Measurement (LINEAR) – CONVERSION

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Techniques

Process overview

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. Nominal values are sometimes allowed and used.

Conversion factors

A conversion factor is used to change the units of a measured quantity without changing its value. The unity bracket method of unit conversion 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. 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 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 tools

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 Units

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, 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-factor

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 numbers

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 factors

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)
`Template:Overline`	indicates that `digits` repeat infinitely (e.g. Template:Gaps corresponds to Template:Gaps)
(H)	of chiefly historical interest

Length

Length
Name of unit	Symbol	Definition	Relation to SI units
ångström	Å	≡ Template:Val	≡ 0.1 nm
astronomical unit	au	≡ Template:Val ≈ Distance from Earth to Sun	≡ Template:Val ^[1]
attometre	am	≡ Template:Val	≡ Template:Val
barleycorn (H)		= Template:Frac in (see note above about rounding)	= 8.4Template:Overline Template:E m
bohr, atomic unit of length	a₀	= Bohr radius of hydrogen	≈ Template:Val^[2]
cable length (imperial)		≡ 608 ft	≈ 185.3184 m
cable length (International)		≡ Template:Frac nmi	≡ 185.2 m
cable length (US)		≡ 720 ft	= 219.456 m
chain (Gunter's; Surveyor's)	ch	≡ 66 ft (US) ≡ 4 rods^[3]	≈ Template:Val
cubit (H)		≡ Distance from fingers to elbow ≈ 18 in	≈ 0.5 m
ell (H)	ell	≡ 45 in ^[4] (In England usually)	= 1.143 m
fathom	ftm	≡ 6 ft ^[4]	= 1.8288 m
femtometre	fm	≡ Template:Val	≡ Template:Val
fermi	fm	≡ Template:Val^[4]	≡ Template:Val
finger		≡ Template:Frac in	= Template:Val
finger (cloth)		≡ Template:Frac in	= 0.1143 m
foot (Benoît) (H)	ft (Ben)		≈ Template:Val
foot (Cape) (H)		Legally defined as 1.033 English feet in 1859	≈ Template:Val
foot (Clarke's) (H)	ft (Cla)		≈ Template:Val
foot (Indian) (H)	ft Ind		≈ Template:Val
foot, metric	mf	≡ 300 mm	≡ 0.3 m
foot, metric (Mesures usuelles) (H)		≡ Template:Frac m	≡ 0.Template:Overline m
foot (International)	ft	≡ 0.3048 m ≡ Template:Frac yd ≡ 12 inches	≡ 0.3048 m
foot (Sear's) (H)	ft (Sear)		≈ Template:Val
foot (US Survey)	ft (US)	≡ Template:Frac m ^[5]	≈ Template:Val
french; charriere	F	≡ Template:Frac mm	= 0.Template:Overline Template:E m
furlong	fur	≡ 10 chains = 660 ft = 220 yd ^[4]	= 201.168 m
hand		≡ 4 in ^[4]	≡ 0.1016 m
inch (International)	in	≡ 2.54 cm ≡ Template:Frac yd ≡ Template:Frac ft	≡ 0.0254 m
league (land)	lea	≈ 1 hour walk, Currently defined in US as 3 Statute miles,^[3] but historically varied from 2 to 9 km	≈ Template:Val
light-day		≡ 24 light-hours	≡ Template:Val
light-hour		≡ 60 light-minutes	≡ Template:Val
light-minute		≡ 60 light-seconds	≡ Template:Val
light-second		≡ Distance light travels in one second in vacuum	≡ Template:Val
light-year	ly	≡ Distance light travels in vacuum in 365.25 days ^[6]	≡ Template:Val
line	ln	≡ Template:Frac in ^[7]	= Template:Gaps m
link (Gunter's; Surveyor's)	lnk	≡ Template:Frac ch ^[4] ≡ 0.66 ft (US) ≡ 7.92 in	≈ Template:Val
link (Ramsden's; Engineer's)	lnk	≡ 1 ft ^[4]	= 0.3048 m
metre (SI base unit) (meter)	m	≡ Distance light travels in Template:Frac of a second in vacuum.^[8]	(SI base unit)
mickey		≡ Template:Frac in	= Template:Val
micrometre (old: micron)	μ; μm	≡ Template:Val	≡ Template:Val
mil; thou	mil	≡ Template:Val	= Template:Val
mil (Sweden and Norway)	mil	≡ 10 km	= Template:Val
mile (geographical) (H)		≡ Template:Val	= Template:Val
mile (international)	mi	≡ 80 chains ≡ Template:Val ≡ Template:Val	≡ Template:Val
mile (tactical or data)		≡ Template:Val	≡ Template:Val
mile (telegraph) (H)	mi	≡ Template:Val	= Template:Val
mile (US Survey)	mi	≡ Template:Val US Survey feet ≡ (Template:Val × Template:Frac) m	≈ Template:Val
nail (cloth)		≡ Template:Frac in ^[4]	= Template:Val
nanometre	nm	≡ Template:Val	≡ Template:Val
nautical league	NL; nl	≡ 3 nmi ^[4]	= Template:Val
nautical mile (Admiralty)	NM (Adm); nmi (Adm)	= Template:Val	= Template:Val
nautical mile (international)	NM; nmi	≡ Template:Val^[9]	≡ Template:Val
nautical mile (US pre 1954)		≡ 1853.248 m	≡ 1853.248 m
pace		≡ 2.5 ft ^[4]	= 0.762 m
palm		≡ 3 in ^[4]	= 0.0762 m
parsec	pc	Distant point with a parallax shift of one arc second from a base of one astronomical unit. ≡ Template:Sfrac au^[10]^[11]	≈ Template:Val^[12]
pica		≡ 12 points	Dependent on point measures.
picometre	pm	≡ Template:Val	≡ Template:Val
point (American, English)^[13]^[14]	pt	≡ Template:Frac in	≈ Template:Val
point (Didot; European) ^[14]^[15]	pt	≡ Template:Frac × Template:Frac of pied du roi; After 1878: ≡ Template:Frac cm	≈ Template:Val; After 1878: ≈ Template:Val
point (PostScript) ^[13]	pt	≡ Template:Frac in	= Template:Gaps m
point (TeX) ^[13]	pt	≡ Template:Frac in	= 0.00Template:Overline m
quarter		≡ Template:Frac yd	= 0.2286 m
rod; pole; perch (H)	rd	≡ Template:Frac ft	= 5.0292 m
rope (H)	rope	≡ 20 ft ^[4]	= 6.096 m
shaku (Japan)		≡ 10/33 m	≈ 0.303 0303 m
span (H)		≡ 9 in ^[4]	= 0.2286 m
spat^[16]			≡ Template:Val
stick (H)		≡ 2 in	= 0.0508 m
toise (French, post 1667) (H)	T	≡ 27000/13853 m	≈ 1.949 0363 m
twip	twp	≡ Template:Frac in	= 1.763Template:Overline Template:E m
x unit; siegbahn	xu		≈ Template:Val m ^[4]
yard (International)	yd	≡ 0.9144 m ^[5] ≡ 3 ft ≡ 36 in	≡ 0.9144 m
yoctometre	ym	≡ Template:Val	≡ Template:Val
zeptometre	zm	≡ Template:Val	≡ Template:Val

