Conversion of units

TechniquesEdit

Process overviewEdit

The process of conversion depends on the specific situation and the intended purpose. This may be governed by regulation, contract, technical specifications or other published standards. Engineering judgment may include such factors as:

The precision and accuracy of measurement and the associated uncertainty of measurement.
The statistical confidence interval or tolerance interval of the initial measurement.
The number of significant figures of the measurement.
The intended use of the measurement including the engineering tolerances.
Historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot.

Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement. This is sometimes called soft conversion. It does not involve changing the physical configuration of the item being measured.

By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system. It sometimes involves a slightly different configuration, or size substitution, of the item.^{[clarification needed]} Nominal values are sometimes allowed and used.

Conversion factorsEdit

A conversion factor is used to change the units of a measured quantity without changing its value. The unity bracket method of unit conversion^[1] consists of a fraction in which the denominator is equal to the numerator, but they are in different units. Because of the identity property of multiplication, the value of a quantity will not change as long as it is multiplied by one.^[2] Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.

The following example demonstrates how the unity bracket method^[3] is used to convert the rate 5 kilometers per second to meters per second. The symbols km, m, and s represent kilometer, meter, and second, respectively.

${\frac {5{\cancel {\text{km}}}}{\text{s}}}\cdot$ ${\frac {{1000}{\text{ m}}}{{1}{\cancel {\text{ km}}}}}$ $=$ ${\frac {5000\cdot {\text{m}}}{{\text{s}}\cdot {1}}}=$ ${\frac {5000{\text{ m}}}{\text{s}}}$

Thus, it is found that 5 kilometers per second is equal to 5000 meters per second.

Software toolsEdit

There are many conversion tools. They are found in the function libraries of applications such as spreadsheets databases, in calculators, and in macro packages and plugins for many other applications such as the mathematical, scientific and technical applications.

There are many standalone applications that offer the thousands of the various units with conversions. For example, the free software movement offers a command line utility GNU units for Linux and Windows.

Calculation involving non-SI UnitsEdit

In the cases where non-SI units are used, the numerical calculation of a formula can be done by first working out the pre-factor, and then plug in the numerical values of the given/known quantities.

For example, in the study of Bose–Einstein condensate,^[4] atomic mass $m$ is usually given in daltons, instead of kilograms, and chemical potential μ is often given in Boltzmann constant times nanokelvin. The condensate's healing length is given by:

\xi ={\frac {\hbar }{\sqrt {2m\mu }}}\,.

For a ²³Na condensate with chemical potential of (Boltzmann constant times) 128 nK, the calculation of healing length (in micrometres) can be done in two steps:

Calculate the pre-factorEdit

Assume that $m=1\,{\text{Da}},\mu =k_{\text{B}}\cdot 1\,{\text{nK}}\,,$ this gives

\xi ={\frac {\hbar }{\sqrt {2m\mu }}}=15.574\,\mathrm {\mu } m\,,

which is our pre-factor.

Calculate the numbersEdit

Now, make use of the fact that $\xi \propto {\frac {1}{\sqrt {m\mu }}}$ . With $m=23\,{\text{Da}},\mu =128\,k_{\text{B}}\cdot {\text{nK}}$ , $\xi ={\frac {15.574}{\sqrt {23\cdot 128}}}\,\mathrm {\mu } m=0.287\,\mathrm {\mu } m$ .

This method is especially useful for programming and/or making a worksheet, where input quantities are taking multiple different values; For example, with the pre-factor calculated above, it's very easy to see that the healing length of ¹⁷⁴Yb with chemical potential 20.3 nK is $\xi ={\frac {15.574}{\sqrt {174\cdot 20.3}}}\,\mu m=0.262\,\mathrm {\mu } m$ .

Tables of conversion factorsEdit

This article gives lists of conversion factors for each of a number of physical quantities, which are listed in the index. For each physical quantity, a number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10⁻⁶ metre). Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted.

Legend
Symbol	Definition
≡	exactly equal
≈	approximately equal to
≘	(exactly) corresponds to (different types of quantity describing the same phenomenon)
`digits`	indicates that `digits` repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...)
(H)	of chiefly historical interest

LengthEdit

Length
Name of unit	Symbol	Definition	Relation to SI units
ångström	Å	≡ 1×10⁻¹⁰ m	≡ 0.1 nm
astronomical unit	au	≡ 149597870700 m ≈ Distance from Earth to Sun	≡ 149597870700 m ^[5]
attometre	am	≡ 1×10⁻¹⁸ m	≡ 1×10⁻¹⁸ m
barleycorn (H)		= 1⁄3 in (see note above about rounding)	= 8.46×10⁻³ m
bohr, atomic unit of length	a₀	= Bohr radius of hydrogen	≈ 5.2917721092(17)×10⁻¹¹ m^[6]
cable length (imperial)		≡ 608 ft	≈ 185.3184 m
cable length (International)		≡ 1⁄10 nmi	≡ 185.2 m
cable length (US)		≡ 720 ft	= 219.456 m
chain (Gunter's; Surveyor's)	ch	≡ 66 ft (US) ≡ 4 rods^[7]	≈ 20.11684 m
cubit (H)		≡ Distance from fingers to elbow ≈ 18 in	≈ 0.5 m
ell (H)	ell	≡ 45 in ^[8] (In England usually)	= 1.143 m
fathom	ftm	≡ 6 ft ^[8]	= 1.8288 m
femtometre	fm	≡ 1×10⁻¹⁵ m	≡ 1×10⁻¹⁵ m
fermi	fm	≡ 1×10⁻¹⁵ m^[8]	≡ 1×10⁻¹⁵ m
finger		≡ 7⁄8 in	= 0.022225 m
finger (cloth)		≡ 4+1⁄2 in	= 0.1143 m
foot (Benoît) (H)	ft (Ben)		≈ 0.304799735 m
foot (Cape) (H)		Legally defined as 1.033 English feet in 1859	≈ 0.314858 m
foot (Clarke's) (H)	ft (Cla)		≈ 0.3047972654 m
foot (Indian) (H)	ft Ind		≈ 0.304799514 m
foot, metric	mf	≡ 300 mm	≡ 0.3 m
foot, metric (Mesures usuelles) (H)		≡ 1⁄3 m	≡ 0.3 m
foot (International)	ft	≡ 0.3048 m ≡ 1⁄3 yd ≡ 12 inches	≡ 0.3048 m
foot (Sear's) (H)	ft (Sear)		≈ 0.30479947 m
foot (US Survey)	ft (US)	≡ 1200⁄3937 m ^[9]	≈ 0.304800610 m
french; charriere	F	≡ 1⁄3 mm	= 0.3 ×10⁻³ m
furlong	fur	≡ 10 chains = 660 ft = 220 yd ^[8]	= 201.168 m
hand		≡ 4 in ^[8]	≡ 0.1016 m
inch (International)	in	≡ 2.54 cm ≡ 1⁄36 yd ≡ 1⁄12 ft	≡ 0.0254 m
league (land)	lea	≈ 1 hour walk, Currently defined in US as 3 Statute miles,^[7] but historically varied from 2 to 9 km	≈ 4828 m
light-day		≡ 24 light-hours	≡ 2.59020683712×10¹³ m
light-hour		≡ 60 light-minutes	≡ 1.0792528488×10¹² m
light-minute		≡ 60 light-seconds	≡ 1.798754748×10¹⁰ m
light-second		≡ Distance light travels in one second in vacuum	≡ 299792458 m
light-year	ly	≡ Distance light travels in vacuum in 365.25 days ^[10]	≡ 9.4607304725808×10¹⁵ m
line	ln	≡ 1⁄12 in ^[11]	= 0.002116 m
link (Gunter's; Surveyor's)	lnk	≡ 1⁄100 ch ^[8] ≡ 0.66 ft (US) ≡ 7.92 in	≈ 0.2011684 m
link (Ramsden's; Engineer's)	lnk	≡ 1 ft ^[8]	= 0.3048 m
metre (SI base unit) (meter)	m	≡ Distance light travels in 1⁄299792458 of a second in vacuum.^[12]	(SI base unit)
mickey		≡ 1⁄200 in	= 1.27×10⁻⁴ m
micrometre (old: micron)	μ; μm	≡ 1×10⁻⁶ m	≡ 1×10⁻⁶ m
mil; thou	mil	≡ 1×10⁻³ in	= 2.54×10⁻⁵ m
mil (Sweden and Norway)	mil	≡ 10 km	= 10000 m
mile (geographical) (H)		≡ 6082 ft	= 1853.7936 m
mile (international)	mi	≡ 80 chains ≡ 5280 ft ≡ 1760 yd	≡ 1609.344 m
mile (tactical or data)		≡ 6000 ft	≡ 1828.8 m
mile (telegraph) (H)	mi	≡ 6087 ft	= 1855.3176 m
mile (US Survey)	mi	≡ 5280 US Survey feet ≡ (5280 × 1200⁄3937) m	≈ 1609.347219 m
nail (cloth)		≡ 2+1⁄4 in ^[8]	= 0.05715 m
nanometre	nm	≡ 1×10⁻⁹ m	≡ 1×10⁻⁹ m
nautical league	NL; nl	≡ 3 nmi ^[8]	= 5556 m
nautical mile (Admiralty)	NM (Adm); nmi (Adm)	= 6080 ft	= 1853.184 m
nautical mile (international)	NM; nmi	≡ 1852 m^[13]	≡ 1852 m
nautical mile (US pre 1954)		≡ 1853.248 m	≡ 1853.248 m
pace		≡ 2.5 ft ^[8]	= 0.762 m
palm		≡ 3 in ^[8]	= 0.0762 m
parsec	pc	Distant point with a parallax shift of one arc second from a base of one astronomical unit. ≡ 648000/ $π$ au^[14]^[15]	≈ 30856775814913700 m^[16]
pica		≡ 12 points	Dependent on point measures.
picometre	pm	≡ 1×10⁻¹² m	≡ 1×10⁻¹² m
point (American, English)^[17]^[18]	pt	≡ 1⁄72.272 in	≈ 0.000351450 m
point (Didot; European) ^[18]^[19]	pt	≡ 1⁄12 × 1⁄72 of pied du roi; After 1878: ≡ 5⁄133 cm	≈ 0.00037597 m; After 1878: ≈ 0.00037593985 m
point (PostScript) ^[17]	pt	≡ 1⁄72 in	= 0.0003527 m
point (TeX) ^[17]	pt	≡ 1⁄72.27 in	= 0.0003514598 m
quarter		≡ 1⁄4 yd	= 0.2286 m
rod; pole; perch (H)	rd	≡ 16+1⁄2 ft	= 5.0292 m
rope (H)	rope	≡ 20 ft ^[8]	= 6.096 m
shaku (Japan)		≡ 10/33 m	≈ 0.303 0303 m
span (H)		≡ 9 in ^[8]	= 0.2286 m
spat^[20]			≡ 1×10¹² m
stick (H)		≡ 2 in	= 0.0508 m
toise (French, post 1667) (H)	T	≡ 27000/13853 m	≈ 1.949 0363 m
twip	twp	≡ 1⁄1440 in	= 1.7638×10⁻⁵ m
x unit; siegbahn	xu		≈ 1.0021×10⁻¹³ m ^[8]
yard (International)	yd	≡ 0.9144 m ^[9] ≡ 3 ft ≡ 36 in	≡ 0.9144 m
yoctometre	ym	≡ 1×10⁻²⁴ m	≡ 1×10⁻²⁴ m
zeptometre	zm	≡ 1×10⁻²¹ m	≡ 1×10⁻²¹ m

