User:Egil/Sandbox/units

are 100 m^2

litre 1000 cc The litre was defined in 1901 as the

old litre 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

litre 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

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.

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]

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.

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.

circle 2 pi radian

degree 1|360 circle

arcdeg degree

arcmin 1|60 degree

arcminute arcmin

arcsec 1|60 arcmin

arcsecond arcsec

quadrant 1|4 circle

quintant 1|5 circle

sextant 1|6 circle

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.

Solid angle measure

sphere 4 pi sr

squaredegree 1|180^2 pi^2 sr

squareminute 1|60^2 squaredegree

squaresecond 1|60^2 squareminute

squarearcmin squareminute

squarearcsec squaresecond

sphericalrightangle 0.5 pi sr

octant 0.5 pi sr

Concentration measures

percent 0.01

mill 0.001 Originally established by Congress in 1791

as a unit of money equal to 0.001 dollars,

it has come to refer to 0.001 in general.

Used by some towns to set their property

tax rate, and written with a symbol similar

to the % symbol but with two 0's in the

denominator. [18]

proof 1|200 Alcohol content measured by volume at

60 degrees Fahrenheit. This is a USA

measure. In Europe proof=percent.

ppm 1e-6

partspermillion ppm

ppb 1e-9

partsperbillion ppb USA billion

ppt 1e-12

partspertrillion ppt USA trillion

karat 1|24 measure of gold purity

caratgold karat

gammil mg/l

basispoint 0.01 % Used in finance

fine 1|1000 Measure of gold purity

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

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

water molecules.

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

Temperature

Two types of units are defined: units for computing temperature differences

and functions for converting absolute temperatures. Conversions for

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

with "temp".

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

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

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

degcelsius K scale with water boiling at 0 degrees and

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.

fahrenheit 5|9 degC Fahrenheit defined his temperature scale

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)

rankine degF The Rankine scale has the

degreesrankine Fahrenheit degree, but it's zero

degF is at absolute zero.

reaumur 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.

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

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 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

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

mach 331.46 m/s speed of sound in dry air at STP

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

electron 5.485799110e-4 u

proton 1.00727646688 u

neutron 1.00866491578 u

muon 0.1134289168 u

deuteron 2.01355321271 u

alpha particle 4.0015061747 u

particle wavelengths: the compton wavelength of a particle is

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

Magnetic moments

bohrmagneton e hbar / 2 electronmass

mu B bohrmagneton

nuclearmagneton e hbar / 2 protonmass

mu N nuclearmagneton

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

NIST publication 811

lightsecond c s

lightminute c min

parsec au / tan(arcsec) Unit of length equal to distance

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.

Photometric units

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

nit cd/m^2 Luminance: the intensity per projected

stilb cd / cm^2 area of an extended luminous source.

sb stilb (nit is from latin nitere = to shine.)

apostilb cd/pi m^2

asb apostilb

blondel apostilb Named after a French scientist.

Equivalent luminance measures. These units are units which measure

the luminance of a surface with a specified exitance which obeys

Lambert's law. (Lambert's law specifies that luminous intensity of

a perfectly diffuse luminous surface is proportional to the cosine

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

equivalentlux cd / pi m^2 luminance of a 1 lux surface

equivalentphot cd / pi cm^2 luminance of a 1 phot surface

lambert cd / pi cm^2

footlambert cd / pi ft^2

The bril is used to express "brilliance" of a source of light on a

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

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

have a brilliance of 1 bril.

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

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

sunlum 1.6e9 cd/m^2 at zenith

sunillum 100e3 lux clear sky

sunillum o 10e3 lux overcast sky

sunlum h 6e6 cd/m^2 value at horizon

skylum 8000 cd/m^2 average, clear sky

skylum o 2000 cd/m^2 average, overcast sky

moonlum 2500 cd/m^2

Photographic Exposure Value

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

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

who relied on exposure tables rather than exposure meters. Shortly

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

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

A^2 LS ES

2^EV = --- = -- = --

T K C

Where

A = Relative aperture (f-number)

T = Shutter time in seconds

L = Scene luminance in cd/m2

E = Scene illuminance in lux

S = Arithmetic ISO film speed

K = Reflected-light meter calibration constant

C = Incident-light meter calibration constant

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

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

luminance (or illuminance). Conversion to luminance or illuminance

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

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

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

Calibration constants vary among camera and meter manufacturers: Canon,

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

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

of 250 for incident-light meters with flat receptors.