Area

Area
Name of unit	Symbol	Definition	Relation to SI units
acre (international)	ac	≡ Template:Nowrap = Template:Val	≡ Template:Val
acre (US survey)	ac	≡ 10 sq ch = Template:Val, also Template:Val	≈ Template:Val^[17]
are	a	≡ 100 m²	≡ 100 m²
barn	b	≡ 10⁻²⁸ m²	≡ 10⁻²⁸ m²
barony		≡ Template:Val ac	≡ Template:Val
board	bd	≡ Template:Nowrap	≡ Template:Val
boiler horsepower equivalent direct radiation	bhp EDR	≡ 1 ft² × 1 bhp / (240 BTU_IT/h)	≈ Template:Val
circular inch	circ in	≡ Template:Frac sq in	≈ Template:Val
circular mil; circular thou	circ mil	≡ Template:Frac mil²	≈ Template:Val
cord		≡ 192 bd	≡ Template:Val
cuerda (PR Survey)	cda	≡ 1 cda x 1 cda = Template:Val acre	≡ Template:Val
dunam		≡ Template:Val	≡ Template:Val
guntha (India)		≡ 121 sq yd	≈ 101.17 m²
hectare	ha	≡ Template:Val	≡ Template:Val
hide		≈ 120 ac (variable)	≈ Template:Val
rood	ro	≡ Template:Frac ac	= Template:Val
ping		≡ Template:Frac m × Template:Frac m	≈ Template:Val
section		≡ Template:Nowrap	= Template:Val
shed		≡ 10⁻⁵² m²	= 10⁻⁵² m²
square (roofing)		≡ Template:Nowrap	= Template:Val
square chain (international)	sq ch	≡ Template:Nowrap = Template:Frac ac	≡ Template:Val
square chain (US Survey)	sq ch	≡ Template:Nowrap = Template:Frac US survey acre	≈ Template:Val
square foot	sq ft	≡ Template:Nowrap	≡ Template:Val
square foot (US Survey)	sq ft	≡ Template:Nowrap	≈ Template:Val
square inch	sq in	≡ Template:Nowrap	≡ Template:Val
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	= Template:Val
square link (Gunter's)(US Survey)	sq lnk	≡ Template:Nowrap ≡ Template:Nowrap	≈ Template:Val
square link (Ramsden's)	sq lnk	≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft	= Template:Val
square metre (SI unit)	m²	≡ 1 m × 1 m	= 1 m²
square mil; square thou	sq mil	≡ 1 mil × 1 mil	= Template:Val
square mile	sq mi	≡ 1 mi × 1 mi	≡ Template:Val
square mile (US Survey)	sq mi	≡ 1 mi (US) × 1 mi (US)	≈ Template:Val
square rod/pole/perch	sq rd	≡ 1 rd × 1 rd	= Template:Val
square yard (International)	sq yd	≡ 1 yd × 1 yd	≡ Template:Val
stremma		≡ Template:Val	= Template:Val
township		≡ 36 sq mi (US)	≈ Template:Val
yardland		≈ 30 ac	≈ Template:Val