AreaEdit

Area
Name of unit	Symbol	Definition	Relation to SI units
acre (international)	ac	≡ 1 ch × 10 ch = 4840 sq yd	≡ 4046.8564224 m²
acre (US survey)	ac	≡ 10 sq ch = 4840 sq yd, also 43560 sq ft	≈ 4046.873 m²^[21]
are	a	≡ 100 m²	≡ 100 m²
barn	b	≡ 10⁻²⁸ m²	≡ 10⁻²⁸ m²
barony		≡ 4000 ac	≡ 1.61874256896×10⁷ m²
board	bd	≡ 1 in × 1 ft	≡ 7.74192×10⁻³ m²
boiler horsepower equivalent direct radiation	bhp EDR	≡ 1 ft² × 1 bhp / (240 BTU_IT/h)	≈ 12.958174 m²
circular inch	circ in	≡ π⁄4 sq in	≈ 5.067075×10⁻⁴ m²
circular mil; circular thou	circ mil	≡ π⁄4 mil²	≈ 5.067075×10⁻¹⁰ m²
cord		≡ 192 bd	≡ 1.48644864 m²
cuerda (PR Survey)	cda	≡ 1 cda x 1 cda = 0.971222 acre	≡ 3930.395625 m²
dunam		≡ 1000 m²	≡ 1000 m²
guntha (India)		≡ 121 sq yd	≈ 101.17 m²
hectare	ha	≡ 10000 m²	≡ 10000 m²
hide		≈ 120 ac (variable)	≈ 5×10⁵ m²
rood	ro	≡ 1⁄4 ac	= 1011.7141056 m²
ping		≡ 20⁄11 m × 20⁄11 m	≈ 3.306 m²
section		≡ 1 mi × 1 mi	= 2.589988110336×10⁶ m²
shed		≡ 10⁻⁵² m²	= 10⁻⁵² m²
square (roofing)		≡ 10 ft × 10 ft	= 9.290304 m²
square chain (international)	sq ch	≡ 66 ft × 66 ft = 1⁄10 ac	≡ 404.68564224 m²
square chain (US Survey)	sq ch	≡ 66 ft (US) × 66 ft (US) = 1⁄10 US survey acre	≈ 404.6873 m²
square foot	sq ft	≡ 1 ft × 1 ft	≡ 9.290304×10⁻² m²
square foot (US Survey)	sq ft	≡ 1 ft (US) × 1 ft (US)	≈ 9.2903411613275×10⁻² m²
square inch	sq in	≡ 1 in × 1 in	≡ 6.4516×10⁻⁴ m²
square kilometre	km²	≡ 1 km × 1 km	= 10⁶ m²
square link (Gunter's)(International)	sq lnk	≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft	= 4.0468564224×10⁻² m²
square link (Gunter's)(US Survey)	sq lnk	≡ 1 lnk × 1 lnk ≡ 0.66 ft (US) × 0.66 ft (US)	≈ 4.046872×10⁻² m²
square link (Ramsden's)	sq lnk	≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft	= 0.09290304 m²
square metre (SI unit)	m²	≡ 1 m × 1 m	= 1 m²
square mil; square thou	sq mil	≡ 1 mil × 1 mil	= 6.4516×10⁻¹⁰ m²
square mile	sq mi	≡ 1 mi × 1 mi	≡ 2.589988110336×10⁶ m²
square mile (US Survey)	sq mi	≡ 1 mi (US) × 1 mi (US)	≈ 2.58999847×10⁶ m²
square rod/pole/perch	sq rd	≡ 1 rd × 1 rd	= 25.29285264 m²
square yard (International)	sq yd	≡ 1 yd × 1 yd	≡ 0.83612736 m²
stremma		≡ 1000 m²	= 1000 m²
township		≡ 36 sq mi (US)	≈ 9.323994×10⁷ m²
yardland		≈ 30 ac	≈ 1.2×10⁵ m²

