#

# This file is the units database for use with GNU units, a units conversion

# program by Adrian Mariano adrian@cam.cornell.edu

#

# 14 February 2010 Version 1.50

#

# Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004, 2005, 2006

# 2007, 2008, 2009, 2010

# 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 3 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

# http://physics.nist.gov/cuu/Constants/index.html

# 18. How Many? A Dictionary of Units of Measurement. Available at

# http://www.unc.edu/~rowlett/units/index.html

# 19. Numericana. http://www.numericana.com

# 20. UK history of measurement

# http://www.ukmetrication.com/history.htm

#

# 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"

quarter- 1|4

semi- 0.5

demi- 0.5

hemi- 0.5

half- 0.5

double- 2

triple- 3

treble- 3

kibi- 2^10 # In response to the convention of illegally

mebi- 2^20 # and confusingly using metric prefixes for

gibi- 2^30 # powers of two, the International

tebi- 2^40 # Electrotechnical Commission aproved these

pebi- 2^50 # binary prefixes for use in 1998. If you

exbi- 2^60 # want to refer to "megabytes" using the

Ki- kibi # binary definition, use these prefixes.

Mi- mebi

Gi- gibi

Ti- tebi

Pi- pebi

Ei- exbi

Y- yotta

Z- zetta

E- exa

P- peta

T- tera

G- giga

M- mega

k- kilo

h- hecto

da- deka

d- deci

c- centi

m- milli

u- micro # it should be a mu but u is easy to type

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

eleven 11

twelve 12

thirteen 13

fourteen 14

fifteen 15

sixteen 16

seventeen 17

eighteen 18

nineteen 19

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.

shortbillion 1e9

shorttrillion 1e12

shortquadrillion 1e15

shortquintillion 1e18

shortsextillion 1e21

shortseptillion 1e24

shortoctillion 1e27

shortnonillion 1e30

shortnoventillion shortnonillion

shortdecillion 1e33

shortundecillion 1e36

shortduodecillion 1e39

shorttredecillion 1e42

shortquattuordecillion 1e45

shortquindecillion 1e48

shortsexdecillion 1e51

shortseptendecillion 1e54

shortoctodecillion 1e57

shortnovemdecillion 1e60

shortvigintillion 1e63

centillion 1e303

googol 1e100

longbillion million^2

longtrillion million^3

longquadrillion million^4

longquintillion million^5

longsextillion million^6

longseptillion million^7

longoctillion million^8

longnonillion million^9

longnoventillion longnonillion

longdecillion million^10

longundecillion million^11

longduodecillion million^12

longtredecillion million^13

longquattuordecillion million^14

longquindecillion million^15

longsexdecillion million^16

longseptdecillion million^17

longoctodecillion million^18

longnovemdecillion million^19

longvigintillion million^20

# These numbers fill the gaps left by the long system above.

milliard 1000 million

billiard 1000 million^2

trilliard 1000 million^3

quadrilliard 1000 million^4

quintilliard 1000 million^5

sextilliard 1000 million^6

septilliard 1000 million^7

octilliard 1000 million^8

nonilliard 1000 million^9

noventilliard nonilliard

decilliard 1000 million^10

# For consistency

longmilliard milliard

longbilliard billiard

longtrilliard trilliard

longquadrilliard quadrilliard

longquintilliard quintilliard

longsextilliard sextilliard

longseptilliard septilliard

longoctilliard octilliard

longnonilliard nonilliard

longnoventilliard noventilliard

longdecilliard decilliard

# The long centillion would be 1e600. The googolplex is another

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

#

# The short system prevails in English speaking countries

#

billion shortbillion

trillion shorttrillion

quadrillion shortquadrillion

quintillion shortquintillion

sextillion shortsextillion

septillion shortseptillion

octillion shortoctillion

nonillion shortnonillion

noventillion shortnoventillion

decillion shortdecillion

undecillion shortundecillion

duodecillion shortduodecillion

tredecillion shorttredecillion

quattuordecillion shortquattuordecillion

quindecillion shortquindecillion

sexdecillion shortsexdecillion

septendecillion shortseptendecillion

octodecillion shortoctodecillion

novemdecillion shortnovemdecillion

vigintillion shortvigintillion

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

# #

# 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

L liter # 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

deg degree

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

#

circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi)

spherevolume(r) [m;m^3] 4|3 pi r^3 ; cuberoot(spherevolume/4|3 pi)

spherevol(r) [m;m^3] spherevolume(r) ; ~spherevolume(spherevol)

square(x) x^2 ; sqrt(square)

#

# Solid angle measure

#

sphere 4 pi sr

squaredegree 1|180^2 pi^2 sr

squareminute 1|60^2 squaredegree

squaresecond 1|60^2 squareminute

squarearcmin squareminute

squarearcsec squaresecond

sphericalrightangle 0.5 pi sr

octant 0.5 pi sr

#

# Concentration measures

#

percent 0.01

% 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.