Volume

Volume
Name of unit	Symbol	Definition	Relation to SI units
acre-foot	ac ft	≡ 1 ac x 1 ft = Template:Val	= Template:Val
acre-inch		≡ 1 ac × 1 in	= Template:Val
barrel (imperial)	bl (imp)	≡ 36 gal (imp)	= Template:Val
barrel (petroleum); archaic blue-barrel	bl; bbl	≡ 42 gal (US)	= Template:Val
barrel (US dry)	bl (US)	≡ 105 qt (US) = 105/32 bu (US lvl)	= Template:Val
barrel (US fluid)	fl bl (US)	≡ Template:Frac gal (US)	= Template:Val
board-foot	bdft	≡ 144 cu in	≡ Template:Val
bucket (imperial)	bkt	≡ 4 gal (imp)	= Template:Val
bushel (imperial)	bu (imp)	≡ 8 gal (imp)	= Template:Val
bushel (US dry heaped)	bu (US)	≡ Template:Frac bu (US lvl)	= Template:Val
bushel (US dry level)	bu (US lvl)	≡ Template:Val	= Template:Val
butt, pipe		≡ 126 gal (US) (wine)	= Template:Val
coomb		≡ 4 bu (imp)	= Template:Val
cord (firewood)		≡ Template:Nowrap	= Template:Val
cord-foot		≡ 16 cu ft	= Template:Val
cubic fathom	cu fm	≡ 1 fm × 1 fm × 1 fm	= Template:Val
cubic foot	ft³	≡ 1 ft × 1 ft × 1 ft	≡ Template:Val
cubic inch	in³	≡ 1 in × 1 in × 1 in	≡ Template:Val
cubic metre (SI unit)	m³	≡ 1 m × 1 m × 1 m	≡ 1 m³
cubic mile	cu mi	≡ 1 mi × 1 mi × 1 mi	≡ Template:Val
cubic yard	yd³	≡ 27 cu ft	≡ Template:Val
cup (breakfast)		≡ 10 fl oz (imp)	= Template:Val
cup (Canadian)	c (CA)	≡ 8 fl oz (imp)	= Template:Val
cup (metric)	c	≡ Template:Val	≡ Template:Val
cup (US customary)	c (US)	≡ 8 US fl oz ≡ Template:Frac gal (US)	= Template:Val
cup (US food nutrition labeling)	c (US)	≡ 240 mL^[18]	= Template:Val
dash (imperial)		≡ Template:Frac gi (imp) = Template:Frac pinch (imp)	= Template:Gaps Template:E m³
dash (US)		≡ Template:Frac US fl oz = Template:Frac US pinch	= Template:Val
dessertspoon (imperial)		≡ Template:Frac gi (imp)	= Template:Gaps Template:E m³
drop (imperial)	gtt	≡ Template:Frac fl oz (imp)	= Template:Gaps Template:E m³
drop (imperial) (alt)	gtt	≡ Template:Frac gi (imp)	≈ Template:Val
drop (medical)		≡ Template:Frac mL	= 83.Template:Overline Template:E m³
drop (metric)		≡ Template:Frac mL	= Template:Val
drop (US)	gtt	≡ Template:Frac US fl oz	= Template:Gaps Template:E m³
drop (US) (alt)	gtt	≡ Template:Frac US fl oz	≈ Template:Val
drop (US) (alt)	gtt	≡ Template:Frac US fl oz	≈ Template:Val
fifth		≡ Template:Frac US gal	= Template:Val
firkin		≡ 9 gal (imp)	= Template:Val
fluid drachm (imperial)	fl dr	≡ Template:Frac fl oz (imp)	= Template:Val
fluid dram (US); US fluidram	fl dr	≡ Template:Frac US fl oz	= Template:Val
fluid scruple (imperial)	fl s	≡ Template:Frac fl oz (imp)	= Template:Gaps Template:E m³
gallon (beer)	beer gal	≡ 282 cu in	= Template:Val
gallon (imperial)	gal (imp)	≡ Template:Val	≡ Template:Val
gallon (US dry)	gal (US)	≡ Template:Frac bu (US lvl)	= Template:Val
gallon (US fluid; Wine)	gal (US)	≡ 231 cu in	≡ Template:Val
gill (imperial); Noggin	gi (imp); nog	≡ 5 fl oz (imp)	= Template:Val
gill (US)	gi (US)	≡ 4 US fl oz	= Template:Val
hogshead (imperial)	hhd (imp)	≡ 2 bl (imp)	= Template:Val
hogshead (US)	hhd (US)	≡ 2 fl bl (US)	= Template:Val
jigger (bartending)		≡ Template:Frac US fl oz	≈ Template:Val
kilderkin		≡ 18 gal (imp)	= Template:Val
lambda	λ	≡ 1 mm³	= Template:Val
last		≡ 80 bu (imp)	= Template:Val
litre (liter)	L or l	≡ 1 dm³ ^[19]	≡ 0.001 m³
load		≡ 50 cu ft	= Template:Val
minim (imperial)	min	≡ Template:Frac fl oz (imp) = 1/60 fl dr (imp)	= Template:Gaps Template:E m³
minim (US)	min	≡ Template:Frac US fl oz = Template:Frac US fl dr	= Template:Val
ounce (fluid imperial)	fl oz (imp)	≡ Template:Frac gal (imp)	≡ Template:Val
ounce (fluid US customary)	US fl oz	≡ Template:Frac gal (US)	≡ Template:Val
ounce (fluid US food nutrition labeling)	US fl oz	≡ 30 mL^[18]	≡ Template:Val
peck (imperial)	pk	≡ 2 gal (imp)	= Template:Val
peck (US dry)	pk	≡ Template:Frac US lvl bu	= Template:Val
perch	per	≡ Template:Nowrap	= Template:Val
pinch (imperial)		≡ Template:Frac gi (imp) = 1/16 tsp (imp)	= Template:Gaps Template:E m³
pinch (US)		≡ Template:Frac US fl oz = 1/16 US tsp	= Template:Val
pint (imperial)	pt (imp)	≡ Template:Frac gal (imp)	= Template:Val
pint (US dry)	pt (US dry)	≡ Template:Frac bu (US lvl) ≡ Template:Frac gal (US dry)	= Template:Val
pint (US fluid)	pt (US fl)	≡ Template:Frac gal (US)	= Template:Val
pony		≡ Template:Frac US fl oz	= Template:Val
pottle; quartern		≡ Template:Frac gal (imp) = 80 fl oz (imp)	= Template:Val
quart (imperial)	qt (imp)	≡ Template:Frac gal (imp)	= Template:Val
quart (US dry)	qt (US)	≡ Template:Frac bu (US lvl) = Template:Frac gal (US dry)	= Template:Val
quart (US fluid)	qt (US)	≡ Template:Frac gal (US fl)	= Template:Val
quarter; pail		≡ 8 bu (imp)	= Template:Val
register ton		≡ 100 cu ft	= Template:Val
sack (US)		≡ 3 bu (US lvl)	= Template:Val
seam		≡ 8 bu ^[16]	= Template:Val
shot (US)		usually 1.5 US fl oz^[16]	≈ Template:Val
strike (imperial)		≡ 2 bu (imp)	= Template:Val
strike (US)		≡ 2 bu (US lvl)	= Template:Val
tablespoon (Australian metric)			≡ Template:Val
tablespoon (Canadian)	tbsp	≡ Template:Frac fl oz (imp)	= Template:Val
tablespoon (imperial)	tbsp	≡ Template:Frac fl oz (imp)	= Template:Val
tablespoon (metric)			≡ Template:Val
tablespoon (US customary)	tbsp	≡ Template:Frac US fl oz	= Template:Val
tablespoon (US food nutrition labeling)	tbsp	≡ 15 mL^[18]	= Template:Val
teaspoon (Canadian)	tsp	≡ Template:Frac fl oz (imp)	= Template:Gaps Template:E m³
teaspoon (imperial)	tsp	≡ Template:Frac gi (imp)	= Template:Gaps Template:E m³
teaspoon (metric)		≡ Template:Val	≡ Template:Val
teaspoon (US customary)	tsp	≡ Template:Frac US fl oz	= Template:Val
teaspoon (US food nutrition labeling)	tsp	≡ 5 mL^[18]	= Template:Val
timber foot		≡ 1 cu ft	= Template:Val
ton (displacement)		≡ 35 cu ft	= Template:Val
ton (freight)		≡ 40 cu ft	= Template:Val
ton (water)		≡ 28 bu (imp)	= Template:Val
tun		≡ 252 gal (wine)	= Template:Val
wey (US)		≡ 40 bu (US lvl)	= Template:Val

Plane angle

Plane angle
Name of unit	Symbol	Definition	Relation to SI units
NATO mil	(various)	≡ Template:Frac rad	≈ Template:Val
Swedish streck		≡ Template:Frac rad	≈ Template:Val
milliradian	mrad	≡ Template:Frac rad	≈ Template:Val
Warsaw Pact mil		≡ Template:Frac rad	≈ Template:Val
arcminute; MOA	'	≡ Template:Frac	≈ Template:Val
arcsecond	"	≡ Template:Frac	≈ Template:Val
centesimal minute of arc	'	≡ Template:Frac grad	≈ Template:Val
centesimal second of arc	"	≡ Template:Frac grad	≈ Template:Val
degree (of arc)	°	≡ Template:Frac of a revolution ≡ Template:Frac rad	≈ Template:Val
grad; gradian; gon	grad	≡ Template:Frac of a revolution ≡ Template:Frac rad ≡ 0.9°	Template:Nowrap
octant		≡ 45°	≈ Template:Val
quadrant		≡ 90°	≈ Template:Val
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°	≈ Template:Val
sign		≡ 30°	≈ Template:Val

Solid angle

Solid angle
Name of unit	Symbol	Definition	Relation to SI units
spat		Template:Nowrap^[16] – The solid angle subtended by a sphere at its centre.	Template:Nowrap
square degree	deg²; sq.deg.; (°)²	Template:Nowrap	Template:Nowrap
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.^[16]	= 1 sr