VolumeEdit

Volume
Name of unit	Symbol	Definition	Relation to SI units
acre-foot	ac ft	≡ 1 ac x 1 ft = 43560 cu ft	= 1233.48183754752 m³
acre-inch		≡ 1 ac × 1 in	= 102.79015312896 m³
barrel (imperial)	bl (imp)	≡ 36 gal (imp)	= 0.16365924 m³
barrel (petroleum); archaic blue-barrel	bl; bbl	≡ 42 gal (US)	= 0.158987294928 m³
barrel (US dry)	bl (US)	≡ 105 qt (US) = 105/32 bu (US lvl)	= 0.115628198985075 m³
barrel (US fluid)	fl bl (US)	≡ 31+1⁄2 gal (US)	= 0.119240471196 m³
board-foot	bdft	≡ 144 cu in	≡ 2.359737216×10⁻³ m³
bucket (imperial)	bkt	≡ 4 gal (imp)	= 0.01818436 m³
bushel (imperial)	bu (imp)	≡ 8 gal (imp)	= 0.03636872 m³
bushel (US dry heaped)	bu (US)	≡ 1+1⁄4 bu (US lvl)	= 0.0440488377086 m³
bushel (US dry level)	bu (US lvl)	≡ 2150.42 cu in	= 0.03523907016688 m³
butt, pipe		≡ 126 gal (US) (wine)	= 0.476961884784 m³
coomb		≡ 4 bu (imp)	= 0.14547488 m³
cord (firewood)		≡ 8 ft × 4 ft × 4 ft	= 3.624556363776 m³
cord-foot		≡ 16 cu ft	= 0.453069545472 m³
cubic fathom	cu fm	≡ 1 fm × 1 fm × 1 fm	= 6.116438863872 m³
cubic foot	ft³	≡ 1 ft × 1 ft × 1 ft	≡ 0.028316846592 m³
cubic inch	in³	≡ 1 in × 1 in × 1 in	≡ 16.387064×10⁻⁶ m³
cubic metre (SI unit)	m³	≡ 1 m × 1 m × 1 m	≡ 1 m³
cubic mile	cu mi	≡ 1 mi × 1 mi × 1 mi	≡ 4168181825.440579584 m³
cubic yard	yd³	≡ 27 cu ft	≡ 0.764554857984 m³
cup (breakfast)		≡ 10 fl oz (imp)	= 284.130625×10⁻⁶ m³
cup (Canadian)	c (CA)	≡ 8 fl oz (imp)	= 227.3045×10⁻⁶ m³
cup (metric)	c	≡ 250.0×10⁻⁶ m³	≡ 250.0×10⁻⁶ m³
cup (US customary)	c (US)	≡ 8 US fl oz ≡ 1⁄16 gal (US)	= 236.5882365×10⁻⁶ m³
cup (US food nutrition labeling)	c (US)	≡ 240 mL^[22]	= 2.4×10⁻⁴ m³
dash (imperial)		≡ 1⁄384 gi (imp) = 1⁄2 pinch (imp)	= 369.961751302083×10⁻⁹ m³
dash (US)		≡ 1⁄96 US fl oz = 1⁄2 US pinch	= 308.057599609375×10⁻⁹ m³
dessertspoon (imperial)		≡ 1⁄12 gi (imp)	= 11.8387760416×10⁻⁶ m³
drop (imperial)	gtt	≡ 1⁄288 fl oz (imp)	= 98.6564670138×10⁻⁹ m³
drop (imperial) (alt)	gtt	≡ 1⁄1824 gi (imp)	≈ 77.886684×10⁻⁹ m³
drop (medical)		≡ 1⁄12 mL	= 83.3×10⁻⁹ m³
drop (metric)		≡ 1⁄20 mL	= 50.0×10⁻⁹ m³
drop (US)	gtt	≡ 1⁄360 US fl oz	= 82.14869322916×10⁻⁹ m³
drop (US) (alt)	gtt	≡ 1⁄456 US fl oz	≈ 64.85423149671×10⁻⁹ m³
drop (US) (alt)	gtt	≡ 1⁄576 US fl oz	≈ 51.34293326823×10⁻⁹ m³
fifth		≡ 1⁄5 US gal	= 757.0823568×10⁻⁶ m³
firkin		≡ 9 gal (imp)	= 0.04091481 m³
fluid drachm (imperial)	fl dr	≡ 1⁄8 fl oz (imp)	= 3.5516328125×10⁻⁶ m³
fluid dram (US); US fluidram	fl dr	≡ 1⁄8 US fl oz	= 3.6966911953125×10⁻⁶ m³
fluid scruple (imperial)	fl s	≡ 1⁄24 fl oz (imp)	= 1.18387760416×10⁻⁶ m³
gallon (beer)	beer gal	≡ 282 cu in	= 4.621152048×10⁻³ m³
gallon (imperial)	gal (imp)	≡ 4.54609 L	≡ 4.54609×10⁻³ m³
gallon (US dry)	gal (US)	≡ 1⁄8 bu (US lvl)	= 4.40488377086×10⁻³ m³
gallon (US fluid; Wine)	gal (US)	≡ 231 cu in	≡ 3.785411784×10⁻³ m³
gill (imperial); Noggin	gi (imp); nog	≡ 5 fl oz (imp)	= 142.0653125×10⁻⁶ m³
gill (US)	gi (US)	≡ 4 US fl oz	= 118.29411825×10⁻⁶ m³
hogshead (imperial)	hhd (imp)	≡ 2 bl (imp)	= 0.32731848 m³
hogshead (US)	hhd (US)	≡ 2 fl bl (US)	= 0.238480942392 m³
jigger (bartending)		≡ 1+1⁄2 US fl oz	≈ 44.36×10⁻⁶ m³
kilderkin		≡ 18 gal (imp)	= 0.08182962 m³
lambda	λ	≡ 1 mm³	= 1×10⁻⁹ m³
last		≡ 80 bu (imp)	= 2.9094976 m³
litre (liter)	L or l	≡ 1 dm³ ^[23]	≡ 0.001 m³
load		≡ 50 cu ft	= 1.4158423296 m³
minim (imperial)	min	≡ 1⁄480 fl oz (imp) = 1/60 fl dr (imp)	= 59.1938802083×10⁻⁹ m³
minim (US)	min	≡ 1⁄480 US fl oz = 1⁄60 US fl dr	= 61.611519921875×10⁻⁹ m³
ounce (fluid imperial)	fl oz (imp)	≡ 1⁄160 gal (imp)	≡ 28.4130625×10⁻⁶ m³
ounce (fluid US customary)	US fl oz	≡ 1⁄128 gal (US)	≡ 29.5735295625×10⁻⁶ m³
ounce (fluid US food nutrition labeling)	US fl oz	≡ 30 mL^[22]	≡ 3×10⁻⁵ m³
peck (imperial)	pk	≡ 2 gal (imp)	= 9.09218×10⁻³ m³
peck (US dry)	pk	≡ 1⁄4 US lvl bu	= 8.80976754172×10⁻³ m³
perch	per	≡ 16+1⁄2 ft × 1+1⁄2 ft × 1 ft	= 0.700841953152 m³
pinch (imperial)		≡ 1⁄192 gi (imp) = 1/16 tsp (imp)	= 739.92350260416×10⁻⁹ m³
pinch (US)		≡ 1⁄48 US fl oz = 1/16 US tsp	= 616.11519921875×10⁻⁹ m³
pint (imperial)	pt (imp)	≡ 1⁄8 gal (imp)	= 568.26125×10⁻⁶ m³
pint (US dry)	pt (US dry)	≡ 1⁄64 bu (US lvl) ≡ 1⁄8 gal (US dry)	= 550.6104713575×10⁻⁶ m³
pint (US fluid)	pt (US fl)	≡ 1⁄8 gal (US)	= 473.176473×10⁻⁶ m³
pony		≡ 3⁄4 US fl oz	= 22.180147171875×10⁻⁶ m³
pottle; quartern		≡ 1⁄2 gal (imp) = 80 fl oz (imp)	= 2.273045×10⁻³ m³
quart (imperial)	qt (imp)	≡ 1⁄4 gal (imp)	= 1.1365225×10⁻³ m³
quart (US dry)	qt (US)	≡ 1⁄32 bu (US lvl) = 1⁄4 gal (US dry)	= 1.101220942715×10⁻³ m³
quart (US fluid)	qt (US)	≡ 1⁄4 gal (US fl)	= 946.352946×10⁻⁶ m³
quarter; pail		≡ 8 bu (imp)	= 0.29094976 m³
register ton		≡ 100 cu ft	= 2.8316846592 m³
sack (US)		≡ 3 bu (US lvl)	= 0.10571721050064 m³
seam		≡ 8 bu ^[20]	= 0.29095 m³
shot (US)		usually 1.5 US fl oz^[20]	≈ 44.4×10⁻⁶ m³
strike (imperial)		≡ 2 bu (imp)	= 0.07273744 m³
strike (US)		≡ 2 bu (US lvl)	= 0.07047814033376 m³
tablespoon (Australian metric)			≡ 20.0×10⁻⁶ m³
tablespoon (Canadian)	tbsp	≡ 1⁄2 fl oz (imp)	= 14.20653125×10⁻⁶ m³
tablespoon (imperial)	tbsp	≡ 5⁄8 fl oz (imp)	= 17.7581640625×10⁻⁶ m³
tablespoon (metric)			≡ 15×10⁻⁶ m³
tablespoon (US customary)	tbsp	≡ 1⁄2 US fl oz	= 14.78676478125×10⁻⁶ m³
tablespoon (US food nutrition labeling)	tbsp	≡ 15 mL^[22]	= 15×10⁻⁶ m³
teaspoon (Canadian)	tsp	≡ 1⁄6 fl oz (imp)	= 4.735510416×10⁻⁶ m³
teaspoon (imperial)	tsp	≡ 1⁄24 gi (imp)	= 5.91938802083×10⁻⁶ m³
teaspoon (metric)		≡ 5.0×10⁻⁶ m³	≡ 5.0×10⁻⁶ m³
teaspoon (US customary)	tsp	≡ 1⁄6 US fl oz	= 4.92892159375×10⁻⁶ m³
teaspoon (US food nutrition labeling)	tsp	≡ 5 mL^[22]	= 5×10⁻⁶ m³
timber foot		≡ 1 cu ft	= 0.028316846592 m³
ton (displacement)		≡ 35 cu ft	= 0.99108963072 m³
ton (freight)		≡ 40 cu ft	= 1.13267386368 m³
ton (water)		≡ 28 bu (imp)	= 1.01832416 m³
tun		≡ 252 gal (wine)	= 0.953923769568 m³
wey (US)		≡ 40 bu (US lvl)	= 1.4095628066752 m³