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

Reflected-light meter calibration constant with ISO 100 film

k1250 12.5 (cd/m2) / lx s For Canon, Nikon, and Sekonic

k1400 14 (cd/m2) / lx s For Minolta and Pentax

Incident-light meter calibration constant with ISO 100 film

c250 250 lx / lx s flat-disc receptor

Exposure value to scene luminance with ISO 100 film

For Minolta or Pentax

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

For Canon, Nikon or Sekonic

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

Exposure value to scene illuminance with ISO 100 film

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

Astronomical time measurements

Astronmical time measurement is a complicated matter. The rotation of the

earth and motion of the planets is not uniform. Originally the second was

defined relative to the "mean solar day". It is necessary to use the mean

day because the earth's orbit is elliptical so the length of the day varies

throughout the year. Simon Newcomb discovered that there were significant

irregularities in the rotation of the earth and he came up with equations

using the location of a fictitious mean sun. The length of the second was

determined from the tropical year obtained from Newcomb's equations. This

second was officially used from 1960 to 1967, at which point atomic clocks

replaced astronomical measurements for a standard of time.

The measures that appear below are probably obtained from an "ephemeris"

which is a set of equations that predicts the locations of the planets over

time.

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 mean interval between vernal

equinoxes. Differs from the

sidereal year by 1 part in

26000 due to precession of the

earth about its rotational axis

combined with precession of the

perihelion of the earth's

orbit.

gaussianyear 365.2690 days The orbital period of a body in

circular orbit at a distance of

1 au from the sun. Calculated

from Kepler's third law.

elipseyear 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 23.934469444 hour 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

Time between full moons. Full

synodicmonth lunarmonth moon occur when the sun and

lunation synodicmonth moon are on opposite sides of

lune 1|30 lunation the earth. Since the earth

lunour 1|24 lune moves around the sun, the moon

has to revolve a bit farther 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.

The Hartree system of atomic units, derived from fundamental units

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

the coulomb constant.

Fundamental units

atomicmass electronmass

atomiccharge e

atomicaction hbar

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

atomiclength bohrradius

atomictime hbar^3/coulombconst^2 atomicmass e^4 Period of first

bohr orbit

atomicvelocity atomiclength / atomictime

atomicenergy hbar / atomictime

hartree atomicenergy

Hartree hartree

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

thermalcoulomb J/K entropy

thermalampere W/K entropy flow

thermalfarad J/K^2

thermalohm K^2/W thermal resistance

fourier thermalohm

thermalhenry J K^2/W^2 thermal inductance

thermalvolt K thermal potential difference

United States units

linear measure

The US Metric Law of 1866 gave the exact relation 1 meter = 39.37 inches.

From 1893 until 1959, the foot was exactly 1200|3937 meters. In 1959

the definition was changed to bring the US into agreement with other

countries. Since then, 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.

U.S. 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 (unit) 5.5 USyard

perch rod

furlong 40 rod From "furrow long"

statutemile USmile

league 3 USmile Intended to be an an hour's walk

surveyor's measure

surveyorschain 66 surveyft

surveyorspole 1|4 surveyorschain

surveyorslink 1|100 surveyorschain

chain surveyorschain

surveychain chain

ch chain

link surveyorslink

acre 10 chain^2

intacre 43560 ft^2 Acre based on international ft

acrefoot acre surveyfoot

section USmile^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

nautical measure

fathom 6 USft 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 fathom

navycablelength 720 USft used for depth in water

marineleague 3 nauticalmile

geographicalmile brnauticalmile

knot nauticalmile / hr

click km

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

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

Apothecaries' weight

appound troypound

apounce troyounce

apdram 1|8 apounce

apscruple 1|3 apdram

Liquid measure

gal gallon

quart 1|4 gallon

pint 1|2 quart

gill 1|4 pint

usgallon 231 in^3

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 Why this particular value? Often

rounded to 1.25 bushels.