Mass

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)	≈ Template:Val^[3]
atomic unit of mass, electron rest mass	m_e		≈ Template:Val^[20]
bag (coffee)		≡ 60 kg	= 60 kg
bag (Portland cement)		≡ 94 lb av	= Template:Val
barge		≡ Template:Frac short ton	= Template:Val
carat	kt	≡ Template:Frac gr	= Template:Val Template:Overline mg
carat (metric)	ct	≡ 200 mg	= 200 mg
clove		≡ 8 lb av	= Template:Val
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	≈ Template:Val^[3]
dram (apothecary; troy)	dr t	≡ 60 gr	= Template:Val
dram (avoirdupois)	dr av	≡ Template:Frac gr	= Template:Val
electronvolt	eV	≡ 1 eV (energy unit) / c²	= Template:Val^[3]
gamma	γ	≡ 1 μg	= 1 μg
grain	gr	≡ Template:Frac lb av	≡ Template:Val
grave	gv	grave was the original name of the kilogram	≡ 1 kg
hundredweight (long)	long cwt or cwt	≡ 112 lb av	= Template:Val
hundredweight (short); cental	sh cwt	≡ 100 lb av	= Template:Val
kilogram (kilogramme)	kg	≈ mass of the prototype near Paris ≈ mass of 1 litre of water	(SI base unit)^[8]
kip	kip	≡ Template:Val av	= Template:Val
mark		≡ 8 oz t	= Template:Val
mite		≡ Template:Frac gr	= Template:Val
mite (metric)		≡ Template:Frac g	= 50 mg
ounce (apothecary; troy)	oz t	≡ Template:Frac lb t	= Template:Val
ounce (avoirdupois)	oz av	≡ Template:Frac lb	= Template:Val
ounce (US food nutrition labelling)	oz	≡ 28 g^[18]	= 28 g
pennyweight	dwt; pwt	≡ Template:Frac oz t	= Template:Val
point		≡ Template:Frac ct	= 2 mg
pound (avoirdupois)	lb av	≡ Template:Val = Template:Val grains	≡ Template:Val
pound (metric)		≡ 500 g	= 500 g
pound (troy)	lb t	≡ Template:Val grains	= Template:Val
quarter (imperial)		≡ Template:Frac long cwt = 2 st = 28 lb av	= Template:Val
quarter (informal)		≡ Template:Frac short ton	= Template:Val
quarter, long (informal)		≡ Template:Frac long ton	= Template:Val
quintal (metric)	q	≡ 100 kg	= 100 kg
scruple (apothecary)	s ap	≡ 20 gr	= Template:Val
sheet		≡ Template:Frac lb av	= 647.9891 mg
slug; geepound; hyl	slug	≡ $g 0$ × 1 lb av × 1 s²/ft	≈ Template:Val
stone	st	≡ 14 lb av	= Template:Val
ton, assay (long)	AT	≡ 1 mg × 1 long ton ÷ 1 oz t	= 32.Template:Overline g
ton, assay (short)	AT	≡ 1 mg × 1 short ton ÷ 1 oz t	= 29.1Template:Overline g
ton, long	long tn or ton	≡ Template:Val	= Template:Val
ton, short	sh tn	≡ Template:Val	= Template:Val
tonne (mts unit)	t	≡ Template:Val	= Template:Val
wey		≡ 252 lb = 18 st	= Template:Val (variants exist)
Zentner	Ztr.	Definitions vary.^[16]^[21]

Density

Density
Name of unit	Symbol	Definition	Relation to SI units
gram per millilitre	g/mL	≡ g/mL	= Template:Val
kilogram per cubic metre (SI unit)	kg/m³	≡ kg/m³	= 1 kg/m³
kilogram per litre	kg/L	≡ kg/L	= Template:Val
ounce (avoirdupois) per cubic foot	oz/ft³	≡ oz/ft³	≈ Template:Val
ounce (avoirdupois) per cubic inch	oz/in³	≡ oz/in³	≈ Template:Val
ounce (avoirdupois) per gallon (imperial)	oz/gal	≡ oz/gal	≈ Template:Val
ounce (avoirdupois) per gallon (US fluid)	oz/gal	≡ oz/gal	≈ Template:Val
pound (avoirdupois) per cubic foot	lb/ft³	≡ lb/ft³	≈ Template:Val
pound (avoirdupois) per cubic inch	lb/in³	≡ lb/in³	≈ Template:Val
pound (avoirdupois) per gallon (imperial)	lb/gal	≡ lb/gal	≈ Template:Val
pound (avoirdupois) per gallon (US fluid)	lb/gal	≡ lb/gal	≈ Template:Val
slug per cubic foot	slug/ft³	≡ slug/ft³	≈ Template:Val

Time

Time
Name of unit	Symbol	Definition	Relation to SI units
Atomic unit of time	au	≡ a₀/(α⋅c)	≈ Template:Val
Callippic cycle		≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d	= Template:Val or Template:Val^{[note 1]}
Century	c	≡ 100 years (100 a)	= Template:Val^{[note 2]}^{[note 3]}
Day	d	= 24 h = Template:Val min	= Template:Val^{[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)	≈ Template:Val
Decade	dec	≡ 10 years (10 a)	= Template:Val^{[note 2]}^{[note 3]}
Fortnight	fn	≡ 2 wk	= Template:Val^{[note 3]}
Helek		≡ Template:Frac h	= 3.Template:Overline s
Hipparchic cycle		≡ 4 Callippic cycles - 1 d	= Template:Val
Hour	h	≡ 60 min	= Template:Val^{[note 3]}
Jiffy	j	≡ Template:Frac s	= 16.Template:Overline ms
Jiffy (alternative)	ja	≡ Template:Frac s	= 10 ms
Ke (quarter of an hour)		≡ Template:Frac h = Template:Frac d = 15 min	= 900 s
Ke (traditional)		≡ Template:Frac d = 14.4 min	= 864 s
Lustre; Lustrum		≡ 5 a of 365 d^{[note 4]}	= Template:Val
Metonic cycle; enneadecaeteris		≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a	= Template:Val
Millennium		≡ Template:Val years (Template:Val)	= Template:Val^{[note 2]}^{[note 3]}
Milliday	md	≡ Template:Frac 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^[22]	= Template:Val^{[note 3]}
Month (Greg. av.)	mo	= Template:Val	≈ Template:Val^{[note 3]}
Month (hollow)	mo	≡ 29 d^[22]	= Template:Val^{[note 3]}
Month (synodic)	mo	Cycle time of moon phases ≈ Template:Val (average)	≈ Template:Val
Octaeteris		= 48 mo (full) + 48 mo (hollow) + 3 mo (full)^[23]^[24] = 8 a of 365.25 d = 2922 d	= Template:Val^{[note 3]}
Planck time		≡ (Template:Frac)^{Template:Frac}	≈ Template:Val^[25]
Second (SI base unit)	s	≡ Time of Template:Val 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^[8] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of Template:Val metres.	(SI base unit)
Shake		≡ 10⁻⁸ s	= 10 ns
Sigma		≡ 10⁻⁶ s	= 1 μs
Sothic cycle		≡ Template:Val a of 365 d	= Template:Val
Svedberg	S	≡ 10⁻¹³ s	= 100 fs
Week	wk	≡ 7 d = 168 h = Template:Val	= Template:Val^{[note 3]}
Year (common)	Template:Nowrap	365 d	= Template:Val^{[note 3]}^[26]
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.	= Template:Val^{[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	= Template:Val
Year (leap)	a, y, or yr	366 d	= Template:Val^{[note 3]}^[26]
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 Template:Val d, each day being Template:Val SI seconds^[27]	≈ Template:Val
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 Template:Val	≈ Template:Val
Notes: ↑ see Callippic cycle for explanation of the differences ↑ ^2.0 ^2.1 ^2.2 This is based on the average Gregorian year. See above for definition of year lengths. ↑ ^3.00 ^3.01 ^3.02 ^3.03 ^3.04 ^3.05 ^3.06 ^3.07 ^3.08 ^3.09 ^3.10 ^3.11 ^3.12 ^3.13 ^3.14 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