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

#

# Temperature

#

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

# and functions for converting absolute temperatures. Conversions for

# differences start with "deg" and conversions for absolute temperature start

# with "temp".

#

TEMPERATURE kelvin

TEMPERATURE_DIFFERENCE kelvin

tempC(x) [;K] x K + stdtemp ; (tempC +(-stdtemp))/K # In 1741 Anders Celsius

tempcelsius(x) [;K] tempC(x); ~tempC(tempcelsius) # introduced a temperature

degcelsius K # scale with water boiling at 0 degrees and

degC K # freezing at 100 degrees at standard

# pressure. After his death the fixed points

# were reversed and the scale was called the

# centigrade scale. Due to the difficulty of

# accurately measuring the temperature of

# melting ice at standard pressure, the

# centigrade scale was replaced in 1954 by

# the Celsius scale which is defined by

# subtracting 273.15 from the temperature in

# Kelvins. This definition differed slightly

# from the old centigrade definition, but the

# Kelvin scale depends on the triple point of

# water rather than a melting point, so it

# can be measured accurately.

tempF(x) [;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32

tempfahrenheit(x) [;K] tempF(x) ; ~tempF(tempfahrenheit)

degfahrenheit 5|9 degC # Fahrenheit defined his temperature scale

degF 5|9 degC # by setting 0 to the coldest temperature

# he could produce in his lab with a salt

# water solution and by setting 96 degrees to

# body heat. In Fahrenheit's words:

#

# Placing the thermometer in a mixture of

# sal ammoniac or sea salt, ice, and water

# a point on the scale will be found which

# is denoted as zero. A second point is

# obtained if the same mixture is used

# without salt. Denote this position as

# 30. A third point, designated as 96, is

# obtained if the thermometer is placed in

# the mouth so as to acquire the heat of a

# healthy man." (D. G. Fahrenheit,

# Phil. Trans. (London) 33, 78, 1724)

degreesrankine degF # The Rankine scale has the

degrankine degreesrankine # Fahrenheit degree, but its 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.

# Gas mark is implemented below but in a terribly ugly way. There is

# a simple formula, but it requires a conditional which is not

# presently supported.

#

# The formula to convert to degrees Fahrenheit is:

#

# 25 log2(gasmark) + k_f gasmark<=1

# 25 (gasmark-1) + k_f gasmark>=1

#

# k_f = 275

#

gasmark[degR] \

.0625 634.67 \

.125 659.67 \

.25 684.67 \

.5 709.67 \

1 734.67 \

2 759.67 \

3 784.67 \

4 809.67 \

5 834.67 \

6 859.67 \

7 884.67 \

8 909.67 \

9 934.67 \

10 959.67

# 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 1.602176487e-19 C # electron charge

h 6.62606896e-34 J s # Planck constant

hbar h / 2 pi

spin hbar

G 6.67428e-11 N m^2 / kg^2 # Newtonian gravitational constant

# This is the NIST 2002 value.

# Note that NIST increased the

# uncertainty of G to 1500 ppm

# as a result of disagreements

# between experiments performed in

# the late 1990s. Some other

# sources give conflicting values

# with a much lower uncertainty.

coulombconst 1/4 pi epsilon0 # listed as "k" sometimes

# Physico-chemical constants

atomicmassunit 1.660538782e-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

kboltzmann 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 2.8977685e-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 2006 recommended value

# of the constant is 483597.891 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 10973731.568527 /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 7.2973525376e-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 2.17644e-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 5.4857990943e-4 u

m_e electronmass

protonmass 1.00727646677 u

m_p protonmass

neutronmass 1.00866491597 u

m_n neutronmass

muonmass 0.1134289256 u

m_mu muonmass

deuteronmass 2.013553212724 u

m_d deuteronmass

alphaparticlemass 4.001506179127 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 4.49044786e-26 J/T # Muon magnetic moment

mu_p 1.410606662e-26 J/T # Proton magnetic moment

mu_e 928.476377e-26 J/T # Electron magnetic moment

mu_n 0.96623641e-26 J/T # Neutron magnetic moment

mu_d 0.433073465e-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