint usfluidounce 1|16 uspint fluiddram 1|8 usfloz minimvolume 1|60 fluiddram qt quart pt pint floz fluidounce usfloz usfluidounce fldr fluiddram liquidbarrel 31.5 usgallon usbeerbarrel 2 beerkegs beerkeg 15.5 usgallon # Various among brewers ponykeg 1|2 beerkeg winekeg 12 usgallon petroleumbarrel 42 usgallon # Originated in Pennsylvania oil barrel petroleumbarrel # fields, from the winetierce bbl barrel hogshead 2 liquidbarrel usfirkin 9 gallon

Dry measures: The Winchester Bushel was defined by William III in 1702 and

legally adopted in the US in 1836.

usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5 bu bushel # inch diameter (rounded) peck 1|4 bushel uspeck 1|4 usbushel brpeck 1|4 brbushel pk peck drygallon 1|2 uspeck dryquart 1|4 drygallon drypint 1|2 dryquart drybarrel 7056 in^3 # Used in US for fruits, vegetables, # and other dry commodities except for # cranberries. cranberrybarrel 5826 in^3 # US cranberry barrel heapedbushel 1.278 usbushel# The following explanation for this

                                  #   value was provided by Wendy Krieger
                                  #   <os2fan2@yahoo.com> based on
                                  #   guesswork.  The cylindrical vessel is
                                  #   18.5 inches in diameter and 1|2 inch
                                  #   thick.  A heaped bushel includes the
                                  #   contents of this cylinder plus a heap
                                  #   on top.  The heap is a cone 19.5
                                  #   inches in diameter and 6 inches
                                  #   high.  With these values, the volume
                                  #   of the bushel is 684.5 pi in^3 and
                                  #   the heap occupies 190.125 pi in^3.
                                  #   Therefore, the heaped bushel is
                                  #   874.625|684.5 bushels.  This value is
                                  #   approximately 1.2777575 and it rounds
                                  #   to the value listed for the size of
                                  #   the heaped bushel.  Sometimes the
                                  #   heaped bushel is reported as 1.25
                                  #   bushels.  This same explanation gives
                                  #   that value if the heap is taken to
                                  #   have an 18.5 inch diameter.  

Grain measures. The bushel as it is used by farmers in the USA is actually

a measure of mass which varies for different commodities. Canada uses the

same bushel masses for most commodities, but not for oats.

wheatbushel 60 lb soybeanbushel 60 lb cornbushel 56 lb ryebushel 56 lb barleybushel 48 lb oatbushel 32 lb ricebushel 45 lb canada_oatbushel 34 lb

Wine and Spirits measure

ponyvolume 1 usfloz jigger 1.5 usfloz # Can vary between 1 and 2 usfloz shot jigger # Sometimes 1 usfloz eushot 25 ml # EU standard spirits measure fifth 1|5 usgallon winebottle 750 ml # US industry standard, 1979 winesplit 1|4 winebottle wineglass 4 usfloz magnum 1.5 liter # Standardized in 1979, but given # as 2 qt in some references metrictenth 375 ml metricfifth 750 ml metricquart 1 liter

Old British bottle size

reputedquart 1|6 brgallon reputedpint 1|2 reputedquart brwinebottle reputedquart # Very close to 1|5 winegallon

French champagne bottle sizes

split 200 ml jeroboam 2 magnum rehoboam 3 magnum methuselah 4 magnum salmanazar 6 magnum balthazar 8 magnum nebuchadnezzar 10 magnum



Water is “hard” if it contains various minerals, expecially calcium

carbonate.



clarkdegree 1|70000 # Content by weigh of calcium carbonate gpg grains/gallon # Divide by water’s density to convert to # a dimensionless concentration measure



Shoe measures



shoeiron 1|48 inch # Used to measure leather in soles shoeounce 1|64 inch # Used to measure non-sole shoe leather

USA shoe sizes. These express the length of the shoe or the length

of the “last”, the form that the shoe is made on. But note that

this only captures the length. It appears that widths change 1/4

inch for each letter within the same size, and if you change the

length by half a size then the width changes between 1/8 inch and

1/4 inch. But this may not be standard. If you know better, please

contact me.

shoesize_delta 1|3 inch # USA shoe sizes differ by this amount shoe_men0 8.25 inch shoe_women0 (7+11|12) inch shoe_boys0 (3+11|12) inch shoe_girls0 (3+7|12) inch

shoesize_men(n) [;inch] shoe_men0 + n shoesize_delta ;
(shoesize_men+(-shoe_men0))/shoesize_delta shoesize_women(n) [;inch] shoe_women0 + n shoesize_delta ;
(shoesize_women+(-shoe_women0))/shoesize_delta shoesize_boys(n) [;inch] shoe_boys0 + n shoesize_delta ;
(shoesize_boys+(-shoe_boys0))/shoesize_delta shoesize_girls(n) [;inch] shoe_girls0 + n shoesize_delta ;
(shoesize_girls+(-shoe_girls0))/shoesize_delta

European shoe size. According to

http://www.shoeline.com/footnotes/shoeterm.shtml#paris points

sizes in Europe are measured with Paris points which simply measure

the length of the shoe.

europeshoesize 2|3 cm



USA slang units



buck US$ fin 5 US$ sawbuck 10 US$ usgrand 1000 US$ greenback US$ key kg # usually of marijuana, 60’s lid 1 oz # Another 60’s weed unit footballfield usfootballfield usfootballfield 100 yards canadafootballfield 110 yards # And 65 yards wide marathon 26 miles + 385 yards



British



The length measure in the UK was defined by a bronze bar manufactured in

1844. Various conversions were sanctioned for convenience at different

times, which makes conversions before 1963 a confusing matter. Apparently

previous conversions were never explicitly revoked. Four different

conversion factors appear below. Multiply them times an imperial length

units as desired. unit. The Weights and Measures Act of 1963 switched the

UK away from their bronze standard and onto a definition of the yard in terms

of the meter. This happened after an international agreement in 1959 to

align the world’s measurement systems.

UK UKlength_SJJ
UK- UK british- UK

UKlength_B 0.9143992 meter / yard # Benoit found the yard to be # 0.9143992 m at a weights and # measures conference around # 1896. Legally sanctioned # in 1898. UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and # Johnson found the yard to be # 0.91439841 meters.
# Used starting in the 1930’s. UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio # for the meter and inch. This # value was used as the legal # conversion ratio when the # metric system was legalized # for contract in 1864. UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter # to be 1.09362311 yards. This # conversion was legalized # around 1878. brnauticalmile 6080 ft # Used until 1970 when the UK brknot brnauticalmile / hr # switched to the international brcable 1|10 brnauticalmile # nautical mile. admiraltymile brnauticalmile admiraltyknot brknot admiraltycable brcable seamile 6000 ft shackle 15 fathoms # Adopted 1949 by British navy

British Imperial weight is mostly the same as US weight. A few extra

units are added here.

clove 7 lb stone 14 lb tod 28 lb brquarterweight 1|4 brhundredweight brhundredweight 8 stone longhundredweight brhundredweight longton 20 brhundredweight brton longton

British Imperial volume measures

brminim 1|60 brdram brscruple 1|3 brdram fluidscruple brscruple brdram 1|8 brfloz brfluidounce 1|20 brpint brfloz brfluidounce brgill 1|4 brpint brpint 1|2 brquart brquart 1|4 brgallon brgallon 4.54609 l # The British Imperial gallon was # defined in 1824 to be the volume of # water which weighed 10 pounds at 62 # deg F with a pressure of 30 inHg. # It was also defined as 277.274 in^3, # Which is slightly in error. In # 1963 it was defined to be the volume # occupied by 10 pounds of distilled # water of density 0.998859 g/ml weighed # in air of density 0.001217 g/ml # against weights of density 8.136 g/ml. # This gives a value of approximately # 4.5459645 liters, but the old liter # was in force at this time. In 1976 # the definition was changed to exactly # 4.54609 liters using the new # definition of the liter (1 dm^3). brbarrel 36 brgallon # Used for beer brbushel 8 brgallon brheapedbushel 1.278 brbushel brquarter 8 brbushel brchaldron 36 brbushel

Obscure British volume measures. These units are generally traditional

measures whose definitions have fluctuated over the years. Often they

depended on the quantity being measured. They are given here in terms of

British Imperial measures. For example, the puncheon may have historically

been defined relative to the wine gallon or beer gallon or ale gallon

rather than the British Imperial gallon.

bag 4 brbushel bucket 4 brgallon kilderkin 2 brfirkin last 40 brbushel noggin brgill pottle 0.5 brgallon pin 4.5 brgallon puncheon 72 brgallon seam 8 brbushel coomb 4 brbushel boll 6 brbushel
firlot 1|4 boll brfirkin 9 brgallon # Used for ale and beer cran 37.5 brgallon # measures herring, about 750 fish brhogshead 63 brgallon brbeerbutt 2 brhogshead registerton 100 ft^3 # Used for internal capacity of ships shippington 40 ft^3 # Used for ship’s cargo freight or timber brshippington 42 ft^3 # freightton shippington # Both register ton and shipping ton derive # from the “tun cask” of wine. displacementton 35 ft^3 # Approximate volume of a longton weight of # sea water. Measures water displaced by # ships. waterton 224 brgallon strike 70.5 l # 16th century unit, sometimes # defined as .5, 2, or 4 bushels # depending on the location. It # probably doesn’t make a lot of # sense to define in terms of imperial # bushels. Zupko gives a value of # 2 Winchester grain bushels or about # 70.5 liters. amber 4 brbushel# Used for dry and liquid capacity [18]

obscure British lengths

barleycorn 1|3 UKinch # Given in Realm of Measure as the # difference between successive shoe sizes nail 1|16 UKyard # Originally the width of the thumbnail, # or 1|16 ft. This took on the general # meaning of 1|16 and settled on the # nail of a yard or 1|16 yards as its # final value. [12] pole 16.5 UKft # This was 15 Saxon feet, the Saxon rope 20 UKft # foot (aka northern foot) being longer englishell 45 UKinch flemishell 27 UKinch ell englishell # supposed to be measure from elbow to # fingertips span 9 UKinch # supposed to be distance from thumb # to pinky with full hand extension goad 4.5 UKft # used for cloth, possibly named after the # stick used for prodding animals.