Frequency

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

Speed or velocity

Speed
Name of unit	Symbol	Definition	Relation to SI units
foot per hour	fph	≡ 1 ft/h	= 8.4Template:Overline Template:E m/s
foot per minute	fpm	≡ 1 ft/min	= Template:Val
foot per second	fps	≡ 1 ft/s	= Template:Val
furlong per fortnight		≡ furlong/fortnight	≈ Template:Val
inch per hour	iph	≡ 1 in/h	= 7.0Template:Overline Template:E m/s
inch per minute	ipm	≡ 1 in/min	= 4.2Template:Overline Template:E m/s
inch per second	ips	≡ 1 in/s	= Template:Val
kilometre per hour	km/h	≡ 1 km/h	= 2.Template:Overline Template:E m/s
knot	kn	≡ 1 nmi/h = 1.852 km/h	= 0.51Template:Overline m/s
knot (Admiralty)	kn	≡ 1 NM (Adm)/h = Template:Val^[28]	= Template:Val Template:Overline 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	= Template:Val
mile per minute	mpm	≡ 1 mi/min	= Template:Val
mile per second	mps	≡ 1 mi/s	= Template:Val
speed of light in vacuum	c	≡ Template:Val	= Template:Val
speed of sound in air	s	Template:Val to Template:Val (Template:Convert)^{[note 1]}	≈ Template:Val
Note ↑ ^1.0 ^1.1 The speed of sound varies especially with temperature and pressure from about Template:Val (Template:Convert) in air at sea level to about Template:Val (Template:Convert) at jet altitudes (Template:Convert).^[29]

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

Flow (volume)

Flow
Name of unit	Symbol	Definition	Relation to SI units
cubic foot per minute	CFMTemplate:Citation needed	≡ 1 ft³/min	= Template:Val
cubic foot per second	ft³/s	≡ 1 ft³/s	= Template:Val
cubic inch per minute	in³/min	≡ 1 in³/min	= Template:Val Template:Overline Template:E m³/s
cubic inch per second	in³/s	≡ 1 in³/s	= Template:Val
cubic metre per second (SI unit)	m³/s	≡ 1 m³/s	= 1 m³/s
gallon (US fluid) per day	GPDTemplate:Citation needed	≡ 1 gal/d	= Template:Val Template:Overline Template:E m³/s
gallon (US fluid) per hour	GPHTemplate:Citation needed	≡ 1 gal/h	= Template:Val Template:Overline Template:E m³/s
gallon (US fluid) per minute	GPMTemplate:Citation needed	≡ 1 gal/min	= Template:Val
litre per minute	l/min or L/min	≡ 1 L/min	= 1.Template:Overline Template:E m³/s

Acceleration

Acceleration
Name of unit	Symbol	Definition	Relation to SI units
foot per hour per second	fph/s	≡ 1 ft/(h⋅s)	= 8.4Template:Overline Template:E m/s²
foot per minute per second	fpm/s	≡ 1 ft/(min⋅s)	= Template:Val
foot per second squared	fps²	≡ 1 ft/s²	= Template:Val
gal; galileo	Gal	≡ 1 cm/s²	= 10⁻² m/s²
inch per minute per second	ipm/s	≡ 1 in/(min⋅s)	= 4.2Template:Overline Template:E m/s²
inch per second squared	ips²	≡ 1 in/s²	= Template:Val
knot per second	kn/s	≡ 1 kn/s	≈ 5.1Template:Overline Template:E 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)	= Template:Val
mile per minute per second	mpm/s	≡ 1 mi/(min⋅s)	= 26.8224 m/s²
mile per second squared	mps²	≡ 1 mi/s²	= Template:Val
standard gravity	$g 0$	≡ Template:Val	= Template:Val

Force

Template:See also

Force
Name of unit	Symbol	Definition	Relation to SI units
atomic unit of force		≡ Template:Frac	≈ Template:Val^[30]
dyne (CGS unit)	dyn	≡ g⋅cm/s²	= 10⁻⁵ N
kilogram-force; kilopond; grave-force	kgf; kp; gvf	≡ $g 0$ × 1 kg	= Template:Val
kip; kip-force	kip; kipf; klbf	≡ $g 0$ × Template:Val	= Template:Val
milligrave-force, gravet-force	mgvf; gvtf	≡ $g 0$ × 1 g	= Template:Val
long ton-force	tnfTemplate:Citation needed	≡ $g 0$ × 1 long ton	= Template:Val
newton (SI unit)	N	A force capable of giving a mass of one kilogram an acceleration of one metre per second per second.^[31]	= 1 N = 1 kg⋅m/s²
ounce-force	ozf	≡ $g 0$ × 1 oz	= Template:Val
pound-force	lbf	≡ $g 0$ × 1 lb	= Template:Val
poundal	pdl	≡ 1 lb⋅ft/s²	= Template:Val
short ton-force	tnfTemplate:Citation needed	≡ $g 0$ × 1 short ton	= Template:Val
sthene (mts unit)	sn	≡ 1 t⋅m/s²	= 10³ N

