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GNU units and units.dat; Units of Measurement and Unit Conversion

GNU units and units.dat; Units of Measurement and Unit Conversion - Physics Forum

GNU units and units.dat; Units of Measurement and Unit Conversion - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

GNU units and units.dat; Units of Measurement and Unit Conversion

This message is being posted to usenet so that the Google usenet
archive will have a searchable copy of the GNU units units.dat file,
which is a very good source of information on units of measurement.
Hence, when people are doing a Google usenet search on information
regarding units of measurement, hopefully this post will be helpful
to them. It is also being posted to let Windows users know about a
native Windows port of the GNU units program.

GNU units is a free and open source program for converting between
various units of measurement. The GNU units program can handle
multiplicative scale changes as well as nonlinear conversions such as
Fahrenheit to Celsius, or between wire gauges. GNU units comes with
an annotated, extendable, editable database file (i.e., units.dat)
defining over two thousand units of measurement.

Below can be found a native port binary for Windows of GNU units
version 1.80:

[Only registered users see links. ]

Just a note concerning the description of GNU units on the above
webpage. It says therein "Units can only handle multiplicative scale
changes. For example, it cannot convert Celsius to Fahrenheit but it
can convert temperature differences between those temperature
scales." This is incorrect. Apparently whoever wrote up that
description got confused, as GNU units (and its Windows port) can
handle nonlinear conversion of unit scales, such as converting
Celsius to Fahrenheit, or vice versa. See, e.g., the following:

""
You have: tempF(72)
You want: tempC
22.222222
""

Below are two linear conversions demonstrating the archaic and
bizarre conversions which this program is able to handle:

""
You have: 7.31 furlongs per fortnight
You want: meters per day
* 105.03843
/ 0.0095203247
You have: 2 millifortnights
You want: hours
* 0.672
/ 1.4880952
""

Notice in the above two examples that it also gives the reciprocal,
as this number can be useful.

As I said, the native Windows port of GNU units mentioned above is
version 1.80. Version 1.85 of GNU units is out, but a Windows port of
that version has not been published yet. I recommend that anyone
using this Windows version download the source code tarball to GNU
units 1.85 and get the units.dat file out from it to replace the
units.dat file in version 1.80 of the Windows port. Doing so will
give you 355 more units definitions, as the units.dat file that comes
with version 1.85 contains 2438 units definitions, whereas the
units.dat file that comes with version 1.80 has 2083 units
definitions.

The source code to the latest version can be downloaded from one of
the below two URLs:

The GNU units units.dat file is annotated and contains a lot of
information. It's a very good source of information on units of
measurement.

Below is the GNU units user's manual:

[Only registered users see links. ]

Below is the GNU units homepage:

[Only registered users see links. ]

Below is a short Wikipedia article on the GNU units program:

[Only registered users see links. ])

Under the hyphens directly below is the complete text of the
units.dat file which comes with GNU units 1.85.

----------

#
# This file is the units database for use with GNU units, a units conversion
# program by Adrian Mariano [Only registered users see links. ]
#
# 26 April 2005 Version 1.44
#
# Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004, 2005
# Free Software Foundation, Inc
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor,
# Boston, MA 02110-1301 USA
#
################################################## ##########################
#
# Improvements and corrections are welcome.
#
# Most units data was drawn from
# 1. NIST Special Publication 811, 1995 Edition
# 2. CRC Handbook of Chemistry and Physics 70th edition
# 3. Oxford English Dictionary
# 4. Websters New Universal Unabridged Dictionary
# 5. Units of Measure by Stephen Dresner
# 6. A Dictionary of English Weights and Measures by Ronald Zupko
# 7. British Weights and Measures by Ronald Zupko
# 8. Realm of Measure by Isaac Asimov
# 9. United States standards of weights and measures, their
# creation and creators by Arthur H. Frazier.
# 10. French weights and measures before the Revolution: a
# dictionary of provincial and local units by Ronald Zupko
# 11. Weights and Measures: their ancient origins and their
# development in Great Britain up to AD 1855 by FG Skinner
# 12. The World of Measurements by H. Arthur Klein
# 13. For Good Measure by William Johnstone
# 14. NTC's Encyclopedia of International Weights and Measures
# by William Johnstone
# 15. Sizes by John Lord
# 16. Sizesaurus by Stephen Strauss
# 17. CODATA Recommended Values of Physical Constants available at
# [Only registered users see links. ]
# 18. How Many? A Dictionary of Units of Measurement. Available at
# [Only registered users see links. ]
# 19. Numericana. [Only registered users see links. ]
# 20. UK history of measurement
# [Only registered users see links. ]
#
# Thanks to Jeff Conrad for assistance in ferreting out unit definitions.
#
################################################## #########################
#
# If units you use are missing or defined incorrectly, please contact me.
#
# I added shoe size information but I'm not convinced that it's correct.
# If you know anything about shoe sizes please contact me.
#
################################################## #########################