misc obscure British units

rood 1|4 acre englishcarat troyounce/151.5 # Originally intended to be 4 grain # but this value ended up being # used in the London diamond market mancus 2 oz mast 2.5 lb nailkeg 100 lbs basebox 31360 in^2 # Used in metal plating

alternate spellings

metre meter gramme gram litre liter dioptre diopter aluminium aluminum sulphur sulfur



Units derived the human body (may not be very accurate)



geometricpace 5 ft # distance between points where the same # foot hits the ground pace 2.5 ft # distance between points where alternate # feet touch the ground USmilitarypace 30 in # United States official military pace USdoubletimepace 36 in # United States official doubletime pace fingerbreadth 7|8 in # The finger is defined as either the width fingerlength 4.5 in # or length of the finger finger fingerbreadth palmwidth hand # The palm is a unit defined as either the width palmlength 8 in # or the length of the hand hand 4 inch # width of hand shaftment 6 inch # Distance from tip of outstretched thumb to the # opposite side of the palm of the hand. The # ending -ment is from the old English word # for hand. [18]



Cooking measures



Common abbreviations

tbl tablespoon tbsp tablespoon tblsp tablespoon Tb tablespoon tsp teaspoon saltspoon 1|4 tsp

US measures

uscup 8 usfloz ustablespoon 1|16 uscup usteaspoon 1|3 ustablespoon ustbl ustablespoon ustbsp ustablespoon ustblsp ustablespoon ustsp usteaspoon metriccup 250 ml stickbutter 1|4 lb # Butter in the USA is sold in one # pound packages that contain four # individually wrapped pieces. The # pieces are marked into tablespoons, # making it possible to measure out # butter by volume by slicing the # butter.

US can sizes.

number1can 10 usfloz number2can 19 usfloz number2.5can 3.5 uscups number3can 4 uscups number5can 7 uscups number10can 105 usfloz

British measures

brcup 1|2 brpint brteacup 1|3 brpint brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon brdessertspoon 2 brteaspoon dessertspoon brdessertspoon dsp dessertspoon brtsp brteaspoon brtbl brtablespoon brtbsp brtablespoon brtblsp brtablespoon

Australian

australiatablespoon 20 ml austbl australiatablespoon austbsp australiatablespoon austblsp australiatablespoon australiateaspoon 1|4 australiatablespoon austsp australiateaspoon

Chinese

catty 0.5 kg
oldcatty 4|3 lbs # Before metric conversion. tael 1|16 oldcatty # Should the tael be defined both ways? mace 0.1 tael oldpicul 100 oldcatty picul 100 catty # Chinese usage

Indian

seer 14400 grain # British Colonial standard ser seer maund 40 seer pakistanseer 1 kg pakistanmaund 40 pakistanseer chittak 1|16 seer tola 1|5 chittak ollock 1|4 liter # Is this right?

Japanese

japancup 200 ml

densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum

so you can convert ‘2 cups sugar’ to grams, for example, or in the other

direction grams could be converted to ‘cup flour_scooped’.

butter 8 oz/uscup butter_clarified 6.8 oz/uscup cocoa_butter 9 oz/uscup shortening 6.75 oz/uscup # vegetable shortening oil 7.5 oz/uscup cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the
cakeflour_spooned 4 oz/uscup # measuring method. “Scooped”, or
cakeflour_scooped 4.5 oz/uscup # “dip and sweep” refers to dipping a
flour_sifted 4 oz/uscup # measure into a bin, and then sweeping flour_spooned 4.25 oz/uscup # the excess off the top. “Spooned”
flour_scooped 5 oz/uscup # means to lightly spoon into a measure breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a
breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top.
cornstarch 120 grams/uscup dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa dutchcocoa_spooned 92 g/uscup dutchcocoa_scooped 95 g/uscup cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa cocoa_spooned 82 g/uscup cocoa_scooped 95 g/uscup heavycream 232 g/uscup milk 242 g/uscup sourcream 242 g/uscup molasses 11.25 oz/uscup cornsyrup 11.5 oz/uscup honey 11.75 oz/uscup sugar 200 g/uscup powdered_sugar 4 oz/uscup brownsugar_light 217 g/uscup # packed brownsugar_dark 239 g/uscup

baking_powder 4.6 grams / ustsp salt 6 g / ustsp koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt koshersalt_morton 4.8 g / ustsp # Morton kosher salt # Values are from the nutrition info # on the packages

Egg weights and volumes for a USA large egg

egg 50 grams eggwhite 30 grams eggyolk 18.6 grams eggvolume 3 ustablespoons + 1|2 ustsp eggwhitevolume 2 ustablespoons eggyolkvolume 3.5 ustsp



Density measures. Density has traditionally been measured on a variety of

bizarre nonlinear scales.



Density of a sugar syrup is frequently measured in candy making procedures.

In the USA the boiling point of the syrup is measured. Some recipes instead

specify the density using degrees Baume. Conversion between degrees Baume

and the boiling point measure has proved elusive. One food science text

claimed that the boiling point elevation formula could be used. This formula

gives the elevation 1000 (.512) x / (100-x) 342.3 for sucrose. However,

it disagrees significantly with a table that appeared in another text

which gave the table below. However, this table cannot be converted reliably

to a density measure because the brix table stops at 80% concentration.



temp(C) conc (%)

100 30

101 40

102 50

103 60

106 70

112 80

123 90

140 95

151 97

160 98.2

166 99.5

171 99.6



Degrees Baume is used in European recipes to specify the density of a sugar

syrup. An entirely different definition is used for densities below

1 g/cm^3. An arbitrary constant appears in the definition. This value is

equal to 145 in the US, but was according to [], the old scale used in

Holland had a value of 144, and the new scale or Gerlach scale used 146.78.

baumeconst 144 # US value baume(d) [1;g/cm^3] (baumeconst/(baumeconst+-d)) g/cm^3 ;
(baume+((-g)/cm^3)) baumeconst / baume

twaddell(x) [1;g/cm^3] (1 + 0.005 x) g / cm^3 ; 200 (twaddell / (g/cm^3) +- 1)

The degree quevenne is a unit for measuring the density of milk.

quevenne(x) [1;g/cm^3] (1 + 0.001 x) g / cm^3 ; 1000 (quevenne / (g/cm^3) +- 1)

Degrees brix measures sugar concentration by weigh as a percentage, so a

solution that is 3 degrees brix is 3% sugar by weight. This unit was named

after Adolf Brix who invented a hydrometer that read this percentage

directly. This table converts brix to density at 20 degrees Celsius.

brix[g/cm^3]
0.0 0.9982, 0.5 1.0002, 1.0 1.0021
1.5 1.0040, 2.0 1.0060, 2.5 1.0079
3.0 1.0099, 3.5 1.0119, 4.0 1.0139
5.0 1.0178, 5.5 1.0198, 6.0 1.0218
6.5 1.0238, 7.0 1.0259, 7.5 1.0279
8.0 1.0299, 8.5 1.0320, 9.0 1.0340
9.5 1.0361, 10.0 1.0381, 11.0 1.0423
12.0 1.0465, 13.0 1.0507, 14.0 1.0549
15.0 1.0592, 16.0 1.0635, 17.0 1.0678
18.0 1.0722, 19.0 1.0766, 20.0 1.0810
22.0 1.0899, 24.0 1.0990, 26.0 1.1082
28.0 1.1175, 30.0 1.1270, 32.0 1.1366
34.0 1.1464, 36.0 1.1562, 38.0 1.1663
40.0 1.1765, 42.0 1.1868, 44.0 1.1972
46.0 1.2079, 48.0 1.2186, 50.0 1.2295
52.0 1.2406, 54.0 1.2518, 56.0 1.2632
58.0 1.2747, 60.0 1.2864, 62.0 1.2983
64.0 1.3103, 66.0 1.3224, 68.0 1.3348
70.0 1.3472, 72.0 1.3599, 74.0 1.3726
76.0 1.3855, 78.0 1.3986, 80.0 1.4117
82.0 1.4250, 84.0 1.4383

Density measure invented by the American Petroleum Institute. Lighter

petroleum products are more valuable, and they get a higher API degree.

apidegree(x) [1;g/cm^3] 141.5 g/cm^3 / (x+131.5) ;
141.5 (g/cm^3) / apidegree + (-131.5)



Units derived from imperial system



ouncedal oz ft / s^2 # force which accelerates an ounce # at 1 ft/s^2 poundal lb ft / s^2 # same thing for a pound tondal ton ft / s^2 # and for a ton pdl poundal osi ounce force / inch^2 # used in aviation psi pound force / inch^2 psia psi # absolute pressure tsi ton force / inch^2 reyn psi sec slug lbf s^2 / ft slugf slug force slinch lbf s^2 / inch # Mass unit derived from inch second slinchf slinch force # pound-force system. Used in space # applications where in/sec^2 was a # natural acceleration measure. geepound slug lbf lb force tonf ton force lbm lb kip 1000 lbf # from kilopound ksi kip / in^2 mil 0.001 inch thou 0.001 inch circularinch 1|4 pi in^2 # area of a one-inch diameter circle circleinch circularinch # A circle with diameter d inches has # an area of d^2 circularinches cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter # has volume d^2 h cylinder inches circularmil 1|4 pi mil^2 # area of one-mil diameter circle cmil circularmil

cental 100 pound centner cental caliber 0.01 inch # for measuring bullets duty ft lbf celo ft / s^2 jerk ft / s^3 australiapoint 0.01 inch # The “point” is used to measure rainfall # in Australia sabin ft^2 # Measure of sound absorption equal to the # absorbing power of one square foot of # a perfectly absorbing material. The # sound absorptivity of an object is the # area times a dimensionless # absorptivity coefficient. standardgauge 4 ft + 8.5 in # Standard width between railroad track flag 5 ft^2 # Construction term referring to sidewalk. rollwallpaper 30 ft^2 # Area of roll of wall paper fillpower in^3 / ounce # Density of down at standard pressure. # The best down has 750-800 fillpower. pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA. buttonline 1|40 inch # The line was used in 19th century USA # to measure width of buttons. scoopnumber /quart # Ice cream scoops are labeled with a
# number specifying how many scoops
# fill a quart. beespace 1|4 inch # Bees will fill any space that is smaller # than the bee space and leave open # spaces that are larger. The size of # the space varies with species.
diamond 8|5 ft # Marking on US tape measures that is # useful to carpenters who wish to place # five studs in an 8 ft distance. Note # that the numbers appear in red every # 16 inches as well, giving six # divisions in 8 feet.
retmaunit 1.75 in # Height of rack mountable equipment. U retmaunit # Equipment should be 1|32 inch narrower # than its U measurement indicates to # allow for clearance, so 4U=(6+31|32)in # RETMA stands for the former name of # the standardizing organization, Radio # Electronics Television Manufacturers # Association. This organization is now # called the Electronic Industries # Alliance (EIA) and the rack standard # is specified in EIA RS-310-D.



