User:Egil/Sandbox/units
Info from units that should be included
[edit]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.