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

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

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

wheatbushel 60 lb

soybeanbushel 60 lb

cornbushel 56 lb

ryebushel 56 lb

barleybushel 48 lb

oatbushel 32 lb

ricebushel 45 lb

canada oatbushel 34 lb

Wine and Spirits measure

ponyvolume 1 usfloz

jigger 1.5 usfloz Can vary between 1 and 2 usfloz

shot jigger Sometimes 1 usfloz

eushot 25 ml EU standard spirits measure

fifth 1|5 usgallon

winebottle 750 ml US industry standard, 1979

winesplit 1|4 winebottle

wineglass 4 usfloz

magnum 1.5 liter Standardized in 1979, but given

as 2 qt in some references

metrictenth 375 ml

metricfifth 750 ml

metricquart 1 liter

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.

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

European shoe size. According to

http://www.shoeline.com/footnotes/shoeterm.shtmlparis 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$

grand 1000 US$

greenback US$

key kg usually of marijuana, 60's

lid 1 oz Another 60's weed unit

footballfield 100 yards

marathon 26 miles + 385 yards

British

UK 1200000|3937014 m/ft The UK lengths were defined by

british- UK a bronze bar manufactured in

UK- UK 1844. Measurement of that bar

revealed the dimensions given

here.

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

long ton 20 brhundredweight

brton long_ton

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. 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

Units derived from imperial system

ouncedal oz ft / s^2 force which accelerates an ounce

at 1 ft/s^2

poundal lb ft / s^2 same thing for a pound

tondal ton ft / s^2 and for a ton

pdl poundal

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

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

Other units of work, energy, power, etc

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

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

electrichorsepower 746 W

boilerhorsepower 9809.50 W

waterhorsepower 746.043 W

brhorsepower 745.70 W

donkeypower 250 W

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.

Rvalue degF ft^2 hr / btu

Uvalue 1/Rvalue

europeanUvalue watt / m^2 K

RSI degC m^2 / W

clo 0.155 degC m^2 / W Supposed to be the insulance

required to keep a resting person

comfortable indoors. The value

given is from NIST and the CRC,

but [5] gives a slightly different

value of 0.875 ft^2 degF hr / btu.

tog 0.1 degC m^2 / W Also used for clothing.

Misc other measures

ENTROPY ENERGY / TEMPERATURE

clausius 1e3 cal/K A unit of physical entropy

langley thermcalorie/cm^2 Used in radiation theory

poncelet 100 kg force m / s

tonrefrigeration ton 144 btu / lb day One ton refrigeration is

the rate of heat extraction required

turn one ton of water to ice in

a day. Ice is defined to have a

latent heat of 144 btu/lb.

tonref tonrefrigeration

refrigeration tonref / ton

frigorie 1000 cal_fifteen Used in refrigeration engineering.

tnt 1e9 cal_th / ton So you can write tons-tnt. This

is a defined, not measured, value.

airwatt 8.5 (ft^3/min) inH2O Measure of vacuum power as

pressure times air flow.

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

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

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

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

perm 0C grain / hr ft^2 inHg

perm zero perm_0C

perm 0 perm_0C

perm perm_0C

perm 23C grain / hr ft^2 in Hg23C

perm twentythree perm_23C

Counting measures

pair 2

brace (grouping)) 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

gross 144

greatgross 12 gross

tithe 1|10 From Anglo-Saxon word for tenth

Paper counting measure

shortquire 24

quire 25

shortream 480

ream 500

perfectream 516

bundle 2 reams

bale 5 bundles

Paper measures

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.

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

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.

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.

nybble 4 bits Half of a byte. Sometimes

equal to different lengths

such as 3 bits.

nibble nybble

meg megabyte Some people consider these

units along with the kilobyte

gig gigabyte to be defined according to

powers of 2 with the kilobyte

equal to 2^10 bytes, the

megabyte equal to 2^20 bytes and

the gigabyte equal to 2^30 bytes

but these usages are forbidden

by SI. Binary prefixes have

been defined by IEC to replace

the SI prefixes. Use them to

get the binary values: KiB, MiB,

and GiB.

jiffy 0.01 sec This is defined in the Jargon File

jiffies jiffy (http://www.jargon.org) as being the

duration of a clock tick for measuring

wall-clock time. Supposedly the value

used to be 1|60 sec or 1|50 sec

depending on the frequency of AC power,

but then 1|100 sec became more common.