Other units of work, energy, power, etc



ENERGY joule WORK joule

Calories: energy to raise a gram of water one degree celsius

cal_IT 4.1868 J # International Table calorie cal_th 4.184 J # Thermochemical calorie cal_fifteen 4.18580 J # Energy to go from 14.5 to 15.5 degC cal_twenty 4.18190 J # Energy to go from 19.5 to 20.5 degC cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC calorie cal_IT cal calorie calorie_IT cal_IT thermcalorie cal_th calorie_th thermcalorie Calorie kilocalorie # the food Calorie thermie 1e6 cal_fifteen # Heat required to raise the # temperature of a tonne of # water from 14.5 to 15.5 degC.

btu definitions: energy to raise a pound of water 1 degF

btu cal lb degF / gram K # international table BTU britishthermalunit btu btu_IT btu btu_th cal_th lb degF / gram K btu_mean cal_mean lb degF / gram K quad quadrillion btu

ECtherm 1.05506e8 J # Exact definition, close to 1e5 btu UStherm 1.054804e8 J # Exact definition therm UStherm toe 1e10 cal_IT # ton oil equivalent. Energy released # by burning one metric ton of oil. [18] tonscoal 1|2.3 toe # Energy in metric ton coal from [18]. naturalgas toe / 1270 m^3 # Energy released from natural gas # from [18]. (At what pressure?)

Celsius heat unit: energy to raise a pound of water 1 degC

celsiusheatunit cal lb degC / gram K chu celsiusheatunit

POWER watt

The horsepower is supposedly the power of one horse pulling. Obviously

different people had different horses.

ushorsepower 550 foot pound force / sec # Invented by James Watt hp horsepower metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in electrichorsepower 746 W # Germany boilerhorsepower 9809.50 W waterhorsepower 746.043 W brhorsepower 745.70 W donkeypower 250 W chevalvapeur metrichorsepower

Thermal insulance: Thermal conductivity has dimension power per area per

(temperature difference per length thickness) which comes out to W / K m. If

the thickness is fixed, then the conductance will have units of W / K m^2.

Thermal insulance is the reciprocal.

THERMAL_CONDUCTANCE POWER/AREA (TEMPERATURE_DIFFERENCE/LENGTH) THERMAL_INSULANCE 1/THERMAL_CONDUCTANCE THERMAL_CONDUCTIVITY THERMAL_CONDUCTANCE / LENGTH THERMAL_INSULATION THERMAL_INSULANCE LENGTH Rvalue degF ft^2 hr / btu Uvalue 1/Rvalue europeanUvalue watt / m^2 K RSI degC m^2 / W clo 0.155 degC m^2 / W # Supposed to be the insulance # required to keep a resting person # comfortable indoors. The value # given is from NIST and the CRC, # but [5] gives a slightly different # value of 0.875 ft^2 degF hr / btu. tog 0.1 degC m^2 / W # Also used for clothing.

Misc other measures

ENTROPY ENERGY / TEMPERATURE clausius 1e3 cal/K # A unit of physical entropy langley thermcalorie/cm^2 # Used in radiation theory poncelet 100 kg force m / s tonrefrigeration ton 144 btu / lb day # One ton refrigeration is # the rate of heat extraction required # turn one ton of water to ice in # a day. Ice is defined to have a # latent heat of 144 btu/lb. tonref tonrefrigeration refrigeration tonref / ton frigorie 1000 cal_fifteen# Used in refrigeration engineering. tnt 1e9 cal_th / ton# So you can write tons-tnt. This # is a defined, not measured, value. airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as # pressure times air flow.



Permeability: The permeability or permeance, n, of a substance determines

how fast vapor flows through the substance. The formula W = n A dP

holds where W is the rate of flow (in mass/time), n is the permeability,

A is the area of the flow path, and dP is the vapor pressure difference.



perm_0C grain / hr ft^2 inHg perm_zero perm_0C perm_0 perm_0C perm perm_0C perm_23C grain / hr ft^2 in Hg23C perm_twentythree perm_23C



Counting measures



pair 2 brace 2
nest 3 # often used for items like bowls that # nest together hattrick 3 # Used in sports, especially cricket and ice # hockey to report the number of goals. dicker 10 dozen 12 bakersdozen 13 score 20 flock 40 timer 40 shock 60 toncount 100 # Used in sports in the UK longhundred 120 # From a germanic counting system gross 144 greatgross 12 gross tithe 1|10 # From Anglo-Saxon word for tenth

Paper counting measure

shortquire 24 quire 25 shortream 480 ream 500
perfectream 516 bundle 2 reams bale 5 bundles



Paper measures



USA paper sizes

lettersize 8.5 inch 11 inch legalsize 8.5 inch 14 inch ledgersize 11 inch 17 inch executivesize 7.25 inch 10.5 inch Apaper 8.5 inch 11 inch Bpaper 11 inch 17 inch Cpaper 17 inch 22 inch Dpaper 22 inch 34 inch Epaper 34 inch 44 inch

pointthickness mil

The metric paper sizes are defined so that if a sheet is cut in half

along the short direction, the result is two sheets which are

similar to the original sheet. This means that for any metric size,

the long side is close to sqrt(2) times the length of the short

side. Each series of sizes is generated by repeated cuts in half,

with the values rounded down to the nearest millimeter.

A0paper 841 mm 1189 mm # The basic size in the A series A1paper 594 mm 841 mm # is defined to have an area of A2paper 420 mm 594 mm # one square meter. A3paper 297 mm 420 mm A4paper 210 mm 297 mm A5paper 148 mm 210 mm A6paper 105 mm 148 mm A7paper 74 mm 105 mm A8paper 52 mm 74 mm A9paper 37 mm 52 mm A10paper 26 mm 37 mm

B0paper 1000 mm 1414 mm # The basic B size has an area B1paper 707 mm 1000 mm # of sqrt(2) square meters.
B2paper 500 mm 707 mm B3paper 353 mm 500 mm B4paper 250 mm 353 mm B5paper 176 mm 250 mm B6paper 125 mm 176 mm B7paper 88 mm 125 mm B8paper 62 mm 88 mm B9paper 44 mm 62 mm B10paper 31 mm 44 mm

C0paper 917 mm 1297 mm # The basic C size has an area C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters. C2paper 458 mm 648 mm C3paper 324 mm 458 mm # Intended for envelope sizes C4paper 229 mm 324 mm C5paper 162 mm 229 mm C6paper 114 mm 162 mm C7paper 81 mm 114 mm C8paper 57 mm 81 mm C9paper 40 mm 57 mm C10paper 28 mm 40 mm

gsm (Grams per Square Meter), a sane, metric paper weight measure

gsm grams / meter^2

In the USA, a collection of crazy historical paper measures are used. Paper

is measured as a weight of a ream of that particular type of paper. This is

sometimes called the “substance” or “basis” (as in “substance 20” paper).

The standard sheet size or “basis size” varies depending on the type of

paper. As a result, 20 pound bond paper and 50 pound text paper are actually

about the same weight. The different sheet sizes were historically the most

convenient for printing or folding in the different applications. These

different basis weights are standards maintained by American Society for

Testing Materials (ASTM) and the American Forest and Paper Association

(AF&PA).

poundbookpaper lb / 25 inch 38 inch ream lbbook poundbookpaper poundtextpaper poundbookpaper lbtext poundtextpaper poundoffsetpaper poundbookpaper # For offset printing lboffset poundoffsetpaper poundbiblepaper poundbookpaper # Designed to be lightweight, thin, lbbible poundbiblepaper # strong and opaque. poundtagpaper lb / 24 inch 36 inch ream lbtag poundtagpaper poundbagpaper poundtagpaper lbbag poundbagpaper poundnewsprintpaper poundtagpaper lbnewsprint poundnewsprintpaper poundposterpaper poundtagpaper lbposter poundposterpaper poundtissuepaper poundtagpaper lbtissue poundtissuepaper poundwrappingpaper poundtagpaper lbwrapping poundwrappingpaper poundwaxingpaper poundtagpaper lbwaxing poundwaxingpaper poundglassinepaper poundtagpaper lbglassine poundglassinepaper poundcoverpaper lb / 20 inch 26 inch ream lbcover poundcoverpaper poundindexpaper lb / 25.5 inch 30.5 inch ream lbindex poundindexpaper poundindexbristolpaper poundindexpaper lbindexbristol poundindexpaper poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and lbbond poundbondpaper # durable for repeated poundwritingpaper poundbondpaper # filing, and it resists lbwriting poundwritingpaper # ink penetration.
poundledgerpaper poundbondpaper lbledger poundledgerpaper poundcopypaper poundbondpaper lbcopy poundcopypaper poundblottingpaper lb / 19 inch 24 inch ream lbblotting poundblottingpaper poundblankspaper lb / 22 inch 28 inch ream lbblanks poundblankspaper poundpostcardpaper lb / 22.5 inch 28.5 inch ream lbpostcard poundpostcardpaper poundweddingbristol poundpostcardpaper lbweddingbristol poundweddingbristol poundbristolpaper poundweddingbristol lbbristol poundbristolpaper poundboxboard lb / 1000 ft^2 lbboxboard poundboxboard poundpaperboard poundboxboard lbpaperboard poundpaperboard