Plane angleEdit

Plane angle
Name of unit	Symbol	Definition	Relation to SI units
NATO mil	(various)	≡ 2π⁄6400 rad	≈ 0.981748×10⁻³ rad
Swedish streck		≡ 2π⁄6300 rad	≈ 0.997302×10⁻³ rad
milliradian	mrad	≡ 1⁄1000 rad	≈ 1×10⁻³ rad
Warsaw Pact mil		≡ 2π⁄6000 rad	≈ 1.047167×10⁻³ rad
arcminute; MOA	'	≡ 1°⁄60	≈ 0.290888×10⁻³ rad
arcsecond	"	≡ 1°⁄3600	≈ 4.848137×10⁻⁶ rad
centesimal minute of arc	'	≡ 1⁄100 grad	≈ 0.157080×10⁻³ rad
centesimal second of arc	"	≡ 1⁄10000 grad	≈ 1.570796×10⁻⁶ rad
degree (of arc)	°	≡ 1⁄360 of a revolution ≡ π⁄180 rad	≈ 17.453293×10⁻³ rad
grad; gradian; gon	grad	≡ 1⁄400 of a revolution ≡ π⁄200 rad ≡ 0.9°	≈ 15.707963×10⁻³ rad
octant		≡ 45°	≈ 0.785398 rad
quadrant		≡ 90°	≈ 1.570796 rad
radian (SI unit)	rad	The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians.	= 1 rad
sextant		≡ 60°	≈ 1.047198 rad
sign		≡ 30°	≈ 0.523599 rad

Solid angleEdit

Solid angle
Name of unit	Symbol	Definition	Relation to SI units
spat		≡ 4π sr^[20] – The solid angle subtended by a sphere at its centre.	≈ 12.56637 sr
square degree	deg²; sq.deg.; (°)²	≡ (π⁄180)² sr	≈ 0.30462×10⁻³ sr
steradian (SI unit)	sr	The solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r². A sphere subtends 4π sr.^[20]	= 1 sr

MassEdit

Notes:

See Weight for detail of mass/weight distinction and conversion.
Avoirdupois is a system of mass based on a pound of 16 ounces, while Troy weight is the system of mass where 12 troy ounces equals one troy pound.
In this table, the symbol $g 0$ is used to denote standard gravity in order to avoid confusion with the (upright) g symbol for gram.

Mass
Name of unit	Symbol	Definition	Relation to SI units
atomic mass unit, unified	u; AMU	Same as dalton (see below)	≈ 1.660539040(20)×10⁻²⁷ kg^[7]
atomic unit of mass, electron rest mass	m_e		≈ 9.10938291(40)×10⁻³¹ kg^[24]
bag (coffee)		≡ 60 kg	= 60 kg
bag (Portland cement)		≡ 94 lb av	= 42.63768278 kg
barge		≡ 22+1⁄2 short ton	= 20411.65665 kg
carat	kt	≡ 3+1⁄6 gr	= 205.1965483 mg
carat (metric)	ct	≡ 200 mg	= 200 mg
clove		≡ 8 lb av	= 3.62873896 kg
crith		≡ mass of 1 L of hydrogen gas at STP	≈ 89.9349 mg
dalton	Da	1/12 the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest	≈ 1.660538921(73)×10⁻²⁷ kg^[7]
dram (apothecary; troy)	dr t	≡ 60 gr	= 3.8879346 g
dram (avoirdupois)	dr av	≡ 27+11⁄32 gr	= 1.7718451953125 g
electronvolt	eV	≡ 1 eV (energy unit) / c²	= 1.78266184(45)×10⁻³⁶ kg^[7]
gamma	γ	≡ 1 μg	= 1 μg
grain	gr	≡ 1⁄7000 lb av	≡ 64.79891 mg
grave	gv	grave was the original name of the kilogram	≡ 1 kg
hundredweight (long)	long cwt or cwt	≡ 112 lb av	= 50.80234544 kg
hundredweight (short); cental	sh cwt	≡ 100 lb av	= 45.359237 kg
kilogram (kilogramme)	kg	≈ mass of the prototype near Paris ≈ mass of 1 litre of water	(SI base unit)^[12]
kip	kip	≡ 1000 lb av	= 453.59237 kg
mark		≡ 8 oz t	= 248.8278144 g
mite		≡ 1⁄20 gr	= 3.2399455 mg
mite (metric)		≡ 1⁄20 g	= 50 mg
ounce (apothecary; troy)	oz t	≡ 1⁄12 lb t	= 31.1034768 g
ounce (avoirdupois)	oz av	≡ 1⁄16 lb	= 28.349523125 g
ounce (US food nutrition labelling)	oz	≡ 28 g^[22]	= 28 g
pennyweight	dwt; pwt	≡ 1⁄20 oz t	= 1.55517384 g
point		≡ 1⁄100 ct	= 2 mg
pound (avoirdupois)	lb av	≡ 0.45359237 kg = 7000 grains	≡ 0.45359237 kg
pound (metric)		≡ 500 g	= 500 g
pound (troy)	lb t	≡ 5760 grains	= 0.3732417216 kg
quarter (imperial)		≡ 1⁄4 long cwt = 2 st = 28 lb av	= 12.70058636 kg
quarter (informal)		≡ 1⁄4 short ton	= 226.796185 kg
quarter, long (informal)		≡ 1⁄4 long ton	= 254.0117272 kg
quintal (metric)	q	≡ 100 kg	= 100 kg
scruple (apothecary)	s ap	≡ 20 gr	= 1.2959782 g
sheet		≡ 1⁄700 lb av	= 647.9891 mg
slug; geepound; hyl	slug	≡ $g 0$ × 1 lb av × 1 s²/ft	≈ 14.593903 kg
stone	st	≡ 14 lb av	= 6.35029318 kg
ton, assay (long)	AT	≡ 1 mg × 1 long ton ÷ 1 oz t	= 32.6 g
ton, assay (short)	AT	≡ 1 mg × 1 short ton ÷ 1 oz t	= 29.16 g
ton, long	long tn or ton	≡ 2240 lb	= 1016.0469088 kg
ton, short	sh tn	≡ 2000 lb	= 907.18474 kg
tonne (mts unit)	t	≡ 1000 kg	= 1000 kg
wey		≡ 252 lb = 18 st	= 114.30527724 kg (variants exist)
Zentner	Ztr.	Definitions vary.^[20]^[25]

DensityEdit

Density
Name of unit	Symbol	Definition	Relation to SI units
gram per millilitre	g/mL	≡ g/mL	= 1000 kg/m³
kilogram per cubic metre (SI unit)	kg/m³	≡ kg/m³	= 1 kg/m³
kilogram per litre	kg/L	≡ kg/L	= 1000 kg/m³
ounce (avoirdupois) per cubic foot	oz/ft³	≡ oz/ft³	≈ 1.001153961 kg/m³
ounce (avoirdupois) per cubic inch	oz/in³	≡ oz/in³	≈ 1.729994044×10³ kg/m³
ounce (avoirdupois) per gallon (imperial)	oz/gal	≡ oz/gal	≈ 6.236023291 kg/m³
ounce (avoirdupois) per gallon (US fluid)	oz/gal	≡ oz/gal	≈ 7.489151707 kg/m³
pound (avoirdupois) per cubic foot	lb/ft³	≡ lb/ft³	≈ 16.01846337 kg/m³
pound (avoirdupois) per cubic inch	lb/in³	≡ lb/in³	≈ 2.767990471×10⁴ kg/m³
pound (avoirdupois) per gallon (imperial)	lb/gal	≡ lb/gal	≈ 99.77637266 kg/m³
pound (avoirdupois) per gallon (US fluid)	lb/gal	≡ lb/gal	≈ 119.8264273 kg/m³
slug per cubic foot	slug/ft³	≡ slug/ft³	≈ 515.3788184 kg/m³