On linux systems, this term is used and

for the Intel based chips, it does have

the value of .01 sec. The Jargon File

also lists two other definitions:

millisecond, and the time taken for

light to travel one foot.

Musical measures. Musical intervals expressed as ratios. Multiply

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

musicalcent can be used to convert ratios to cents.

Perfect intervals

octave 2

majorsecond musicalfifth^2 / octave

majorthird 5|4

minorthird 6|5

musicalfourth 4|3

musicalfifth 3|2

majorsixth musicalfourth majorthird

minorsixth musicalfourth minorthird

majorseventh musicalfifth majorthird

minorseventh musicalfifth minorthird

pythagoreanthird majorsecond musicalfifth^2 / octave

syntoniccomma pythagoreanthird / majorthird

pythagoreancomma musicalfifth^12 / octave^7

Equal tempered definitions

semitone octave^(1|12)

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

Musical note lengths.

wholenote !

halfnote 1|2 wholenote

quarternote 1|4 wholenote

eighthnote 1|8 wholenote

sixteenthnote 1|16 wholenote

thirtysecondnote 1|32 wholenote

sixtyfourthnote 1|64 wholenote

dotted 3|2

doubledotted 7|4

breve doublewholenote

semibreve wholenote

minimnote halfnote

crochet quarternote

quaver eighthnote

semiquaver sixteenthnote

demisemiquaver thirtysecondnote

hemidemisemiquaver sixtyfourthnote

semidemisemiquaver hemidemisemiquaver

yarn and cloth measures

yarn linear density

woolyarnrun 1600 yard/pound 1600 yds of "number 1 yarn" weighs

a pound.

yarncut 300 yard/pound Less common system used in

Pennsylvania for wool yarn

cottonyarncount 840 yard/pound

linenyarncount 300 yard/pound Also used for hemp and ramie

worstedyarncount 1680 ft/pound

metricyarncount meter/gram

denier 1|9 tex used for silk and rayon

manchesteryarnnumber drams/1000 yards old system used for silk

pli lb/in

typp 1000 yd/lb

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

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.

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].

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

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

crown 5 shilling

brpenny 0.01 britainpound

pence penny

tuppence 2 pence

tuppenny tuppence

oldpenny oldpence

oldtuppence 2 oldpence

oldtuppenny oldtuppence

threepence 3 oldpence threepence never refers to new money

threepenny threepence

oldthreepence threepence

oldthreepenny threepence

oldhalfpenny halfoldpenny

oldhapenny oldha'penny

brpony 25 britainpound

Canadian currency

loony 1 canadadollar This coin depicts a loon

toony 2 canadadollar

Oceanographic flow

sverdrup 1e6 m^3 / sec Used to express flow of ocean

currents. Named after Norwegian

oceanographer H. Sverdrup.

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

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

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

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

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

molecular mass is known.

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:

g00 (-1)

g000 (-2)

g0000 (-3)

g00000 (-4)

g000000 (-5)

g0000000 (-6)

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

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

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

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

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

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

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

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

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

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

nearest 0.00001 inch.

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

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

than steel, iron and zinc.

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

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

is piecewise linear. It was used for aluminum sheets.

The following is from the Appendix to ASTM B 258

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

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

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

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

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

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

formula for converting gage to thickness or weight.

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

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

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

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

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

closer).

This gauge was established in 1893 for purposes of taxation.

Old plate gauge for iron

Manufacturers Standard Gage

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

indicate thicker sheets.

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.

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.

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.

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

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

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

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

A few German units as currently in use.

zentner 50 kg

doppelzentner 2 zentner

pfund 500 g

Some definitions using ISO 8859-1 characters

¢ cent

£ britainpound

¥ japanyen

ångström angstrom

Å angstrom

röntgen roentgen

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.