When paper is marked in units of M, it means the weight of 1000 sheets of the

given size of paper. To convert this to paper weight, divide by the size of

the paper in question.

paperM lb / 1000



Printing



fournierpoint 0.1648 inch / 12 # First definition of the printers # point made by Pierre Fournier who # defined it in 1737 as 1|12 of a # cicero which was 0.1648 inches. olddidotpoint 1|72 frenchinch # Fran?ois Ambroise Didot, one of # a family of printers, changed # Fournier’s definition around 1770 # to fit to the French units then in # use.
bertholdpoint 1|2660 m # H. Berthold tried to create a # metric version of the didot point # in 1878.
INpoint 0.4 mm # This point was created by a # group directed by Fermin Didot in # 1881 and is associated with the # imprimerie nationale. It doesn’t # seem to have been used much. germandidotpoint 0.376065 mm # Exact definition appears in DIN # 16507, a German standards document # of 1954. Adopted more broadly in # 1966 by ??? metricpoint 3|8 mm # Proposed in 1977 by Eurograf point 1|72.27 inch # The American point was invented printerspoint point # by Nelson Hawks in 1879 and # dominates USA publishing. # It was standardized by the American # Typefounders Association at the # value of 0.013837 inches exactly. # Knuth uses the approximation given # here (which is very close). The # comp.fonts FAQ claims that this # value is supposed to be 1|12 of a # pica where 83 picas is equal to 35 # cm. But this value differs from # the standard.
texscaledpoint 1|65536 point # The TeX typesetting system uses texsp texscaledpoint # this for all computations. computerpoint 1|72 inch # The American point was rounded computerpica 12 computerpoint # to an even 1|72 inch by computer postscriptpoint computerpoint # people at some point. pspoint postscriptpoint Q 1|4 mm # Used in Japanese phototypesetting # Q is for quarter frenchprinterspoint olddidotpoint
didotpoint germandidotpoint # This seems to be the dominant value europeanpoint didotpoint # for the point used in Europe cicero 12 didotpoint

stick 2 inches

Type sizes

excelsior 3 point brilliant 3.5 point diamondtype 4 point pearl 5 point agate 5.5 point # Originally agate type was 14 lines per # inch, giving a value of 1|14 in. ruby agate # British nonpareil 6 point mignonette 6.5 point emerald mignonette # British minion 7 point brevier 8 point bourgeois 9 point longprimer 10 point smallpica 11 point pica 12 point english 14 point columbian 16 point greatprimer 18 point paragon 20 point meridian 44 point canon 48 point

German type sizes

nonplusultra 2 didotpoint brillant 3 didotpoint diamant 4 didotpoint perl 5 didotpoint nonpareille 6 didotpoint kolonel 7 didotpoint petit 8 didotpoint borgis 9 didotpoint korpus 10 didotpoint corpus korpus garamond korpus mittel 14 didotpoint tertia 16 didotpoint text 18 didotpoint kleine_kanon 32 didotpoint kanon 36 didotpoint grobe_kanon 42 didotpoint missal 48 didotpoint kleine_sabon 72 didotpoint grobe_sabon 84 didotpoint



Information theory units. Note that the name “entropy” is used both

to measure information and as a physical quantity.



INFORMATION bit

nat ln(2) bits # Entropy measured base e hartley log2(10) bits # Entropy of a uniformly # distributed random variable # over 10 symbols.



Computer



bps bit/sec # Sometimes the term “baud” is # incorrectly used to refer to # bits per second. Baud refers # to symbols per second. Modern # modems transmit several bits # per symbol. byte 8 bit # Not all machines had 8 bit B byte # bytes, but these days most of # them do. But beware: for # transmission over modems, a # few extra bits are used so # there are actually 10 bits per # byte. octet 8 bits # The octet is always 8 bits nybble 4 bits # Half of a byte. Sometimes # equal to different lengths # such as 3 bits.
nibble nybble
meg megabyte # Some people consider these # units along with the kilobyte gig gigabyte # to be defined according to # powers of 2 with the kilobyte # equal to 2^10 bytes, the # megabyte equal to 2^20 bytes and # the gigabyte equal to 2^30 bytes # but these usages are forbidden # by SI. Binary prefixes have # been defined by IEC to replace # the SI prefixes. Use them to # get the binary values: KiB, MiB, # and GiB. jiffy 0.01 sec # This is defined in the Jargon File jiffies jiffy # (http://www.jargon.org) as being the # duration of a clock tick for measuring # wall-clock time. Supposedly the value # used to be 1|60 sec or 1|50 sec # depending on the frequency of AC power, # but then 1|100 sec became more common. # On linux systems, this term is used and # for the Intel based chips, it does have # the value of .01 sec. The Jargon File # also lists two other definitions: # millisecond, and the time taken for # light to travel one foot. cdromspeed 150 kB/s # CD-ROM “1X” transfer rate (audio is # higher at 172 kB/s) Are these right?? dvdspeed 1350 KiB/s # Is this right??



Musical measures. Musical intervals expressed as ratios. Multiply

two intervals together to get the sum of the interval. The function

musicalcent can be used to convert ratios to cents.



Perfect intervals

octave 2 majorsecond musicalfifth^2 / octave majorthird 5|4 minorthird 6|5
musicalfourth 4|3 musicalfifth 3|2 majorsixth musicalfourth majorthird minorsixth musicalfourth minorthird majorseventh musicalfifth majorthird minorseventh musicalfifth minorthird

pythagoreanthird majorsecond musicalfifth^2 / octave syntoniccomma pythagoreanthird / majorthird pythagoreancomma musicalfifth^12 / octave^7

Equal tempered definitions

semitone octave^(1|12) musicalcent(x) [1;1] semitone^(x/100) ; 100 log(musicalcent)/log(semitone)



Musical note lengths.



wholenote ! MUSICAL_NOTE_LENGTH wholenote halfnote 1|2 wholenote quarternote 1|4 wholenote eighthnote 1|8 wholenote sixteenthnote 1|16 wholenote thirtysecondnote 1|32 wholenote sixtyfourthnote 1|64 wholenote dotted 3|2 doubledotted 7|4 breve doublewholenote semibreve wholenote minimnote halfnote crochet quarternote quaver eighthnote semiquaver sixteenthnote demisemiquaver thirtysecondnote hemidemisemiquaver sixtyfourthnote semidemisemiquaver hemidemisemiquaver



yarn and cloth measures



yarn linear density

woolyarnrun 1600 yard/pound # 1600 yds of “number 1 yarn” weighs # a pound.
yarncut 300 yard/pound # Less common system used in # Pennsylvania for wool yarn cottonyarncount 840 yard/pound linenyarncount 300 yard/pound # Also used for hemp and ramie worstedyarncount 1680 ft/pound metricyarncount meter/gram denier 1|9 tex # used for silk and rayon manchesteryarnnumber drams/1000 yards # old system used for silk pli lb/in typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound asbestoscut 100 yd/lb # used for glass and asbestos yarn

tex gram / km # rational metric yarn measure, meant drex 0.1 tex # to be used for any kind of yarn poumar lb / 1e6 yard

yarn and cloth length

skeincotton 80*54 inch # 80 turns of thread on a reel with a # 54 in circumference (varies for other # kinds of thread) cottonbolt 120 ft # cloth measurement woolbolt 210 ft bolt cottonbolt heer 600 yards cut 300 yards # used for wet-spun linen yarn lea 300 yards

sailmakersyard 28.5 in sailmakersounce oz / sailmakersyard 36 inch

silkmomme momme / 25 yards 1.49 inch # Traditional silk weight silkmm silkmomme # But it is also defined as # lb/100 yd 45 inch. The two # definitions are slightly different # and neither one seems likely to be # the true source definition.



drug dosage



mcg microgram # Frequently used for vitamins iudiptheria 62.8 microgram # IU is for international unit iupenicillin 0.6 microgram iuinsulin 41.67 microgram drop 1|20 ml # The drop was an old “unit” that was # replaced by the minim. But I was # told by a pharmacist that in his # profession, the conversion of 20 # drops per ml is actually used. bloodunit 450 ml # For whole blood. For blood # components, a blood unit is the # quanity of the component found in a # blood unit of whole blood. The # human body contains about 12 blood # units of whole blood.



misc medical measure



frenchcathetersize 1|3 mm # measure used for the outer diameter # of a catheter



fixup units for times when prefix handling doesn’t do the job



hectare hectoare megohm megaohm kilohm kiloohm microhm microohm megalerg megaerg # ‘L’ added to make it pronounceable [18].



Money



Note that US$ is the primitive unit so other currencies are

generally given in US$.