TimeEdit

Time
Name of unit	Symbol	Definition	Relation to SI units
Atomic unit of time	au	≡ a₀/(α⋅c)	≈ 2.418884254×10⁻¹⁷ s
Callippic cycle		≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d	= 2.396736 Gs or 2.3983776 Gs^{[note 1]}
Century	c	≡ 100 years (100 a)	= 3.1556952 Gs^{[note 2]}^{[note 3]}
Day	d	= 24 h = 1440 min	= 86.4 ks^{[note 3]}
Day (sidereal)	d	≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame)	≈ 86.1641 ks
Decade	dec	≡ 10 years (10 a)	= 315.569520 Ms^{[note 2]}^{[note 3]}
Fortnight	fn	≡ 2 wk	= 1.2096 Ms^{[note 3]}
Helek		≡ 1⁄1080 h	= 3.3 s
Hipparchic cycle		≡ 4 Callippic cycles - 1 d	= 9.593424 Gs
Hour	h	≡ 60 min	= 3.6 ks^{[note 3]}
Jiffy	j	≡ 1⁄60 s	= 16.6 ms
Jiffy (alternative)	ja	≡ 1⁄100 s	= 10 ms
Ke (quarter of an hour)		≡ 1⁄4 h = 1⁄96 d = 15 min	= 900 s
Ke (traditional)		≡ 1⁄100 d = 14.4 min	= 864 s
Lustre; Lustrum		≡ 5 a of 365 d^{[note 4]}	= 157.68 Ms
Metonic cycle; enneadecaeteris		≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a	= 599.616 Ms
Millennium		≡ 1000 years (1000 a)	= 31.556952 Gs^{[note 2]}^{[note 3]}
Milliday	md	≡ 1⁄1000 d	= 86.4 s
Minute	min	≡ 60 s, due to leap seconds sometimes 59 s or 61 s,	= 60 s^{[note 3]}
Moment		≡ 90 s	= 90 s
Month (full)	mo	≡ 30 d^[26]	= 2.592×10⁶ s^{[note 3]}
Month (Greg. av.)	mo	= 30.436875 d	≈ 2.6297 Ms^{[note 3]}
Month (hollow)	mo	≡ 29 d^[26]	= 2.5056 Ms^{[note 3]}
Month (synodic)	mo	Cycle time of moon phases ≈ 29.530589 d (average)	≈ 2.551 Ms
Octaeteris		= 48 mo (full) + 48 mo (hollow) + 3 mo (full)^[27]^[28] = 8 a of 365.25 d = 2922 d	= 252.4608 Ms^{[note 3]}
Planck time		≡ (Gℏ⁄c⁵)^1⁄2	≈ 5.39116×10⁻⁴⁴ s^[29]
Second (SI base unit)	s	≡ Time of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0 K^[12] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of 299792458 metres.	(SI base unit)
Shake		≡ 10⁻⁸ s	= 10 ns
Sigma		≡ 10⁻⁶ s	= 1 μs
Sothic cycle		≡ 1461 a of 365 d	= 46.074096 Gs
Svedberg	S	≡ 10⁻¹³ s	= 100 fs
Week	wk	≡ 7 d = 168 h = 10080 min	= 604.8 ks^{[note 3]}
Year (common)	a, y, or yr	365 d	= 31.536 Ms^{[note 3]}^[30]
Year (Gregorian)	a, y, or yr	= 365.2425 d average, calculated from common years (365 d) plus leap years (366 d) on most years divisible by 4. See leap year for details.	= 31.556952 Ms^{[note 3]}
Year (Julian)	a, y, or yr	= 365.25 d average, calculated from common years (365 d) plus one leap year (366 d) every four years	= 31.5576 Ms
Year (leap)	a, y, or yr	366 d	= 31.6224 Ms^{[note 3]}^[30]
Year (mean tropical)	a, y, or yr	Conceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, ^{[Converter 1]} approximately 365.24219 d, each day being 86400 SI seconds^[31]	≈ 31.556925 Ms
Year (sidereal)	a, y, or yr	≡ Time taken for Sun to return to the same position with respect to the stars of the celestial sphere, approximately 365.256363 d	≈ 31.5581497632 Ms
Notes: ^ see Callippic cycle for explanation of the differences ^ ^a ^b ^c This is based on the average Gregorian year. See above for definition of year lengths. ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o Where UTC is observed, the length of this unit may increase or decrease depending on the number of leap seconds which occur during the time interval in question. ^ The length of ancient lustral cycles was not constant; see Lustrum for more details

FrequencyEdit

Frequency
Name of unit	Symbol	Definition	Relation to SI units
Actions per minute	APM	≡ 1/60 Hz	≈ 0.0167 Hz
Cycle per second	cps	≡ 1 Hz	= 1 cps = 1 Hz
degree per second	deg/s	≡ 1 °/s ≡ 1/360 Hz	= 0.0027 Hz
hertz (SI unit)	Hz	≡ One cycle per second	= 1 Hz = 1/s
Radian per second	rad/s	≡ 1/(2π) Hz	≈ 0.159155 Hz
revolutions per minute	rpm	≡ One unit rpm equals one rotation completed around a fixed axis in one minute of time.	≈ 0.104719755 rad/s

Speed or velocityEdit

Speed
Name of unit	Symbol	Definition	Relation to SI units
foot per hour	fph	≡ 1 ft/h	= 8.46×10⁻⁵ m/s
foot per minute	fpm	≡ 1 ft/min	= 5.08×10⁻³ m/s
foot per second	fps	≡ 1 ft/s	= 3.048×10⁻¹ m/s
furlong per fortnight		≡ furlong/fortnight	≈ 1.663095×10⁻⁴ m/s
inch per hour	iph	≡ 1 in/h	= 7.05×10⁻⁶ m/s
inch per minute	ipm	≡ 1 in/min	= 4.23×10⁻⁴ m/s
inch per second	ips	≡ 1 in/s	= 2.54×10⁻² m/s
kilometre per hour	km/h	≡ 1 km/h	= 2.7×10⁻¹ m/s
knot	kn	≡ 1 nmi/h = 1.852 km/h	= 0.514 m/s
knot (Admiralty)	kn	≡ 1 NM (Adm)/h = 1.853184 km/h^[32]	= 0.514773 m/s
mach number	M	Ratio of the speed to the speed of sound^{[note 1]} in the medium (unitless).	≈ 340 m/s in air at sea level ≈ 295 m/s in air at jet altitudes
metre per second (SI unit)	m/s	≡ 1 m/s	= 1 m/s
mile per hour	mph	≡ 1 mi/h	= 0.44704 m/s
mile per minute	mpm	≡ 1 mi/min	= 26.8224 m/s
mile per second	mps	≡ 1 mi/s	= 1609.344 m/s
speed of light in vacuum	c	≡ 299792458 m/s	= 299792458 m/s
speed of sound in air	s	1225 to 1062 km/h (761–660 mph or 661–574 kn)^{[note 1]}	≈ 340 to 295 m/s
Note ^ ^a ^b The speed of sound varies especially with temperature and pressure from about 340 m/s (1,225 km/h or 761 mph or 661 kn) in air at sea level to about 300 m/s (1,062 km/h or 660 mph or 573 kn) at jet altitudes (12200 m or 40000 ft).^[33]

A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.

Flow (volume)Edit

Flow
Name of unit	Symbol	Definition	Relation to SI units
cubic foot per minute	CFM^{[citation needed]}	≡ 1 ft³/min	= 4.719474432×10⁻⁴ m³/s
cubic foot per second	ft³/s	≡ 1 ft³/s	= 0.028316846592 m³/s
cubic inch per minute	in³/min	≡ 1 in³/min	= 2.7311773×10⁻⁷ m³/s
cubic inch per second	in³/s	≡ 1 in³/s	= 1.6387064×10⁻⁵ m³/s
cubic metre per second (SI unit)	m³/s	≡ 1 m³/s	= 1 m³/s
gallon (US fluid) per day	GPD^{[citation needed]}	≡ 1 gal/d	= 4.381263638×10⁻⁸ m³/s
gallon (US fluid) per hour	GPH^{[citation needed]}	≡ 1 gal/h	= 1.051503273×10⁻⁶ m³/s
gallon (US fluid) per minute	GPM^{[citation needed]}	≡ 1 gal/min	= 6.30901964×10⁻⁵ m³/s
litre per minute	l/min or L/min	≡ 1 L/min	= 1.6×10⁻⁵ m³/s

AccelerationEdit

Acceleration
Name of unit	Symbol	Definition	Relation to SI units
foot per hour per second	fph/s	≡ 1 ft/(h⋅s)	= 8.46×10⁻⁵ m/s²
foot per minute per second	fpm/s	≡ 1 ft/(min⋅s)	= 5.08×10⁻³ m/s²
foot per second squared	fps²	≡ 1 ft/s²	= 3.048×10⁻¹ m/s²
gal; galileo	Gal	≡ 1 cm/s²	= 10⁻² m/s²
inch per minute per second	ipm/s	≡ 1 in/(min⋅s)	= 4.23×10⁻⁴ m/s²
inch per second squared	ips²	≡ 1 in/s²	= 2.54×10⁻² m/s²
knot per second	kn/s	≡ 1 kn/s	≈ 5.14×10⁻¹ m/s²
metre per second squared (SI unit)	m/s²	≡ 1 m/s²	= 1 m/s²
mile per hour per second	mph/s	≡ 1 mi/(h⋅s)	= 4.4704×10⁻¹ m/s²
mile per minute per second	mpm/s	≡ 1 mi/(min⋅s)	= 26.8224 m/s²
mile per second squared	mps²	≡ 1 mi/s²	= 1.609344×10³ m/s²
standard gravity	$g 0$	≡ 9.80665 m/s²	= 9.80665 m/s²