Pressure or mechanical stress

Pressure
Name of unit	Symbol	Definition	Relation to SI units
atmosphere (standard)	atm		≡ Template:Val^[32]
atmosphere (technical)	at	≡ 1 kgf/cm²	= Template:Val^[32]
bar	bar	≡ Template:Val Pa	≡ 10⁵ Pa
barye (CGS unit)		≡ 1 dyn/cm²	= 0.1 Pa
centimetre of mercury	cmHg	≡ Template:Val × 1 cm × $g 0$	≈ Template:Val^[32]
centimetre of water (4 °C)	cmH₂O	≈ 999.972 kg/m³ × 1 cm × $g 0$	≈ Template:Val^[32]
foot of mercury (conventional)	ftHg	≡ Template:Val × 1 ft × $g 0$	≈ Template:Val^[32]
foot of water (39.2 °F)	ftH₂O	≈ 999.972 kg/m³ × 1 ft × $g 0$	≈ Template:Val^[32]
inch of mercury (conventional)	inHg	≡ Template:Val × 1 in × $g 0$	≈ Template:Val^[32]
inch of water (39.2 °F)	inH₂O	≈ 999.972 kg/m³ × 1 in × $g 0$	≈ Template:Val^[32]
kilogram-force per square millimetre	kgf/mm²	≡ 1 kgf/mm²	= Template:Val^[32]
kip per square inch	ksi	≡ 1 kipf/sq in	≈ Template:Val^[32]
long ton per square foot		≡ 1 long ton × $g 0$ / 1 sq ft	≈ Template:Val
micrometre of mercury	μmHg	≡ Template:Val × 1 μm × $g 0$ ≈ 0.001 torr	≈ Template:Val^[32]
millimetre of mercury	mmHg	≡ Template:Val × 1 mm × $g 0$ ≈ 1 torr	≈ Template:Val^[32]
millimetre of water (3.98 °C)	mmH₂O	≈ 999.972 kg/m³ × 1 mm × $g 0$ = Template:Val	= Template:Val
pascal (SI unit)	Pa	≡ N/m² = kg/(m⋅s²)	= 1 Pa^[33]
pièze (mts unit)	pz	≡ Template:Val	= Template:Val = 1 kPa
pound per square foot	psf	≡ 1 lbf/ft²	≈ Template:Val^[32]
pound per square inch	psi	≡ 1 lbf/in²	≈ Template:Val^[32]
poundal per square foot	pdl/sq ft	≡ 1 pdl/sq ft	≈ Template:Val^[32]
short ton per square foot		≡ 1 short ton × $g 0$ / 1 sq ft	≈ Template:Val
torr	torr	≡ Template:Frac Pa	≈ Template:Val^[32]

Torque or moment of force

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

Energy

Energy
Name of unit	Symbol	Definition	Relation to SI units
barrel of oil equivalent	boe	≈ Template:Val	≈ Template:Val
British thermal unit (ISO)	BTU_ISO	≡ Template:Val	= Template:Val
British thermal unit (International Table)	BTU_IT		= Template:Val
British thermal unit (mean)	BTU_mean		≈ Template:Val
British thermal unit (thermochemical)	BTU_th		≈ Template:Val
British thermal unit (39 °F)	BTU_39 °F		≈ Template:Val
British thermal unit (59 °F)	BTU_59 °F	≡ Template:Val	= Template:Val
British thermal unit (60 °F)	BTU_60 °F		≈ Template:Val
British thermal unit (63 °F)	BTU_63 °F		≈ Template:Val
calorie (International Table)	cal_IT	≡ Template:Val	= Template:Val
calorie (mean)	cal_mean	Template:Frac of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm	≈ Template:Val
calorie (thermochemical)	cal_th	≡ 4.184 J	= Template:Val
Calorie (US; FDA)	Cal	≡ 1 kcal = Template:Val	= Template:Val
calorie (3.98 °C)	cal_3.98 °C		≈ Template:Val
calorie (15 °C)	cal_15 °C	≡ 4.1855 J	= Template:Val
calorie (20 °C)	cal_20 °C		≈ Template:Val
Celsius heat unit (International Table)	CHU_IT	≡ 1 BTU_IT × 1 K/°R	= Template:Val
cubic centimetre of atmosphere; standard cubic centimetre	cc atm; scc	≡ 1 atm × 1 cm³	= Template:Val
cubic foot of atmosphere; standard cubic foot	cu ft atm; scf	≡ 1 atm × 1 ft³	= Template:Val
cubic foot of natural gas		≡ Template:Val	= Template:Val
cubic yard of atmosphere; standard cubic yard	cu yd atm; scy	≡ 1 atm × 1 yd³	= Template:Val
electronvolt	eV	≡ e × 1 V	≡ Template:Val
erg (CGS unit)	erg	≡ 1 g⋅cm²/s²	= 10⁻⁷ J
foot-pound force	ft lbf	≡ $g 0$ × 1 lb × 1 ft	= Template:Val
foot-poundal	ft pdl	≡ 1 lb⋅ft²/s²	= Template:Val
gallon-atmosphere (imperial)	imp gal atm	≡ 1 atm × 1 gal (imp)	= Template:Val
gallon-atmosphere (US)	US gal atm	≡ 1 atm × 1 gal (US)	= Template:Val
hartree, atomic unit of energy	E_h	≡ m_e⋅α²⋅c² (= 2 Ry)	≈ Template:Val
horsepower-hour	hp⋅h	≡ 1 hp × 1 h	= Template:Val
inch-pound force	in lbf	≡ $g 0$ × 1 lb × 1 in	= Template:Val
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.^[31]	= 1 J = 1 m⋅N = 1 kg⋅m²/s² = 1 C⋅V = 1 W⋅s
kilocalorie; large calorie	kcal; Cal	≡ Template:Val	= Template:Val
kilowatt-hour; Board of Trade Unit	kW⋅h; B.O.T.U.	≡ 1 kW × 1 h	= Template:Val
litre-atmosphere	l atm; sl	≡ 1 atm × 1 L	= Template:Val
quad		≡ 10¹⁵ BTU_IT	= Template:Val
rydberg	Ry	≡ R_∞⋅ℎ⋅c	≈ Template:Val
therm (E.C.)		≡ Template:Val	= Template:Val
therm (US)		≡ Template:Val	= Template:Val
thermie	th	≡ 1 Mcal_IT	= Template:Val
tonne of coal equivalent	TCE	≡ 7 Gcal_th	= Template:Val
tonne of oil equivalent	toe	≡ 10 Gcal_IT	= Template:Val
ton of TNT	tTNT	≡ 1 Gcal_th	= Template:Val
watt hour	W⋅h	≡ 1 W × 1 h	= Template:Val
watt second	W⋅s	≡ 1 J	= Template:Val