Some European currencies have permanent fixed exchange rates with

the Euro. These rates were taken from the EC’s web site:

http://europa.eu.int/euro/entry.html

Currency exchange rates for April 2005

$ dollar mark germanymark bolivar venezuelabolivar peseta spainpeseta rand southafricarand escudo portugalescudo sol perusol guilder netherlandsguilder hollandguilder netherlandsguilder peso mexicopeso yen japanyen lira italylira rupee indiarupee drachma greecedrachma franc francefranc markka finlandmarkka sucre ecuadorsucre poundsterling britainpound

ISO currency codes

ADP andorrapeseta
AED unitedarabdirham AFA afghanistanafghani ALL albanialek AMD armeniadram AOK angolakwanza ARS argentinapeso ATS austriaschilling AUD australiadollar AWG arubaflorin AZM azerbaijanmanat BAM bosniamarks BBD barbadosdollar BDT bangladeshtaka BEF belgiumfranc BGL bulgarialev BHD bahraindinar BIF burundifranc BMD bermudadollar BND bruneidarussalamdollar BOB boliviaboliviano BRL brazilreal BSD bahamasdollar BTN bhutanngultrum BWP botswanapula BYB belarusruble BZD belizedollar CAD canadadollar CHF switzerlandfranc CLP chilepeso CNY chinayuan COP colombiapeso CRC costaricacolon CUP cubapeso CVE capeverdeescudo CYP cypruspound CZK czechkoruna DEM germanymark DJF djiboutifranc DKK denmarkkrone DOP dominicanrepublicpeso DZD algeriadinar ECS ecuadorsucre EEK estoniakroon EGP egyptpound ERN eritreanakfa ESP spainpeseta ETB ethiopiabirr EUR euro FIM finlandmarkka FJD fijidollar FKP falklandislandspound FRF francefranc GBP britainpound GEL georgialari GHC ghanacedi GIP gibraltarpound GMD gambiadalasi GNF guineafranc GRD greecedrachma GTQ guatemalaquetzal GYD guyanadollar HKD hongkongdollar HNL honduraslempira HRK croatiakuna HTG haitigourde HUF hungaryforint IDR indonesiarupiah IEP irelandpunt ILS israelsheqel INR indiarupee IRR iranrial ISK icelandkrona ITL italylira JMD jamaicadollar JOD jordandinar JPY japanyen KES kenyashilling KGS kyrgyzstansom KHR cambodiariel KMF comorosfranc KPW northkoreawon KRW southkoreawon KWD kuwaitdinar KYD caymanislandsdollar KZT kazakhstantenge LAK laokip LBP lebanonpound LKR srilankarupee LRD liberiadollar LSL lesotholoti LTL lithuanialitas LUF luxembourgfranc LVL latvialats LYD libyadinar MAD moroccodirham MDL moldovaleu MGF madagascarfranc MMK myanmarkyat MNT mongoliatugrik MOP macaupataca MRO mauritaniaouguiya MTL maltalira MUR mauritiusrupee MVR maldivesrufiyaa MWK malawikwacha MXN mexicopeso MYR malaysiaringgit MZM mozambiquemetical NAD namibiadollar NGN nigerianaira NIO nicaraguaoro NLG netherlandsguilder NOK norwaykrone NPR nepalrupee NZD newzealanddollar OMR omanrial PEN perusol PGK papuanewguineakina PHP philippinespeso PKR pakistanrupee PLN polandzloty PTE portugalescudo PYG paraguayguarani QAR qatarrial ROL romanialeu RUB russiaruble RWF rwandafranc SAR saudiarabiariyal SBD solomonislandsdollar SCR seychellesrupee SDD sudandinar SEK swedenkrona SGD singaporedollar SHP sthelenapound SIT sloveniatolar SKK slovakiakoruna SLL sierraleoneleone SOS somaliashilling SRG surinameguilder STD saotomedobra SVC elsalvadorcolon SYP syriapound SZL swazilandlilangeni THB thailandbaht TJR tajikistanruble TMM turkmenistanmanat TND tunisiadinar TOP tongapa’anga TRL turkeylira TTD trinidaddollar TWD taiwandollar TZS tanzaniashilling UAH ukrainehryvnia UGX ugandashilling USD US$ UYU uruguaypeso UZS uzbekistansum VEB venezuelabolivar VND vietnamdong VUV vanuatuvatu WST samoatala XCD eastcarribeandollar YER yemenrial ZAR southafricarand ZMK zambiakwacha ZWD zimbabwedollar

UKP GBP # Not an ISO code, but looks like one, and # sometimes used on usenet.

Precious metals (25 April 2005)

goldprice US$ 433.00 / troyounce silverprice US$ 7.2150 / troyounce

Money on the gold standard, used in the late 19th century and early

20th century.

olddollargold 23.22 grains goldprice # Used until 1934 newdollargold 96|7 grains goldprice # After Jan 31, 1934 dollargold newdollargold poundgold 113 grains goldprice

Nominal masses of US coins. Note that dimes, quarters and half dollars

have weight proportional to value. Before 1965 it was $40 / kg.

USpennyweight 2.5 grams # Since 1982, 48 grains before USnickelweight 5 grams USdimeweight 10 cents / (20 US$ / lb) # Since 1965 USquarterweight 25 cents / (20 US$ / lb) # Since 1965 UShalfdollarweight 50 cents / (20 US$ / lb) # Since 1971 USdollarmass 8.1 grams

British currency

quid britainpound # Slang names fiver 5 quid tenner 10 quid monkey 500 quid brgrand 1000 quid bob shilling

shilling 1|20 britainpound # Before decimalisation, there oldpence 1|12 shilling # were 20 shillings to a pound, farthing 1|4 oldpence # each of twelve old pence guinea 21 shilling # Still used in horse racing crown 5 shilling florin 2 shilling groat 4 oldpence tanner 6 oldpence brpenny 0.01 britainpound pence penny tuppence 2 pence tuppenny tuppence ha’penny halfpenny hapenny ha’penny oldpenny oldpence oldtuppence 2 oldpence oldtuppenny oldtuppence threepence 3 oldpence # threepence never refers to new money threepenny threepence oldthreepence threepence oldthreepenny threepence oldhalfpenny halfoldpenny oldha’penny oldhalfpenny oldhapenny oldha’penny brpony 25 britainpound

Canadian currency

loony 1 canadadollar # This coin depicts a loon toony 2 canadadollar



Units used for measuring volume of wood



cord 448 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood facecord 1|2 cord cordfoot 1|8 cord # One foot long section of a cord cordfeet cordfoot housecord 1|3 cord # Used to sell firewood for residences, # often confusingly called a “cord” boardfoot ft^2 inch # Usually 1 inch thick wood boardfeet boardfoot fbm boardfoot # feet board measure stack 4 yard^3 # British, used for firewood and coal [18] rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly # sometimes called a face cord, but this # value is equal to 1|3 cord. Name # comes from an old Norse word for a # stack of wood.
stere m^3 timberfoot ft^3 # Used for measuring solid blocks of wood standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or # Pittsburg standard. Apparently the # term is short for “standard hundred” # which was meant to refer to 100 pieces # of wood (deals). However, this # particular standard is equal to 120 # deals which are 12 ft by 11 in by 1.5 # inches (not the standard deal).

In Britain, the deal is apparently any piece of wood over 6 feet long, over

7 wide and 2.5 inches thick. The OED doesn’t give a standard size. A piece

of wood less than 7 inches wide is called a “batten”. This unit is now used

exclusively for fir and pine.

deal 12 ft 11 in 2.5 in # The standard North American deal [OED] wholedeal 12 ft 11 in 1.25 in # If it’s half as thick as the standard # deal it’s called a “whole deal”! splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal.



Gas and Liquid flow units



FLUID_FLOW VOLUME / TIME

Some obvious volumetric gas flow units (cu is short for cubic)

cumec m^3/s cusec ft^3/s

Conventional abbreviations for fluid flow units

gph gal/hr gpm gal/min mgd megagal/day cfs ft^3/s cfh ft^3/hour cfm ft^3/min lpm liter/min lfm ft/min # Used to report air flow produced by fans. # Multiply by cross sectional area to get a # flow in cfm.

pru mmHg / (ml/min) # peripheral resistance unit, used in # medicine to assess blood flow in # the capillaries.

Miner’s inch: This is an old historic unit used in the Western United

States. It is generally defined as the rate of flow through a one square

inch hole at a specified depth such as 4 inches. In the late 19th century,

volume of water was sometimes measured in the “24 hour inch”. Values for the

miner’s inch were fixed by state statues. (This information is from a web

site operated by the Nevada Division of Water Planning: The Water Words

Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.)

minersinchAZ 1.5 ft^3/min minersinchCA 1.5 ft^3/min minersinchMT 1.5 ft^3/min minersinchNV 1.5 ft^3/min minersinchOR 1.5 ft^3/min minersinchID 1.2 ft^3/min minersinchKS 1.2 ft^3/min minersinchNE 1.2 ft^3/min minersinchNM 1.2 ft^3/min minersinchND 1.2 ft^3/min minersinchSD 1.2 ft^3/min minersinchUT 1.2 ft^3/min minersinchCO 1.56 ft^3/min minersinchBC 1.68 ft^3/min # British Columbia

Oceanographic flow

sverdrup 1e6 m^3 / sec # Used to express flow of ocean # currents. Named after Norwegian # oceanographer H. Sverdrup.

In vacuum science and some other applications, gas flow is measured

as the product of volumetric flow and pressure. This is useful

because it makes it easy to compare with the flow at standard

pressure (one atmosphere). It also directly relates to the number

of gas molecules per unit time, and hence to the mass flow if the

molecular mass is known.

GAS_FLOW PRESSURE FLUID_FLOW

sccm atm cc/min # ‘s’ is for “standard” to indicate sccs atm cc/sec # flow at standard pressure scfh atm ft^3/hour # scfm atm ft^3/min slpm atm liter/min slph atm liter/hour lusec liter micron Hg / s # Used in vacuum science



Wire Gauge



This area is a nightmare with huge charts of wire gauge diameters

that usually have no clear origin. There are at least 5 competing wire gauge

manufacturing method: a metal rod is heated and drawn through a hole. The

size change can’t be too big. To get smaller wires, the process is repeated

with a series of smaller holes. Generally larger gauges mean smaller wires.

The gauges often have values such as “00” and “000” which are larger sizes

than simply “0” gauge. In the tables that appear below, these gauges must be

specified as negative numbers (e.g. “00” is -1, “000” is -2, etc).

Alternatively, you can use the following units:



g00 (-1) g000 (-2) g0000 (-3) g00000 (-4) g000000 (-5) g0000000 (-6)

American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most

important gauge. ASTM B-258 specifies that this gauge is based on geometric

interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36

which is 0.005 inches exactly. Therefore, the diameter in inches of a wire

is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close

to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the

repeated zero values, use negative numbers in the formula. The same document

also specifies rounding rules which seem to be ignored by makers of tables.

Gauges up to 44 are to be specified with up to 4 significant figures, but no

closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the

nearest 0.00001 inch.