ForceEdit

Force
Name of unit	Symbol	Definition	Relation to SI units
atomic unit of force		≡ m_e⋅α²⋅c²⁄a₀	≈ 8.23872206×10⁻⁸ N^[34]
dyne (CGS unit)	dyn	≡ g⋅cm/s²	= 10⁻⁵ N
kilogram-force; kilopond; grave-force	kgf; kp; gvf	≡ $g 0$ × 1 kg	= 9.80665 N
kip; kip-force	kip; kipf; klbf	≡ $g 0$ × 1000 lb	= 4.4482216152605×10³ N
milligrave-force, gravet-force	mgvf; gvtf	≡ $g 0$ × 1 g	= 9.80665 mN
long ton-force	tnf^{[citation needed]}	≡ $g 0$ × 1 long ton	= 9.96401641818352×10³ N
newton (SI unit)	N	A force capable of giving a mass of one kilogram an acceleration of one metre per second per second.^[35]	= 1 N = 1 kg⋅m/s²
ounce-force	ozf	≡ $g 0$ × 1 oz	= 0.27801385095378125 N
pound-force	lbf	≡ $g 0$ × 1 lb	= 4.4482216152605 N
poundal	pdl	≡ 1 lb⋅ft/s²	= 0.138254954376 N
short ton-force	tnf^{[citation needed]}	≡ $g 0$ × 1 short ton	= 8.896443230521×10³ N
sthene (mts unit)	sn	≡ 1 t⋅m/s²	= 10³ N

Pressure or mechanical stressEdit

Pressure
Name of unit	Symbol	Definition	Relation to SI units
atmosphere (standard)	atm		≡ 101325 Pa^[36]
atmosphere (technical)	at	≡ 1 kgf/cm²	= 9.80665×10⁴ Pa^[36]
bar	bar	≡ 100000 Pa	≡ 10⁵ Pa
barye (CGS unit)		≡ 1 dyn/cm²	= 0.1 Pa
centimetre of mercury	cmHg	≡ 13595.1 kg/m³ × 1 cm × $g 0$	≈ 1.33322×10³ Pa^[36]
centimetre of water (4 °C)	cmH₂O	≈ 999.972 kg/m³ × 1 cm × $g 0$	≈ 98.0638 Pa^[36]
foot of mercury (conventional)	ftHg	≡ 13595.1 kg/m³ × 1 ft × $g 0$	≈ 4.063666×10⁴ Pa^[36]
foot of water (39.2 °F)	ftH₂O	≈ 999.972 kg/m³ × 1 ft × $g 0$	≈ 2.98898×10³ Pa^[36]
inch of mercury (conventional)	inHg	≡ 13595.1 kg/m³ × 1 in × $g 0$	≈ 3.386389×10³ Pa^[36]
inch of water (39.2 °F)	inH₂O	≈ 999.972 kg/m³ × 1 in × $g 0$	≈ 249.082 Pa^[36]
kilogram-force per square millimetre	kgf/mm²	≡ 1 kgf/mm²	= 9.80665×10⁶ Pa^[36]
kip per square inch	ksi	≡ 1 kipf/sq in	≈ 6.894757×10⁶ Pa^[36]
long ton per square foot		≡ 1 long ton × $g 0$ / 1 sq ft	≈ 1.0725178011595×10⁵ Pa
micrometre of mercury	μmHg	≡ 13595.1 kg/m³ × 1 μm × $g 0$ ≈ 0.001 torr	≈ 0.1333224 Pa^[36]
millimetre of mercury	mmHg	≡ 13595.1 kg/m³ × 1 mm × $g 0$ ≈ 1 torr	≈ 133.3224 Pa^[36]
millimetre of water (3.98 °C)	mmH₂O	≈ 999.972 kg/m³ × 1 mm × $g 0$ = 0.999972 kgf/m²	= 9.80638 Pa
pascal (SI unit)	Pa	≡ N/m² = kg/(m⋅s²)	= 1 Pa^[37]
pièze (mts unit)	pz	≡ 1000 kg/m⋅s²	= 10³ Pa = 1 kPa
pound per square foot	psf	≡ 1 lbf/ft²	≈ 47.88026 Pa^[36]
pound per square inch	psi	≡ 1 lbf/in²	≈ 6.894757×10³ Pa^[36]
poundal per square foot	pdl/sq ft	≡ 1 pdl/sq ft	≈ 1.488164 Pa^[36]
short ton per square foot		≡ 1 short ton × $g 0$ / 1 sq ft	≈ 9.5760518×10⁴ Pa
torr	torr	≡ 101325⁄760 Pa	≈ 133.3224 Pa^[36]

Torque or moment of forceEdit

Torque
Name of unit	Symbol	Definition	Relation to SI units
pound-force-foot	lbf⋅ft	≡ $g 0$ × 1 lb × 1 ft	= 1.3558179483314004 N⋅m
poundal-ft	pdl⋅ft	≡ 1 lb⋅ft²/s²	= 4.21401100938048×10⁻² N⋅m
pound force-inch	lbf⋅in	≡ $g 0$ × 1 lb × 1 in	= 0.1129848290276167 N⋅m
kilogram force-meter	kgf⋅m	≡ $g 0$ × N × m	= 9.80665 N⋅m
Newton metre (SI unit)	N⋅m	≡ N × m = kg⋅m²/s²	= 1 N⋅m

EnergyEdit

Energy
Name of unit	Symbol	Definition	Relation to SI units
barrel of oil equivalent	boe	≈ 5.8×10⁶ BTU_59 °F	≈ 6.12×10⁹ J
British thermal unit (ISO)	BTU_ISO	≡ 1.0545×10³ J	= 1.0545×10³ J
British thermal unit (International Table)	BTU_IT		= 1.05505585262×10³ J
British thermal unit (mean)	BTU_mean		≈ 1.05587×10³ J
British thermal unit (thermochemical)	BTU_th		≈ 1.054350×10³ J
British thermal unit (39 °F)	BTU_39 °F		≈ 1.05967×10³ J
British thermal unit (59 °F)	BTU_59 °F	≡ 1.054804×10³ J	= 1.054804×10³ J
British thermal unit (60 °F)	BTU_60 °F		≈ 1.05468×10³ J
British thermal unit (63 °F)	BTU_63 °F		≈ 1.0546×10³ J
calorie (International Table)	cal_IT	≡ 4.1868 J	= 4.1868 J
calorie (mean)	cal_mean	1⁄100 of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm	≈ 4.19002 J
calorie (thermochemical)	cal_th	≡ 4.184 J	= 4.184 J
Calorie (US; FDA)	Cal	≡ 1 kcal = 1000 cal	= 4184 J
calorie (3.98 °C)	cal_3.98 °C		≈ 4.2045 J
calorie (15 °C)	cal_15 °C	≡ 4.1855 J	= 4.1855 J
calorie (20 °C)	cal_20 °C		≈ 4.1819 J
Celsius heat unit (International Table)	CHU_IT	≡ 1 BTU_IT × 1 K/°R	= 1.899100534716×10³ J
cubic centimetre of atmosphere; standard cubic centimetre	cc atm; scc	≡ 1 atm × 1 cm³	= 0.101325 J
cubic foot of atmosphere; standard cubic foot	cu ft atm; scf	≡ 1 atm × 1 ft³	= 2.8692044809344×10³ J
cubic foot of natural gas		≡ 1000 BTU_IT	= 1.05505585262×10⁶ J
cubic yard of atmosphere; standard cubic yard	cu yd atm; scy	≡ 1 atm × 1 yd³	= 77.4685209852288×10³ J
electronvolt	eV	≡ e × 1 V	≡ 1.602176634×10⁻¹⁹ J
erg (CGS unit)	erg	≡ 1 g⋅cm²/s²	= 10⁻⁷ J
foot-pound force	ft lbf	≡ $g 0$ × 1 lb × 1 ft	= 1.3558179483314004 J
foot-poundal	ft pdl	≡ 1 lb⋅ft²/s²	= 4.21401100938048×10⁻² J
gallon-atmosphere (imperial)	imp gal atm	≡ 1 atm × 1 gal (imp)	= 460.63256925 J
gallon-atmosphere (US)	US gal atm	≡ 1 atm × 1 gal (US)	= 383.5568490138 J
hartree, atomic unit of energy	E_h	≡ m_e⋅α²⋅c² (= 2 Ry)	≈ 4.359744×10⁻¹⁸ J
horsepower-hour	hp⋅h	≡ 1 hp × 1 h	= 2.684519537696172792×10⁶ J
inch-pound force	in lbf	≡ $g 0$ × 1 lb × 1 in	= 0.1129848290276167 J
joule (SI unit)	J	The work done when a force of one newton moves the point of its application a distance of one metre in the direction of the force.^[35]	= 1 J = 1 m⋅N = 1 kg⋅m²/s² = 1 C⋅V = 1 W⋅s
kilocalorie; large calorie	kcal; Cal	≡ 1000 cal_IT	= 4.1868×10³ J
kilowatt-hour; Board of Trade Unit	kW⋅h; B.O.T.U.	≡ 1 kW × 1 h	= 3.6×10⁶ J
litre-atmosphere	l atm; sl	≡ 1 atm × 1 L	= 101.325 J
quad		≡ 10¹⁵ BTU_IT	= 1.05505585262×10¹⁸ J
rydberg	Ry	≡ R_∞⋅ℎ⋅c	≈ 2.179872×10⁻¹⁸ J
therm (E.C.)		≡ 100000 BTU_IT	= 105.505585262×10⁶ J
therm (US)		≡ 100000 BTU_59 °F	= 105.4804×10⁶ J
thermie	th	≡ 1 Mcal_IT	= 4.1868×10⁶ J
tonne of coal equivalent	TCE	≡ 7 Gcal_th	= 29.288×10⁹ J
tonne of oil equivalent	toe	≡ 10 Gcal_IT	= 41.868×10⁹ J
ton of TNT	tTNT	≡ 1 Gcal_th	= 4.184×10⁹ J
watt hour	W⋅h	≡ 1 W × 1 h	= 3.6×10³ J
watt second	W⋅s	≡ 1 J	= 1×10⁰ J