Power or heat flow rate

Power
Name of unit	Symbol	Definition	Relation to SI units
atmosphere-cubic centimetre per minute	atm ccmTemplate:Citation needed	≡ 1 atm × 1 cm³/min	= Template:Val
atmosphere-cubic centimetre per second	atm ccsTemplate:Citation needed	≡ 1 atm × 1 cm³/s	= Template:Val
atmosphere-cubic foot per hour	atm cfhTemplate:Citation needed	≡ 1 atm × 1 cu ft/h	= Template:Val
atmosphere-cubic foot per minute	atm cfmTemplate:Citation needed	≡ 1 atm × 1 cu ft/min	= Template:Val
atmosphere-cubic foot per second	atm cfsTemplate:Citation needed	≡ 1 atm × 1 cu ft/s	= Template:Val
BTU (International Table) per hour	BTU_IT/h	≡ 1 BTU_IT/h	≈ Template:Val
BTU (International Table) per minute	BTU_IT/min	≡ 1 BTU_IT/min	≈ Template:Val
BTU (International Table) per second	BTU_IT/s	≡ 1 BTU_IT/s	= Template:Val
calorie (International Table) per second	cal_IT/s	≡ 1 cal_IT/s	= Template:Val
erg per second	erg/s	≡ 1 erg/s	= Template:Val
foot-pound-force per hour	ft⋅lbf/h	≡ 1 ft lbf/h	≈ Template:Val
foot-pound-force per minute	ft⋅lbf/min	≡ 1 ft lbf/min	= Template:Val
foot-pound-force per second	ft⋅lbf/s	≡ 1 ft lbf/s	= Template:Val
horsepower (boiler)	hp	≈ 34.5 lb/h × 970.3 BTU_IT/lb	≈ Template:Val^[34]
horsepower (European electrical)	hp	≡ 75 kp⋅m/s	= Template:Val Template:Citation needed
horsepower (electrical)	hp	≡ 746 W	= Template:Val^[34]
horsepower (mechanical)	hp	≡ 550 ft⋅lbf/s^[34]	= Template:Val
horsepower (metric)	hp or PS	≡ 75 m⋅kgf/s	= Template:Val^[34]
litre-atmosphere per minute	L·atm/min	≡ 1 atm × 1 L/min	= Template:Val
litre-atmosphere per second	L·atm/s	≡ 1 atm × 1 L/s	= Template:Val
lusec	lusec	≡ 1 L·µmHg/s ^[16]	≈ Template:Val
poncelet	p	≡ 100 m⋅kgf/s	= Template:Val
square foot equivalent direct radiation	sq ft EDR	≡ 240 BTU_IT/h	≈ Template:Val
ton of air conditioning		≡ Template:Val of ice melted / 24 h	≈ Template:Val
ton of refrigeration (imperial)		≡ Template:Val × ice_IT / 24 h: ice_IT = 144 °F × 2326 J/kg⋅°F	≈ Template:Val
ton of refrigeration (IT)		≡ Template:Val × ice_IT / 24 h: ice_IT = 144 °F × 2326 J/kg⋅°F	≈ Template:Val
watt (SI unit)	W	The power which in one second of time gives rise to one joule of energy.^[31]	= Template:Val = 1 J/s = 1 N⋅m/s = 1 kg⋅m²/s³

Action

Action
Name of unit	Symbol	Definition	Relation to SI units
atomic unit of action	au	≡ ℏ ≡ Template:Frac	≈ Template:Val^[35]

Dynamic viscosity

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)	≈ Template:Val
pound per foot second	lb/(ft⋅s)	≡ 1 lb/(ft⋅s)	≈ Template:Val
pound-force second per square foot	lbf⋅s/ft²	≡ 1 lbf⋅s/ft²	≈ Template:Val
pound-force second per square inch	lbf⋅s/in²	≡ 1 lbf⋅s/in²	≈ Template:Val

Kinematic viscosity

Kinematic viscosity
Name of unit	Symbol	Definition	Relation to SI units
square foot per second	ft²/s	≡ 1 ft²/s	= Template:Val
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 current

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.^[36]	(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	≈ Template:Val

Electric charge

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	= Template:Val
coulomb	C	≡ charge of exactly 1/(Template:Val) elementary charges^[36]	= 1 C = 1 A⋅s
faraday	F	≡ 1 mol × N_A⋅e	≈ Template:Val
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	≈ Template:Val

Electric dipole

Electric dipole
Name of unit	Symbol	Definition	Relation to SI units
atomic unit of electric dipole moment	ea₀		≈ Template:Val^[37]
coulomb-meter	C⋅m		= 1 C⋅m
debye	D	≡ 10⁻¹⁰ esu⋅Å	≘ Template:Val^[38]

Electromotive force, electric potential difference

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)	= Template:Val
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.^[31]	= 1 V = 1 W/A Template:Nowrap = 1 J/C

Electrical resistance

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.^[31]	= 1 Ω = 1 V/A Template:Nowrap

Capacitance

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.^[31]	= 1 F = 1 C/V Template:Nowrap

Magnetic flux

Magnetic flux
Name of unit	Symbol	Definition	Relation to SI units
maxwell (CGS unit)	Mx	≘ 10⁻⁸ Wb^[34]	= 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.^[31]	= 1 Wb = 1 V⋅s Template:Nowrap

Magnetic flux density

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 ^[39]
tesla (SI unit)	T	≡ Wb/m²	= 1 T = 1 Wb/m² Template:Nowrap

Inductance

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.^[31]	= 1 H = 1 Wb/A Template:Nowrap

Temperature

Template:Details

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] × Template:Frac
degree Fahrenheit	°F	[°F] ≡ [°C] × Template:Frac + 32	[K] ≡ ([°F] + 459.67) × Template:Frac
degree Newton	°N		[K] = [°N] × Template:Frac + 273.15
degree Rankine	°R;	[°R] ≡ [K] × Template:Frac	[K] ≡ [°R] × 5/9
degree Réaumur	°Ré		[K] = [°Ré] × Template:Frac + 273.15
degree Rømer	°Rø		[K] = ([°Rø] − 7.5) × Template:Frac + 273.15
Regulo Gas Mark	GM	[°F] ≡ [GM] × 25 + 300	[K] ≡ [GM] × Template:Frac + 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.^[40]	(SI base unit)

Information entropy

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	≈ Template:Val	= 1 bit
hartley; ban	Hart; ban	≡ ln(10) × nat	≈ Template:Val
bit	bit; b			= 1 bit
nibble		≡ 4 bits		= 2² bit
byte	B	≡ 8 bits		= 2³ bit
kilobyte (decimal)	kB	≡ Template:Val		= Template:Val bit
kibibyte (kilobyte)	KiB; KB	≡ Template:Val		= 2¹³ bit = Template:Val 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 intensity

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 540Template:E hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.^[36]	(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.^[41] Approximately 0.981 cd.^[16]	≈ 0.981 cd

Luminance

Luminance
Name of unit	Symbol	Definition	Relation to SI units
candela per square foot	cd/ft²	≡ cd/ft²	≈ Template:Val
candela per square inch	cd/in²	≡ cd/in²	≈ Template:Val
candela per square metre (SI unit); nit (deprecated^[16])	cd/m²	≡ cd/m²	= 1 cd/m²
footlambert	fL	≡ (1/π) cd/ft²	≈ Template:Val
lambert	L	≡ (10⁴/π) cd/m²	≈ Template:Val
stilb (CGS unit)	sb	≡ 10⁴ cd/m²	= 10⁴ cd/m²

Luminous flux

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 540Template:E hertz and that has a radiant flux of 1/683 watt.^[36]	= 1 lm = 1 cd⋅sr

Illuminance

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

Radiation – source activity

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	≡ Template:Val^[42]	= Template:Val
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.^[43]

Radiation – exposure

Radiation – exposure
Name of unit	Symbol	Definition	Relation to SI units
roentgen	R	1 R ≡ Template:Val^[34]	= Template:Val

The roentgen is not an SI unit and the NIST strongly discourages its continued use.^[44]

Radiation – absorbed dose

Radiation – absorbed dose
Name of unit	Symbol	Definition	Relation to SI units
gray (SI unit)	Gy	≡ 1 J/kg^[45]	= 1 Gy = 1 J/kg = 1 m²⋅s²
rad	rad	≡ 0.01 Gy^[34]	= 0.01 Gy

Radiation – equivalent dose

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^[43]	= 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.