In addition to being used to measure wire thickness, this gauge is used to

measure the thickness of sheets of aluminum, copper, and most metals other

than steel, iron and zinc.

wiregauge(g) [;m] 1|200 92^((36+(-g))/39) in;36+(-39)ln(200 wiregauge/in)/ln(92)

Next we have the SWG, the Imperial or British Standard Wire Gauge. This one

is piecewise linear. It was used for aluminum sheets.

brwiregauge[in]
-6 0.5
-5 0.464
-3 0.4
-2 0.372
3 0.252
6 0.192
10 0.128
14 0.08
19 0.04
23 0.024
26 0.018
28 0.0148
30 0.0124
39 0.0052
49 0.0012
50 0.001

The following is from the Appendix to ASTM B 258



For example, in U.S. gage, the standard for sheet metal is based on the

weight of the metal, not on the thickness. 16-gage is listed as

approximately .0625 inch thick and 40 ounces per square foot (the original

standard was based on wrought iron at .2778 pounds per cubic inch; steel

has almost entirely superseded wrought iron for sheet use, at .2833 pounds

per cubic inch). Smaller numbers refer to greater thickness. There is no

formula for converting gage to thickness or weight.



It’s rather unclear from the passage above whether the plate gauge values are

therefore wrong if steel is being used. Reference [15] states that steel is

in fact measured using this gauge (under the name Manufacturers’ Standard

Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.

But this doesn’t seem to be the correct density of steel (.2833 lb/in3 is

closer).



This gauge was established in 1893 for purposes of taxation.

Old plate gauge for iron

plategauge[(oz/ft^2)/(480*lb/ft^3)]
-5 300
1 180
14 50
16 40
17 36
20 24
26 12
31 7
36 4.5
38 4

Manufacturers Standard Gage

stdgauge[(oz/ft^2)/(501.84*lb/ft^3)]
-5 300
1 180
14 50
16 40
17 36
20 24
26 12
31 7
36 4.5
38 4

A special gauge is used for zinc sheet metal. Notice that larger gauges

indicate thicker sheets.

zincgauge[in]
1 0.002
10 0.02
15 0.04
19 0.06
23 0.1
24 0.125
27 0.5
28 1



Screw sizes



In the USA, screw diameters are reported using a gauge number.

Metric screws are reported as Mxx where xx is the diameter in mm.



screwgauge(g) [;m] (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013



Ring size. All ring sizes are given as the circumference of the ring.



USA ring sizes. Several slightly different definitions seem to be in

circulation. According to [15], the interior diameter of size n ring in

inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The

size 2 ring is inconsistently 0.538in and no 2.5 size is listed.



However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the

diameter and list no special case for size 2. (Or alternatively they are

1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One

reference claimed that the original system was that each size was 1|10 inch

circumference, but that source doesn’t have an explanation for the modern

system which is somewhat different.

ringsize(n) [;in] (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018

Old practice in the UK measured rings using the “Wheatsheaf gauge” with sizes

specified alphabetically and based on the ring inside diameter in steps of

1|64 inch. This system was replaced in 1987 by British Standard 6820 which

specifies sizes based on circumference. Each size is 1.25 mm different from

the preceding size. The baseline is size C which is 40 mm circumference.

The new sizes are close to the old ones. Sometimes it’s necessary to go

beyond size Z to Z+1, Z+2, etc.

sizeAring 37.50 mm sizeBring 38.75 mm sizeCring 40.00 mm sizeDring 41.25 mm sizeEring 42.50 mm sizeFring 43.75 mm sizeGring 45.00 mm sizeHring 46.25 mm sizeIring 47.50 mm sizeJring 48.75 mm sizeKring 50.00 mm sizeLring 51.25 mm sizeMring 52.50 mm sizeNring 53.75 mm sizeOring 55.00 mm sizePring 56.25 mm sizeQring 57.50 mm sizeRring 58.75 mm sizeSring 60.00 mm sizeTring 61.25 mm sizeUring 62.50 mm sizeVring 63.75 mm sizeWring 65.00 mm sizeXring 66.25 mm sizeYring 67.50 mm sizeZring 68.75 mm

Japanese sizes start with size 1 at a 13mm inside diameter and each size is

1|3 mm larger in diameter than the previous one. They are multiplied by pi

to give circumference.

jpringsize(n) [;mm] (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)

The European ring sizes are the length of the circumference in mm minus 40.

euringsize(n) [;mm] (n+40) mm ; euringsize/mm + (-40)



Abbreviations



mph mile/hr mpg mile/gal kph km/hr fL footlambert fpm ft/min fps ft/s rpm rev/min rps rev/sec mi mile smi mile nmi nauticalmile mbh 1e3 btu/hour mcm 1e3 circularmil ipy inch/year # used for corrosion rates ccf 100 ft^3 # used for selling water [18] Mcf 1000 ft^3 # not million cubic feet [18] kp kilopond kpm kp meter kWh kW hour hph hp hour



Compatibility units with unix version



pa Pa ev eV hg Hg oe Oe mh mH us microsec rd rod pf pF gr grain nt N hz Hz hd hogshead dry drygallon/gallon imperial brgallon/gallon # This is a dubious definition # since it fails for fluid ounces # and all units derived from fluid # ounces.
nmile nauticalmile beV GeV bev beV coul C



Radioactivity units



becquerel /s # Activity of radioactive source Bq becquerel # curie 3.7e10 Bq # Defined in 1910 as the radioactivity Ci curie # emitted by the amount of radon that is # in equilibrium with 1 gram of radium. rutherford 1e6 Bq #

RADIATION_DOSE gray gray J/kg # Absorbed dose of radiation Gy gray # rad 1e-2 Gy # From Radiation Absorbed Dose rep 8.38 mGy # Roentgen Equivalent Physical, the amount # of radiation which , absorbed in the # body, would liberate the same amount # of energy as 1 roentgen of X rays # would, or 97 ergs.

sievert J/kg # Dose equivalent: dosage that has the Sv sievert # same effect on human tissues as 200 rem 1e-2 Sv # keV X-rays. Different types of # radiation are weighted by the # Relative Biological Effectiveness # (RBE). # # Radiation type RBE # X-ray, gamma ray 1 # beta rays, > 1 MeV 1 # beta rays, < 1 MeV 1.08 # neutrons, < 1 MeV 4-5 # neutrons, 1-10 MeV 10 # protons, 1 MeV 8.5 # protons, .1 MeV 10 # alpha, 5 MeV 15 # alpha, 1 MeV 20 # # The energies are the kinetic energy # of the particles. Slower particles # interact more, so they are more # effective ionizers, and hence have # higher RBE values. # # rem stands for Roentgen Equivalent # Mammal

roentgen 2.58e-4 C / kg # Ionizing radiation that produces # 1 statcoulomb of charge in 1 cc of # dry air at stp. rontgen roentgen # Sometimes it appears spelled this way sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one # hour at a distance of 1 cm from a # point source of 1 mg of radium # enclosed in platinum .5 mm thick.

eman 1e-7 Ci/m^3 # radioactive concentration mache 3.7e-7 Ci/m^3



Atomic weights. The atomic weight of an element is the ratio of the mass of

a mole of the element to 1|12 of a mole of Carbon 12. The Standard Atomic

Weights apply to the elements as they occur naturally on earth. Elements

which do not occur naturally or which occur with wide isotopic variability do

not have Standard Atomic Weights. For these elements, the atomic weight is

based on the longest lived isotope, as marked in the comments. In some

cases, the comment for these entries also gives a number which is an atomic

weight for a different isotope that may be of more interest than the longest

lived isotope.



actinium 227.0278 aluminum 26.981539 americium 243.0614 # Longest lived. 241.06 antimony 121.760
argon 39.948 arsenic 74.92159 astatine 209.9871 # Longest lived barium 137.327 berkelium 247.0703 # Longest lived. 249.08 beryllium 9.012182 bismuth 208.98037 boron 10.811 bromine 79.904 cadmium 112.411 calcium 40.078 californium 251.0796 # Longest lived. 252.08 carbon 12.011 cerium 140.115 cesium 132.90543 chlorine 35.4527 chromium 51.9961 cobalt 58.93320 copper 63.546 curium 247.0703 dysprosium 162.50 einsteinium 252.083 # Longest lived erbium 167.26 europium 151.965 fermium 257.0951 # Longest lived fluorine 18.9984032 francium 223.0197 # Longest lived gadolinium 157.25 gallium 69.723 germanium 72.61 gold 196.96654 hafnium 178.49 helium 4.002602 holmium 164.93032 hydrogen 1.00794 indium 114.818 iodine 126.90447 iridium 192.217 iron 55.845 krypton 83.80 lanthanum 138.9055 lawrencium 262.11 # Longest lived lead 207.2 lithium 6.941 lutetium 174.967 magnesium 24.3050 manganese 54.93805 mendelevium 258.10 # Longest lived mercury 200.59 molybdenum 95.94 neodymium 144.24 neon 20.1797 neptunium 237.0482 nickel 58.6934 niobium 92.90638 nitrogen 14.00674 nobelium 259.1009 # Longest lived osmium 190.23 oxygen 15.9994 palladium 106.42 phosphorus 30.973762 platinum 195.08 plutonium 244.0642 # Longest lived. 239.05 polonium 208.9824 # Longest lived. 209.98 potassium 39.0983 praseodymium 140.90765 promethium 144.9127 # Longest lived. 146.92 protactinium 231.03588 radium 226.0254 radon 222.0176 # Longest lived rhenium 186.207 rhodium 102.90550 rubidium 85.4678 ruthenium 101.07 samarium 150.36 scandium 44.955910 selenium 78.96 silicon 28.0855 silver 107.8682 sodium 22.989768 strontium 87.62 sulfur 32.066 tantalum 180.9479 technetium 97.9072 # Longest lived. 98.906 tellurium 127.60 terbium 158.92534 thallium 204.3833 thorium 232.0381 thullium 168.93421 tin 118.710 titanium 47.867 tungsten 183.84 uranium 238.0289 vanadium 50.9415 xenon 131.29 ytterbium 173.04 yttrium 88.90585 zinc 65.39 zirconium 91.224



Traditional Japanese units (shakkanhou)



The traditional system of weights and measures is called shakkanhou from the

shaku and the ken. Japan accepted SI units in 1891 and legalized conversions

to the traditional system. In 1909 the inch-pound system was also legalized,

so Japan had three legally approved systems. A change to the metric system

started in 1921 but there was a lot of resistance. The Measurement Law of

October 1999 prohibits sales in anything but SI units. However, the old

units still live on in construction and as the basis for paper sizes of books

and tools used for handicrafts.