Power or heat flow rateEdit

Power
Name of unit	Symbol	Definition	Relation to SI units
atmosphere-cubic centimetre per minute	atm ccm^{[citation needed]}	≡ 1 atm × 1 cm³/min	= 1.68875×10⁻³ W
atmosphere-cubic centimetre per second	atm ccs^{[citation needed]}	≡ 1 atm × 1 cm³/s	= 0.101325 W
atmosphere-cubic foot per hour	atm cfh^{[citation needed]}	≡ 1 atm × 1 cu ft/h	= 0.79700124704 W
atmosphere-cubic foot per minute	atm cfm^{[citation needed]}	≡ 1 atm × 1 cu ft/min	= 47.82007468224 W
atmosphere-cubic foot per second	atm cfs^{[citation needed]}	≡ 1 atm × 1 cu ft/s	= 2.8692044809344×10³ W
BTU (International Table) per hour	BTU_IT/h	≡ 1 BTU_IT/h	≈ 0.293071 W
BTU (International Table) per minute	BTU_IT/min	≡ 1 BTU_IT/min	≈ 17.584264 W
BTU (International Table) per second	BTU_IT/s	≡ 1 BTU_IT/s	= 1.05505585262×10³ W
calorie (International Table) per second	cal_IT/s	≡ 1 cal_IT/s	= 4.1868 W
erg per second	erg/s	≡ 1 erg/s	= 10⁻⁷ W
foot-pound-force per hour	ft⋅lbf/h	≡ 1 ft lbf/h	≈ 3.766161×10⁻⁴ W
foot-pound-force per minute	ft⋅lbf/min	≡ 1 ft lbf/min	= 2.259696580552334×10⁻² W
foot-pound-force per second	ft⋅lbf/s	≡ 1 ft lbf/s	= 1.3558179483314004 W
horsepower (boiler)	hp	≈ 34.5 lb/h × 970.3 BTU_IT/lb	≈ 9809.5 W^[38]
horsepower (European electrical)	hp	≡ 75 kp⋅m/s	= 736 W^{[citation needed]}
horsepower (electrical)	hp	≡ 746 W	= 746 W^[38]
horsepower (mechanical)	hp	≡ 550 ft⋅lbf/s^[38]	= 745.69987158227022 W
horsepower (metric)	hp or PS	≡ 75 m⋅kgf/s	= 735.49875 W^[38]
litre-atmosphere per minute	L·atm/min	≡ 1 atm × 1 L/min	= 1.68875 W
litre-atmosphere per second	L·atm/s	≡ 1 atm × 1 L/s	= 101.325 W
lusec	lusec	≡ 1 L·µmHg/s ^[20]	≈ 1.333×10⁻⁴ W
poncelet	p	≡ 100 m⋅kgf/s	= 980.665 W
square foot equivalent direct radiation	sq ft EDR	≡ 240 BTU_IT/h	≈ 70.337057 W
ton of air conditioning		≡ 2000 lb of ice melted / 24 h	≈ 3504 W
ton of refrigeration (imperial)		≡ 2240 lb × ice_IT / 24 h: ice_IT = 144 °F × 2326 J/kg⋅°F	≈ 3.938875×10³ W
ton of refrigeration (IT)		≡ 2000 lb × ice_IT / 24 h: ice_IT = 144 °F × 2326 J/kg⋅°F	≈ 3.516853×10³ W
watt (SI unit)	W	The power which in one second of time gives rise to one joule of energy.^[35]	= 1 W = 1 J/s = 1 N⋅m/s = 1 kg⋅m²/s³

ActionEdit

Action
Name of unit	Symbol	Definition	Relation to SI units
atomic unit of action	au	≡ ℏ ≡ ℎ⁄2π	≈ 1.05457168×10⁻³⁴ J⋅s^[39]

Dynamic viscosityEdit

Dynamic viscosity
Name of unit	Symbol	Definition	Relation to SI units
pascal second (SI unit)	Pa⋅s	≡ N⋅s/m², kg/(m⋅s)	= 1 Pa⋅s
poise (CGS unit)	P	≡ 1 barye⋅s	= 0.1 Pa⋅s
pound per foot hour	lb/(ft⋅h)	≡ 1 lb/(ft⋅h)	≈ 4.133789×10⁻⁴ Pa⋅s
pound per foot second	lb/(ft⋅s)	≡ 1 lb/(ft⋅s)	≈ 1.488164 Pa⋅s
pound-force second per square foot	lbf⋅s/ft²	≡ 1 lbf⋅s/ft²	≈ 47.88026 Pa⋅s
pound-force second per square inch	lbf⋅s/in²	≡ 1 lbf⋅s/in²	≈ 6894.757 Pa⋅s

Kinematic viscosityEdit

Kinematic viscosity
Name of unit	Symbol	Definition	Relation to SI units
square foot per second	ft²/s	≡ 1 ft²/s	= 0.09290304 m²/s
square metre per second (SI unit)	m²/s	≡ 1 m²/s	= 1 m²/s
stokes (CGS unit)	St	≡ 1 cm²/s	= 10⁻⁴ m²/s

Electric currentEdit

Electric current
Name of unit	Symbol	Definition	Relation to SI units
ampere (SI base unit)	A	≡ one coulomb of charge going past a given point per second.^[40]	(SI base unit)
electromagnetic unit; abampere (CGS unit)	abamp	≘ 10 A	= 10 A
esu per second; statampere (CGS unit)	esu/s	≘ (10 A⋅cm/s) / c	≈ 3.335641×10⁻¹⁰ A

Electric chargeEdit

Electric charge
Name of unit	Symbol	Definition	Relation to SI units
abcoulomb; electromagnetic unit (CGS unit)	abC; emu	≘ 10 C	= 10 C
atomic unit of charge	au	≡ e	= 1.602176634×10⁻¹⁹ C
coulomb	C	≡ charge of exactly 1/(1.602176634×10⁻¹⁹) elementary charges^[40]	= 1 C = 1 A⋅s
faraday	F	≡ 1 mol × N_A⋅e	≈ 96485.3383 C
milliampere hour	mA⋅h	≡ 0.001 A × 1 h	= 3.6 C
statcoulomb; franklin; electrostatic unit (CGS unit)	statC; Fr; esu	≘ (10 A⋅cm) / c	≈ 3.335641×10⁻¹⁰ C

Electric dipoleEdit

Electric dipole
Name of unit	Symbol	Definition	Relation to SI units
atomic unit of electric dipole moment	ea₀		≈ 8.47835281×10⁻³⁰ C⋅m^[41]
coulomb-meter	C⋅m		= 1 C⋅m
debye	D	≡ 10⁻¹⁰ esu⋅Å	≘ 3.33564095×10⁻³⁰ C⋅m^[42]

Electromotive force, electric potential differenceEdit

Voltage, electromotive force
Name of unit	Symbol	Definition	Relation to SI units
abvolt (CGS unit)	abV	≘ 10⁻⁸ V	= 10⁻⁸ V
statvolt (CGS unit)	statV	≘ c⋅(1 μJ/A⋅m)	= 299.792458 V
volt (SI unit)	V	The difference in electric potential across two points along a conducting wire carrying one ampere of constant current when the power dissipated between the points equals one watt.^[35]	= 1 V = 1 W/A = 1 kg⋅m²/(A⋅s³) = 1 J/C

Electrical resistanceEdit

Electrical resistance
Name of unit	Symbol	Definition	Relation to SI units
ohm (SI unit)	Ω	The resistance between two points in a conductor when one volt of electric potential difference, applied to these points, produces one ampere of current in the conductor.^[35]	= 1 Ω = 1 V/A = 1 kg⋅m²/(A²⋅s³)