Licensing

Content obtained and/or adapted from:

Conversion of units, Wikipedia under a CC BY-SA license

↑ Template:Cite journal

↑ "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.

↑ ^3.0 ^3.1 ^3.2 ^3.3 ^3.4 Template:Cite web

↑ ^4.00 ^4.01 ^4.02 ^4.03 ^4.04 ^4.05 ^4.06 ^4.07 ^4.08 ^4.09 ^4.10 ^4.11 ^4.12 ^4.13 Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.

↑ ^5.0 ^5.1 National Bureau of Standards. (June 30, 1959). Refinement of values for the yard and the pound. Federal Register, viewed September 20, 2006 at National Geodetic Survey web site.

↑ Template:Cite web

↑ Klein, Herbert Arthur. (1988). The Science of Measurement: a Historical Survey. Mineola, NY: Dover Publications 0-4862-5839-4.

↑ ^8.0 ^8.1 ^8.2 Template:Citation

↑ International System of Units, Template:Webarchive 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 8.

↑ Template:Cite book

↑ P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.

↑ ^13.0 ^13.1 ^13.2 Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement. New York: Macmillan 0-312-37026-1. p. 152.

↑ ^14.0 ^14.1 De Vinne, Theodore Low (1900). The practice of typography: a treatise on the processes of type-making, the point system, the names, sizes, styles and prices of plain printing types 2nd ed. New York: The Century Co. p. 142–150.

↑ Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking. (1894). New York: Howard Lockwood. p. 521.

↑ ^16.0 ^16.1 ^16.2 ^16.3 ^16.4 ^16.5 ^16.6 ^16.7 ^16.8 Template:Citation

↑ Thompson, A. and Taylor, B.N. (2008). Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology Special Publication 811. p. 57.

↑ ^18.0 ^18.1 ^18.2 ^18.3 ^18.4 Template:Citation

↑ Barry N. Taylor, Ed.,NIST Special Publication 330: The International System of Units (SI) (2001 Edition), Washington: US Government Printing Office, 43,"The 12th Conference Generale des Poids et Mesures (CGPM)...declares that the word "litre" may be employed as a special name for the cubic decimetre".

↑ CODATA Value: atomic unit of mass. (2010). National Institute of Standards and Technology. Retrieved 29 May 2015.

↑ The Swiss Federal Office for Metrology gives Zentner on a German language web page Template:Cite web and quintal on the English translation of that page Template:Cite web; the unit is marked "spécifiquement suisse !"

↑ ^22.0 ^22.1 Pedersen O. (1983). "Glossary" in Coyne, G., Hoskin, M., and Pedersen, O. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican Observatory. Available from Astrophysics Data System.

↑ Template:Citation

↑ Template:Cite web

↑ ^26.0 ^26.1 Richards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books.

↑ Richards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books. p. 587.

↑ Until 1970 the UK Admiralty (and until 1954 the US) used other definitions of the nautical mile and hence the knot. See also #Length

↑ Tom Benson. (2010.) "Mach Number" Template:Webarchive in Beginner's Guide to Aeronautics. NASA.

↑ CODATA Value: atomic unit of force. (2006). National Institute of Standards and Technology. Retrieved September 14, 2008.

↑ ^31.0 ^31.1 ^31.2 ^31.3 ^31.4 ^31.5 ^31.6 ^31.7 Template:Citation

↑ ^32.00 ^32.01 ^32.02 ^32.03 ^32.04 ^32.05 ^32.06 ^32.07 ^32.08 ^32.09 ^32.10 ^32.11 ^32.12 ^32.13 ^32.14 ^32.15 Barry N. Taylor, (April 1995), Guide for the Use of the International System of Units (SI) (NIST Special Publication 811), Washington, DC: US Government Printing Office, pp. 57–68.

↑ Barry N. Taylor, (April 1995), Guide for the Use of the International System of Units (SI) (NIST Special Publication 811), Washington, DC: US Government Printing Office, p. 5.

↑ ^34.0 ^34.1 ^34.2 ^34.3 ^34.4 ^34.5 ^34.6 Template:Citation

↑ International System of Units, Template:Webarchive 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 7.

↑ ^36.0 ^36.1 ^36.2 ^36.3 Template:Cite web

↑ Template:Citation

↑ Robert G. Mortimer Physical chemistry,Academic Press, 2000 Template:ISBN, page 677

↑ Standard for the Use of the International System of Units (SI): The Modern Metric System IEEE/ASTM SI 10-1997. (1997). New York and West Conshohocken, PA: Institute of Electrical and Electronics Engineers and American Society for Testing and Materials. Tables A.1 through A.5.

↑ Template:Cite web

↑ Template:Citation

↑ Ambler Thompson & Barry N. Taylor. (2008). Guide for the Use of the International System of Units (SI). Special Publication 811. Gaithersburg, MD: National Institute of Standards and Technology. p. 10.

↑ ^43.0 ^43.1 Template:Citation

↑ Template:Citation

↑ Ambler Thompson & Barry N. Taylor. (2008). Guide for the Use of the International System of Units (SI). Special Publication 811. Gaithersburg, MD: National Institute of Standards and Technology. p. 5.

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[22] see Callippic cycle for explanation of the differences

[avegreg-23] 2.0 ^2.1 ^2.2 This is based on the average Gregorian year. See above for definition of year lengths.

[leapsec-24] 3.00 ^3.01 ^3.02 ^3.03 ^3.04 ^3.05 ^3.06 ^3.07 ^3.08 ^3.09 ^3.10 ^3.11 ^3.12 ^3.13 ^3.14 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.

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

[sound-35] 1.0 ^1.1 The speed of sound varies especially with temperature and pressure from about Template:Val (Template:Convert)
in air at sea level to about Template:Val (Template:Convert) at jet altitudes (Template:Convert).^[29]

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Measurement (LINEAR) – CONVERSION

Contents

Techniques

Process overview

Conversion factors

Software tools

Calculation involving non-SI Units

Calculate the pre-factor

Calculate the numbers

Tables of conversion factors

Length

Area

Volume

Plane angle

Solid angle

Mass

Density

Time

Frequency

Speed or velocity

Flow (volume)

Acceleration

Force

Pressure or mechanical stress

Torque or moment of force

Energy

Power or heat flow rate

Action

Dynamic viscosity

Kinematic viscosity

Electric current

Electric charge

Electric dipole

Electromotive force, electric potential difference

Electrical resistance

Capacitance

Magnetic flux

Magnetic flux density

Inductance

Temperature

Information entropy

Luminous intensity

Luminance

Luminous flux

Illuminance

Radiation – source activity

Radiation – exposure

Radiation – absorbed dose

Radiation – equivalent dose

Licensing

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