Note that units below use the Hepburn romanization system. Some other

systems would render “mou”, “jou”, and “chou” as “mo”, “jo” and “cho”.



http://www.kansai.gr.jp/culture/build/measure_e.htm

http://www002.tokai.or.jp/hiramatu/onyak/tani-muk.htm

Japanese Proportions. These are still in everyday use. They also

get used as units to represent the proportion of the standard unit.

wari_proportion 1|10 wari wari_proportion bu_proportion 1|100 # The character bu can also be read fun or bun # but usually “bu” is used for units.
rin_proportion 1|1000 mou_proportion 1|10000

Japanese Length Measures



The length system is called kanejaku or

square and originated in China. It was

adopted as Japan’s official measure in 701

by the Taiho Code. This system is still in

common use in architecture and clothing.

kanejakusun sun # Alias to emphasize architectural name kanejaku shaku kanejakujou jou

In context of clothing, shaku is different from architecture

http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html

kujirajaku 10|8 shaku kujirajakusun 1|10 kujirajaku kujirajakubu 1|100 kujirajaku kujirajakujou 10 kujirajaku tan_distance 3 kujirajakujou

ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6 # http://www.homarewood.co.jp/syakusun.htm

mostly unused

chou_distance 60 ken chou chou_distance ri 36 chou

Japanese Area Measures

Tsubo is still used for land size, though the others are more

recognized by their homonyms in the other measurements.

gou_area 1|10 tsubo tsubo 36 shaku^2 # Size of two tatami = ken^2 ?? se 30 tsubo tan_area 10 se chou_area 10 tan_area

Japanese architecture is based on a “standard” size of tatami mat.

Room sizes today are given in number of tatami, and this number

determines the spacing between colums and hence sizes of sliding

doors and paper screens. However, every region has its own slightly

different tatami size. Edoma, used in and around Tokyo and

Hokkaido, is becoming a nationwide standard. Kyouma is used around

Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya.

Note that the tatami all have the aspect ratio 2:1 so that the mats

can tile the room with some of them turned 90 degrees.



http://www.moon2.net/tatami/infotatami/structure.html

edoma (5.82.9) shaku^2 kyouma (6.33.15) shaku^2 chuukyouma (6*3) shaku^2 jou_area edoma tatami jou_area

Japanese Volume Measures

The “shou” is still used for such things as alcohol and seasonings.

Large quantities of paint are still purchased in terms of “to”.

shaku_volume 1|10 gou_volume gou_volume 1|10 shou gou gou_volume shou (4.94.92.7) sun^3 # The character shou which is # the same as masu refers to a # rectangular wooden cup used to # measure liquids and cereal.
# Sake is sometimes served in a masu # Note that it happens to be # EXACTLY 7^4/11^3 liters. to 10 shou
koku 10 to # No longer used; historically a measure of rice

Japanese Weight Measures



http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html

Not really used anymore.

rin_weight 1|10 bu bu_weight 1|10 monme fun 1|10 monme
monme 15|4 g kin 160 monme kan 1000 monme kwan kan # This was the old pronounciation of the unit. # The old spelling persisted a few centuries # longer and was not changed until around # 1950.



A few German units as currently in use.



zentner 50 kg doppelzentner 2 zentner pfund 500 g



Old French distance measures, from French Weights and Measures

Before the Revolution by Zupko



frenchfoot 144|443.296 m # pied de roi, the standard of Paris. pied frenchfoot # Half of the hashimicubit, frenchfeet frenchfoot # instituted by Charlemagne. frenchinch 1|12 frenchfoot # This exact definition comes from frenchthumb frenchinch # a law passed on 10 Dec 1799 which pouce frenchthumb # fixed the meter at # 3 frenchfeet + 11.296 lignes. frenchline 1|12 frenchinch # This is supposed to be the size ligne frenchline # of the average barleycorn frenchpoint 1|12 frenchline toise 6 frenchfeet arpent 180^2 pied^2 # The arpent is 100 square perches, # but the perche seems to vary a lot # and can be 18 feet, 20 feet, or 22 # feet. This measure was described # as being in common use in Canada in # 1934 (Websters 2nd). The value # given here is the Paris standard # arpent. frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence # smaller than the British grain.
frenchpound 9216 frenchgrain



Before the Imperial Weights and Measures Act of 1824, various different

weights and measures were in use in different places.



Scots linear measure

scotsinch 1.00540054 UKinch scotslink 1|100 scotschain scotsfoot 12 scotsinch scotsfeet scotsfoot scotsell 37 scotsinch scotsfall 6 scotsell scotschain 4 scotsfall scotsfurlong 10 scotschain scotsmile 8 scotsfurlong

Scots area measure

scotsrood 40 scotsfall^2 scotsacre 4 scotsrood nook 20 acres # Given in [18] with English acres; apparently # developed after the switch to Imperial units.

Irish linear measure

irishinch UKinch irishpalm 3 irishinch irishspan 3 irishpalm irishfoot 12 irishinch irishfeet irishfoot irishcubit 18 irishinch irishyard 3 irishfeet irishpace 5 irishfeet irishfathom 6 irishfeet irishpole 7 irishyard # Only these values irishperch irishpole # are different from irishchain 4 irishperch # the British Imperial irishlink 1|100 irishchain # or English values for irishfurlong 10 irishchain # these lengths. irishmile 8 irishfurlong #

Irish area measure

irishrood 40 irishpole^2 irishacre 4 irishrood

English wine capacity measures (Winchester measures)

winepint 1|2 winequart winequart 1|4 winegallon winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon, # it was legalized in 1707 by Queen Anne, and # given the definition of 231 cubic inches. It # had been in use for a while as 8 pounds of wine # using a merchant’s pound, but the definition of # the merchant’s pound had become uncertain. A # pound of 15 tower ounces (6750 grains) had been # common, but then a pound of 15 troy ounces # (7200 grains) gained popularity. Because of # the switch in the value of the merchants pound, # the size of the wine gallon was uncertain in # the market, hence the official act in 1707. # The act allowed that a six inch tall cylinder # with a 7 inch diameter was a lawful wine # gallon. (This comes out to 230.9 in^3.) # Note also that in Britain a legal conversion # was established to the 1824 Imperial gallon # then taken as 277.274 in^3 so that the wine # gallon was 0.8331 imperial gallons. This is # 231.1 cubic inches (using the international # inch).
winerundlet 18 winegallon winebarrel 31.5 winegallon winetierce 42 winegallon winehogshead 2 winebarrel winepuncheon 2 winetierce winebutt 2 winehogshead winepipe winebutt winetun 2 winebutt

English beer and ale measures used 1803-1824 and used for beer before 1688

beerpint 1|2 beerquart beerquart 1|4 beergallon beergallon 282 UKinch^3 beerbarrel 36 beergallon beerhogshead 1.5 beerbarrel

English ale measures used from 1688-1803 for both ale and beer

alepint 1|2 alequart alequart 1|4 alegallon alegallon beergallon alebarrel 34 alegallon alehogshead 1.5 alebarrel

Scots capacity measure

Scots dry capacity measure

scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt scotswheatlippies scotswheatlippy scotswheatpeck 4 scotswheatlippy scotswheatfirlot 4 scotswheatpeck scotswheatboll 4 scotswheatfirlot scotswheatchalder 16 scotswheatboll

scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt scotsoatlippies scotsoatlippy scotsoatpeck 4 scotsoatlippy scotsoatfirlot 4 scotsoatpeck scotsoatboll 4 scotsoatfirlot scotsoatchalder 16 scotsoatboll

Scots Tron weight

trondrop 1|16 tronounce tronounce 1|20 tronpound tronpound 9520 grain tronstone 16 tronpound

Irish liquid capacity measure

irishnoggin 1|4 irishpint irishpint 1|2 irishquart irishquart 1|2 irishpottle irishpottle 1|2 irishgallon irishgallon 217.6 UKinch^3 irishrundlet 18 irishgallon irishbarrel 31.5 irishgallon irishtierce 42 irishgallon irishhogshead 2 irishbarrel irishpuncheon 2 irishtierce irishpipe 2 irishhogshead irishtun 2 irishpipe

Irish dry capacity measure

irishpeck 2 irishgallon irishbushel 4 irishpeck irishstrike 2 irishbushel irishdrybarrel 2 irishstrike irishquarter 2 irishbarrel

English Tower weights, abolished in 1528

towerpound 5400 grain towerounce 1|12 towerpound towerpennyweight 1|20 towerounce towergrain 1|32 towerpennyweight

English Mercantile weights, used since the late 12th century

mercpound 6750 grain mercounce 1|15 mercpound mercpennyweight 1|20 mercounce

English weights for lead

leadstone 12.5 lb fotmal 70 lb leadwey 14 leadstone fothers 12 leadwey

English Hay measure

newhaytruss 60 lb # New and old here seem to refer to “new” newhayload 36 newhaytruss # hay and “old” hay rather than a new unit oldhaytruss 56 lb # and an old unit. oldhayload 36 oldhaytruss

English wool measure

woolclove 7 lb woolstone 2 woolclove wooltod 2 woolstone woolwey 13 woolstone woolsack 2 woolwey woolsarpler 2 woolsack woollast 6 woolsarpler



Ancient history units: There tends to be uncertainty in the definitions

of the units in this section

These units are from [11]

Roman measure. The Romans had a well defined distance measure, but their

measures of weight were poor. They adopted local weights in different

regions without distinguishing among them so that there are half a dozen

different Roman “standard” weight systems.