CapacitanceEdit

Capacitor's ability to store charge
Name of unit	Symbol	Definition	Relation to SI units
farad (SI unit)	F	The capacitance between two parallel plates that results in one volt of potential difference when charged by one coulomb of electricity.^[35]	= 1 F = 1 C/V = 1 A²⋅s⁴/(kg⋅m²)

Magnetic fluxEdit

Magnetic flux
Name of unit	Symbol	Definition	Relation to SI units
maxwell (CGS unit)	Mx	≘ 10⁻⁸ Wb^[38]	= 10⁻⁸ Wb
weber (SI unit)	Wb	Magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.^[35]	= 1 Wb = 1 V⋅s = 1 kg⋅m²/(A⋅s²)

Magnetic flux densityEdit

What physicists call magnetic field is called magnetic flux density by electrical engineers and magnetic induction by applied mathematicians and electrical engineers.
Name of unit	Symbol	Definition	Relation to SI units
gauss (CGS unit)	G	≡ Mx/cm² ≘ 10⁻⁴ T	= 10⁻⁴ T ^[43]
tesla (SI unit)	T	≡ Wb/m²	= 1 T = 1 Wb/m² = 1 kg/(A⋅s²)

InductanceEdit

Inductance
Name of unit	Symbol	Definition	Relation to SI units
henry (SI unit)	H	The inductance of a closed circuit that produces one volt of electromotive force when the current in the circuit varies at a uniform rate of one ampere per second.^[35]	= 1 H = 1 Wb/A = 1 kg⋅m²/(A⋅s)²

TemperatureEdit

Temperature
Name of unit	Symbol	Definition	Relation to SI units
degree Celsius	°C	[°C] ≡ [K] − 273.15	[K] ≡ [°C] + 273.15
degree Delisle	°De		[K] = 373.15 − [°De] × 2⁄3
degree Fahrenheit	°F	[°F] ≡ [°C] × 9⁄5 + 32	[K] ≡ ([°F] + 459.67) × 5⁄9
degree Newton	°N		[K] = [°N] × 100⁄33 + 273.15
degree Rankine	°R;	[°R] ≡ [K] × 9⁄5	[K] ≡ [°R] × 5/9
degree Réaumur	°Ré		[K] = [°Ré] × 5⁄4 + 273.15
degree Rømer	°Rø		[K] = ([°Rø] − 7.5) × 40⁄21 + 273.15
Regulo Gas Mark	GM	[°F] ≡ [GM] × 25 + 300	[K] ≡ [GM] × 125⁄9 + 422.038
kelvin (SI base unit)	K	≡ change in the thermodynamic temperature $T$ that results in a change of thermal energy $kT$ by 1.380 649 × 10⁻²³ J.^[44]	(SI base unit)

Information entropyEdit

Information entropy
Name of unit	Symbol	Definition	Relation to SI units	Relation to bits
natural unit of information; nit; nepit	nat
shannon	Sh	≡ ln(2) × nat	≈ 0.693147 nat	= 1 bit
hartley; ban	Hart; ban	≡ ln(10) × nat	≈ 2.302585 nat
bit	bit; b			= 1 bit
nibble		≡ 4 bits		= 2² bit
byte	B	≡ 8 bits		= 2³ bit
kilobyte (decimal)	kB	≡ 1000 B		= 8000 bit
kibibyte (kilobyte)	KiB; KB	≡ 1024 B		= 2¹³ bit = 8192 bit

Modern standards (such as ISO 80000) prefer the shannon to the bit as a unit for a quantity of information entropy, whereas the (discrete) storage space of digital devices is measured in bits. Thus, uncompressed redundant data occupy more than one bit of storage per shannon of information entropy. The multiples of a bit listed above are usually used with this meaning.

Luminous intensityEdit

The candela is the preferred nomenclature for the SI unit.

Luminous intensity
Name of unit	Symbol	Definition	Relation to SI units
candela (SI base unit)	cd	The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.^[40]	(SI base unit)
candlepower (new)	cp	≡ cd The use of candlepower as a unit is discouraged due to its ambiguity.	= 1 cd
candlepower (old, pre-1948)	cp	Varies and is poorly reproducible.^[45] Approximately 0.981 cd.^[20]	≈ 0.981 cd

LuminanceEdit

Luminance
Name of unit	Symbol	Definition	Relation to SI units
candela per square foot	cd/ft²	≡ cd/ft²	≈ 10.763910417 cd/m²
candela per square inch	cd/in²	≡ cd/in²	≈ 1550.0031 cd/m²
candela per square metre (SI unit); nit (deprecated^[20])	cd/m²	≡ cd/m²	= 1 cd/m²
footlambert	fL	≡ (1/π) cd/ft²	≈ 3.4262590996 cd/m²
lambert	L	≡ (10⁴/π) cd/m²	≈ 3183.0988618 cd/m²
stilb (CGS unit)	sb	≡ 10⁴ cd/m²	= 10⁴ cd/m²

Luminous fluxEdit

Luminous flux
Name of unit	Symbol	Definition	Relation to SI units
lumen (SI unit)	lm	The luminous flux of a source that emits monochromatic radiation of frequency 540×10¹² hertz and that has a radiant flux of 1/683 watt.^[40]	= 1 lm = 1 cd⋅sr

IlluminanceEdit

Illuminance
Name of unit	Symbol	Definition	Relation to SI units
footcandle; lumen per square foot	fc	≡ lm/ft²	= 10.763910417 lx
lumen per square inch	lm/in²	≡ lm/in²	≈ 1550.0031 lx
lux (SI unit)	lx	≡ lm/m²	= 1 lx = 1 lm/m²
phot (CGS unit)	ph	≡ lm/cm²	= 10⁴ lx

Radiation – source activityEdit

Radioactivity
Name of unit	Symbol	Definition	Relation to SI units
becquerel (SI unit)	Bq	≡ Number of disintegrations per second	= 1 Bq = 1/s
curie	Ci	≡ 3.7×10¹⁰ Bq^[46]	= 3.7×10¹⁰ Bq
rutherford (H)	Rd	≡ 1 MBq	= 10⁶ Bq

Although becquerel (Bq) and hertz (Hz) both ultimately refer to the same SI base unit (s⁻¹), Hz is used only for periodic phenomena (i.e. repetitions at regular intervals), and Bq is only used for stochastic processes (i.e. at random intervals) associated with radioactivity.^[47]

Radiation – exposureEdit

Radiation – exposure
Name of unit	Symbol	Definition	Relation to SI units
roentgen	R	1 R ≡ 2.58×10⁻⁴ C/kg^[38]	= 2.58×10⁻⁴ C/kg

The roentgen is not an SI unit and the NIST strongly discourages its continued use.^[48]

Radiation – absorbed doseEdit

Radiation – absorbed dose
Name of unit	Symbol	Definition	Relation to SI units
gray (SI unit)	Gy	≡ 1 J/kg^[49]	= 1 Gy = 1 J/kg = 1 m²⋅s²
rad	rad	≡ 0.01 Gy^[38]	= 0.01 Gy

Radiation – equivalent doseEdit

Radiation – equivalent dose
Name of unit	Symbol	Definition	Relation to SI units
Röntgen equivalent man	rem	≡ 0.01 Sv	= 0.01 Sv
sievert (SI unit)	Sv	≡ 1 J/kg^[47]	= 1 Sv = 1 J/kg = 1 m²⋅s²

Although the definitions for sievert (Sv) and gray (Gy) would seem to indicate that they measure the same quantities, this is not the case. The effect of receiving a certain dose of radiation (given as Gy) is variable and depends on many factors, thus a new unit was needed to denote the biological effectiveness of that dose on the body; this is known as the equivalent dose and is shown in Sv. The general relationship between absorbed dose and equivalent dose can be represented as

H = Q ⋅ D

where H is the equivalent dose, D is the absorbed dose, and Q is a dimensionless quality factor. Thus, for any quantity of D measured in Gy, the numerical value for H measured in Sv may be different.^[50]

This article uses material from the Wikipedia article
Metasyntactic variable, which is released under the
Creative Commons
Attribution-ShareAlike 3.0 Unported License.

[26] see Callippic cycle for explanation of the differences

[avegreg-27] This is based on the average Gregorian year. See above for definition of year lengths.

[leapsec-28] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o Where UTC is observed, the length of this unit may increase or decrease
depending on the number of leap seconds which occur during the time interval in question.

[29] The length of ancient lustral cycles was not constant; see Lustrum for more details

[sound-39] The speed of sound varies especially with temperature and pressure from about 340 m/s (1,225 km/h or 761 mph or 661 kn)
in air at sea level to about 300 m/s (1,062 km/h or 660 mph or 573 kn) at jet altitudes (12200 m or 40000 ft).^[33]