################################################## #########################
# #
# Primitive units. Any unit defined to contain a '!' character is a #
# primitive unit which will not be reduced any further. All units should #
# reduce to primitive units. #
# #
################################################## #########################

#
# SI units
#

kg ! # Mass of the international prototype
kilogram kg

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.

################################################## #########################
# #
# 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"

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.

# The British Centillion would be 1e600. The googolplex is another
# familiar large number equal to 10^googol. These numbers give overflows.

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

circle 2 pi radian
degree 1|360 circle
arcdeg degree
arcmin 1|60 degree
arcminute arcmin
' arcmin
arcsec 1|60 arcmin
arcsecond arcsec
" arcsec
'' "
rightangle 90 degrees
quadrant 1|4 circle
quintant 1|5 circle
sextant 1|6 circle

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
#

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
% percent
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.

#
# 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|4*pi*epsilon0 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.

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.

# 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

#
# 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 [Only registered users see links. ]. 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.

# 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
# [Only registered users see links. ]

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 [Only registered users see links. ]

# 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 [Only registered users see links. ] 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]
#

# 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

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
# <[Only registered users see links. ]> 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.

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
# [Only registered users see links. ] 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
#

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.

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

#
# 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

# 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.

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.
#

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

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 # François 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 # ([Only registered users see links. ]) 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.
#

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:
# [Only registered users see links. ]

austriaschilling 1|13.7603 euro
belgiumfranc 1|40.3399 euro
estoniakroon 1|15.6466 euro # Equal to 1|8 germanymark
finlandmarkka 1|5.94573 euro
francefranc 1|6.55957 euro
germanymark 1|1.95583 euro
greecedrachma 1|340.75 euro
irelandpunt 1|0.787564 euro
italylira 1|1936.27 euro
luxembourgfranc 1|40.3399 euro
netherlandsguilder 1|2.20371 euro
portugalescudo 1|200.482 euro
spainpeseta 1|166.386 euro

# 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 4*4*8 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 [Only registered users see links. ].)

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
# systems to add to the confusion. The use of wire gauge is related to the
# 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:
#

# 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.

# 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.

#
# 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.
#

#
# 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.
#

#
# 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".
#
# [Only registered users see links. ]
# [Only registered users see links. ]

# 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.

shaku 1|3.3 m
mou 1|10000 shaku
rin 1|1000 shaku
bu_distance 1|100 shaku
sun 1|10 shaku
jou_distance 10 shaku
jou jou_distance

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

# In context of clothing, shaku is different from architecture
# [Only registered users see links. ]

ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6
# [Only registered users see links. ]

# 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.
#
# [Only registered users see links. ]

# 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 (4.9*4.9*2.7) 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
#
# [Only registered users see links. ]

# 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.
#

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

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

#
# 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

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

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

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.

timepoint 1|5 hour # also given as 1|4
timeminute 1|10 hour
timeostent 1|60 hour
timeounce 1|8 timeostent
timeatom 1|47 timeounce

# 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
#

¼- 1|4
½- 1|2
¾- 3|4
µ- micro
¢ cent
£ britainpound
¥ japanyen
ångström angstrom
Å angstrom
röntgen roentgen
°C degC
°F degF
°K K # °K is incorrect notation
°R degR
° degree

################################################## ##########################
#
# The following units were in the unix units database but do not appear in
# this file:
#
# wey used for cheese, salt and other goods. Measured mass or
# waymass volume depending on what was measured and where the measuring
# took place. A wey of cheese ranged from 200 to 324 pounds.
#
# sack No precise definition
#
# spindle The length depends on the type of yarn
#
# block Defined variously on different computer systems
#
# erlang A unit of telephone traffic defined variously.
# Omitted because there are no other units for this
# dimension. Is this true? What about CCS = 1/36 erlang?
# Erlang is supposed to be dimensionless. One erlang means
# a single channel occupied for one hour.
#
################################################## ##########################