romanfoot 296 mm # There is some uncertainty in this definition romanfeet romanfoot # from which all the other units are derived. pes romanfoot # This value appears in numerous sources. In “The pedes romanfoot # Roman Land Surveyors”, Dilke gives 295.7 mm. romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the romandigit 1|16 romanfoot # same names as the subdivisions of the pound, romanpalm 1|4 romanfoot # but we can’t have the names for different romancubit 18 romaninch # units. romanpace 5 romanfeet # Roman double pace (basic military unit) passus romanpace romanperch 10 romanfeet stade 125 romanpaces stadia stade stadium stade romanmile 8 stadia # 1000 paces romanleague 1.5 romanmile schoenus 4 romanmile

Other values for the Roman foot (from Dilke)

earlyromanfoot 29.73 cm pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC lateromanfoot 29.42 cm

Roman areas

actuslength 120 romanfeet # length of a Roman furrow actus 120*4 romanfeet^2 # area of the furrow squareactus 120^2 romanfeet^2 # actus quadratus acnua squareactus iugerum 2 squareactus iugera iugerum jugerum iugerum jugera iugerum heredium 2 iugera # heritable plot heredia heredium centuria 100 heredia centurium centuria

Roman volumes

sextarius 35.4 in^3 # Basic unit of Roman volume. As always, sextarii sextarius # there is uncertainty. Six large Roman # measures survive with volumes ranging from # 34.4 in^3 to 39.55 in^3. Three of them # cluster around the size given here. # # But the values for this unit vary wildly # in other sources. One reference gives 0.547 # liters, but then says the amphora is a # cubic Roman foot. This gives a value for the # sextarius of 0.540 liters. And the # encyclopedia Brittanica lists 0.53 liters for # this unit. Both [7] and [11], which were # written by scholars of weights and measures, # give the value of 35.4 cubic inches.
cochlearia 1|48 sextarius cyathi 1|12 sextarius acetabula 1|8 sextarius quartaria 1|4 sextarius quartarius quartaria heminae 1|2 sextarius hemina heminae cheonix 1.5 sextarii

Dry volume measures (usually)

semodius 8 sextarius semodii semodius modius 16 sextarius modii modius

Liquid volume measures (usually)

congius 12 heminae congii congius amphora 8 congii amphorae amphora # Also a dry volume measure culleus 20 amphorae quadrantal amphora

Roman weights

libra 5052 grain # The Roman pound varied significantly librae libra # from 4210 grains to 5232 grains. Most of romanpound libra # the standards were obtained from the weight uncia 1|12 libra # of particular coins. The one given here is unciae uncia # based on the Gold Aureus of Augustus which romanounce uncia # was in use from BC 27 to AD 296.
deunx 11 uncia dextans 10 uncia dodrans 9 uncia bes 8 uncia seprunx 7 uncia semis 6 uncia quincunx 5 uncia triens 4 uncia quadrans 3 uncia sextans 2 uncia sescuncia 1.5 uncia semuncia 1|2 uncia siscilius 1|4 uncia sextula 1|6 uncia semisextula 1|12 uncia scriptulum 1|24 uncia scrupula scriptulum romanobol 1|2 scrupula

romanaspound 4210 grain # Old pound based on bronze coinage, the
# earliest money of Rome BC 338 to BC 268.

Egyptian length measure

egyptianroyalcubit 20.63 in # plus or minus .2 in egyptianpalm 1|7 egyptianroyalcubit egyptiandigit 1|4 egyptianpalm egyptianshortcubit 6 egyptianpalm

doubleremen 29.16 in # Length of the diagonal of a square with remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit. # This is divided into 40 digits which are # not the same size as the digits based on # the royal cubit.

Greek length measures

greekfoot 12.45 in # Listed as being derived from the greekfeet greekfoot # Egyptian Royal cubit in [11]. It is greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit. pous greekfoot podes greekfoot orguia 6 greekfoot greekfathom orguia stadion 100 orguia akaina 10 greekfeet plethron 10 akaina greekfinger 1|16 greekfoot homericcubit 20 greekfingers # Elbow to end of knuckles. shortgreekcubit 18 greekfingers # Elbow to start of fingers.

ionicfoot 296 mm
doricfoot 326 mm

olympiccubit 25 remendigit # These olympic measures were not as olympicfoot 2|3 olympiccubit # common as the other greek measures. olympicfinger 1|16 olympicfoot # They were used in agriculture. olympicfeet olympicfoot olympicdakylos olympicfinger olympicpalm 1|4 olympicfoot olympicpalestra olympicpalm olympicspithame 3|4 foot olympicspan olympicspithame olympicbema 2.5 olympicfeet olympicpace olympicbema olympicorguia 6 olympicfeet olympicfathom olympicorguia olympiccord 60 olympicfeet olympicamma olympiccord olympicplethron 100 olympicfeet olympicstadion 600 olympicfeet

Greek capacity measure

greekkotyle 270 ml # This approximate value is obtained xestes 2 greekkotyle # from two earthenware vessels that khous 12 greekkotyle # were reconstructed from fragments. metretes 12 khous # The kotyle is a day’s corn ration choinix 4 greekkotyle # for one man. hekteos 8 choinix medimnos 6 hekteos

Greek weight. Two weight standards were used, an Aegina standard based

on the Beqa shekel and an Athens (attic) standard.

aeginastater 192 grain # Varies up to 199 grain aeginadrachmae 1|2 aeginastater aeginaobol 1|6 aeginadrachmae aeginamina 50 aeginastaters aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot # of water (whichever foot was in use)

atticstater 135 grain # Varies 134-138 grain atticdrachmae 1|2 atticstater atticobol 1|6 atticdrachmae atticmina 50 atticstaters attictalent 60 atticmina # Supposedly the mass of a cubic foot # of water (whichever foot was in use)

“Northern” cubit and foot. This was used by the pre-Aryan civilization in

the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China,

central and Western Europe until modern times when it was displaced by

the metric system.

northerncubit 26.6 in # plus/minus .2 in northernfoot 1|2 northerncubit

sumeriancubit 495 mm kus sumeriancubit sumerianfoot 2|3 sumeriancubit

assyriancubit 21.6 in assyrianfoot 1|2 assyriancubit assyrianpalm 1|3 assyrianfoot assyriansusi 1|20 assyrianpalm susi assyriansusi persianroyalcubit 7 assyrianpalm

Arabic measures. The arabic standards were meticulously kept. Glass weights

accurate to .2 grains were made during AD 714-900.

hashimicubit 25.56 in # Standard of linear measure used # in Persian dominions of the Arabic # empire 7-8th cent. Is equal to two # French feet.

blackcubit 21.28 in arabicfeet 1|2 blackcubit arabicfoot arabicfeet arabicinch 1|12 arabicfoot arabicmile 4000 blackcubit

silverdirhem 45 grain # The weights were derived from these two tradedirhem 48 grain # units with two identically named systems # used for silver and used for trade purposes

silverkirat 1|16 silverdirhem silverwukiyeh 10 silverdirhem silverrotl 12 silverwukiyeh arabicsilverpound silverrotl

tradekirat 1|16 tradedirhem tradewukiyeh 10 tradedirhem traderotl 12 tradewukiyeh arabictradepound traderotl

Miscellaneous ancient units

parasang 3.5 mile # Persian unit of length usually thought # to be between 3 and 3.5 miles biblicalcubit 21.8 in hebrewcubit 17.58 in li 10|27.8 mile # Chinese unit of length # 100 li is considered a day’s march liang 11|3 oz # Chinese weight unit

Medieval time units. According to the OED, these appear in Du Cange

by Papias.

Given in [15], these subdivisions of the grain were supposedly used

by jewelers. The mite may have been used but the blanc could not

have been accurately measured.

mite 1|20 grain
droit 1|24 mite periot 1|20 droit blanc 1|24 periot



Some definitions using ISO 8859-1 characters



?- 1|4 ?- 1|2 ?- 3|4 ?- micro ? cent ? britainpound ? japanyen ?ngstr?m angstrom ? angstrom r?ntgen roentgen ?C degC ?F degF ?K K # ?K is incorrect notation ?R degR ? degree



Localisation



!locale en_US hundredweight ushundredweight ton uston scruple apscruple fluidounce usfluidounce gallon usgallon
bushel usbushel quarter quarterweight cup uscup tablespoon ustablespoon teaspoon usteaspoon horsepower ushorsepower dollar US$ cent $ 0.01 penny cent minim minimvolume pony ponyvolume grand usgrand firkin usfirkin acre usacre acrefoot usacrefoot billion usbillion trillion ustrillion quadrillion usquadrillion quintillion usquintillion sextillion ussextillion septillion usseptillion octillion usoctillion nonillion usnonillion noventillion usnoventillion decillion usdecillion undecillion usundecillion duodecillion usduodecillion tredecillion ustredecillion quattuordecillion usquattuordecillion quindecillion usquindecillion sexdecillion ussexdecillion septendecillion usseptendecillion octodecillion usoctodecillion novemdecillion usnovemdecillion vigintillion usvigintillion !endlocale

!locale en_GB hundredweight brhundredweight ton brton scruple brscruple fluidounce brfluidounce gallon brgallon bushel brbushel quarter brquarter chaldron brchaldron cup brcup teacup brteacup tablespoon brtablespoon teaspoon brteaspoon horsepower brhorsepower dollar US$ cent $ 0.01 penny brpenny minim minimnote pony brpony grand brgrand firkin brfirkin acre intacre acrefoot intacrefoot billion brbillion trillion brtrillion quadrillion brquadrillion quintillion brquintillion sextillion brsextillion septillion brseptillion octillion broctillion nonillion brnonillion noventillion brnoventillion decillion brdecillion undecillion brundecillion duodecillion brduodecillion tredecillion brtredecillion quattuordecillion brquattuordecillion quindecillion brquindecillion sexdecillion brsexdecillion septendecillion brseptendecillion octodecillion broctodecillion novemdecillion brnovemdecillion vigintillion brvigintillion !endlocale