 Conversion of Units
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Conversion of Units

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:

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 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 ? 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 microns) can be done in two steps:

#### Calculate the pre-factor

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

$\xi ={\frac {\hbar }{\sqrt {2m\mu }}}=15.574\,\mu m\,,$ which is our pre-factor.

#### Calculate the numbers

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

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 $\xi ={\frac {15.574}{\sqrt {174*20.3}}}\,\mu m=0.262\,\mu m$ .

## 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
digits indicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...)
(H) of chiefly historical interest

### Length

Length
Name of unit Symbol Definition Relation to SI units
ångström Å ? ? 0.1 nm
astronomical unit AU ?
? Distance from Earth to Sun
? 
attometre am ? ?
barleycorn (H)   = ​ in (see note above about rounding) ? 8.46×10-3 m
bohr, atomic unit of length a0 = Bohr radius of hydrogen ? 
cable length (imperial)   ? 608 ft ? 185.3184 m
cable length (International)   ? ​ nmi ? 185.2 m
cable length (US)   ? 720 ft = 219.456 m
chain (Gunter's; Surveyor's) ch ? 66 ft (US) ? 4 rods  ?
cubit (H)   ? Distance from fingers to elbow ? 18 in ? 0.5 m
ell (H) ell ? 45 in  (In England usually) = 1.143 m
fathom ftm ? 6 ft  = 1.8288 m
femtometre fm ? ?
fermi fm ?  ?
finger   ? ​ in =
finger (cloth)   ? ​ in = 0.1143 m
foot (Benoît) (H) ft (Ben) ?
foot (Cape) (H)   Legally defined as 1.033 English feet in 1859 ?
foot (Clarke's) (H) ft (Cla) ?
foot (Indian) (H) ft Ind ?
foot, metric mf ? 300 mm ? 0.3 m
foot, metric (Mesures usuelles) (H) ? ​ m ? 0.3 m
foot (International) ft ? 0.3048 m ? ​ yd ? 12 inches ? 0.3048 m
foot (Sear's) (H) ft (Sear) ?
foot (US Survey) ft (US) ? ​ m  ?
french; charriere F ? ​ mm = 0.3 ×10-3 m
furlong fur ? 10 chains = 660 ft = 220 yd  = 201.168 m
hand   ? 4 in  ? 0.1016 m
inch (International) in ? 2.54 cm ? ​ yd ? ​ ft ? 0.0254 m
league (land) lea ? 1 hour walk, Currently defined in US as 3 Statute miles, but historically varied from 2 to 9 km ?
light-day   ? 24 light-hours ?
light-hour   ? 60 light-minutes ?
light-minute   ? 60 light-seconds ?
light-second   ? Distance light travels in one second in vacuum ?
light-year ly ? Distance light travels in vacuum in 365.25 days  ?
line ln ? ​ in  = 0.002116 m
link (Gunter's; Surveyor's) lnk ? ​ ch  ? 0.66 ft (US) ? 7.92 in ?
link (Ramsden's; Engineer's) lnk ? 1 ft  = 0.3048 m
metre (SI base unit)
(meter)
m ? Distance light travels in ​ of a second in vacuum.
? ​ of the distance from equator to pole.
? 1 m
mickey   ? ​ in =
micrometre (old: micron) μ; μm ? ?
mil; thou mil ? =
mil (Sweden and Norway) mil ? 10 km =
mile (geographical) (H) ? =
mile (international) mi ? 80 chains ? ? ?
mile (tactical or data) ? ?
mile (telegraph) (H) mi ? =
mile (US Survey) mi ? US Survey feet ? ( × ​) m ?
nail (cloth)   ? ​ in  =
nanometre nm ? ?
nautical league NL; nl ? 3 nmi  =
nautical mile (international) NM; nmi ?  ?
nautical mile (US pre 1954) ? 1853.248 m ? 1853.248 m
pace   ? 2.5 ft  = 0.762 m
palm   ? 3 in  = 0.0762 m
parsec pc Distant point with a parallax shift of one arc second from a base of one astronomical unit.
? AU
? 
pica   ? 12 points Dependent on point measures.
picometre pm ? ?
point (American, English) pt ? ​ in ?
point (Didot; European)  pt ? ​ × ​ of pied du roi;

After 1878:
? ​ cm
? ;

After 1878:
?
point (PostScript)  pt ? ​ in = 0.0003527 m
point (TeX)  pt ? ​ in = 0.0003514598 m
quarter   ? ​ yd = 0.2286 m
rod; pole; perch (H) rd ? ​ ft = 5.0292 m
rope (H) rope ? 20 ft  = 6.096 m
shaku (Japan) ? 10/33 m ? 0.303 0303 m
span (H)   ? 9 in  = 0.2286 m
spat  ?
stick (H)   ? 2 in = 0.0508 m
toise (French, post 1667) (H) T ? 27000/13853 m ? 1.949 0363 m
twip twp ? ​ in = 1.7638×10-5 m
x unit; siegbahn xu ? m 
yard (International) yd ? 0.9144 m  ? 3 ft ? 36 in ? 0.9144 m
yoctometre ym ? ?
zeptometre zm ? ?

### Area

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

### Volume

Volume
Name of unit Symbol Definition Relation to SI units
acre-foot ac ft ? 1 ac x 1 ft = =
acre-inch   ? 1 ac × 1 in =
barrel (imperial) bl (imp) ? 36 gal (imp) =
barrel (petroleum); archaic blue-barrel bl; bbl ? 42 gal (US) =
barrel (US dry) bl (US) ? 105 qt (US) = 105/32 bu (US lvl) =
barrel (US fluid) fl bl (US) ? ​ gal (US) =
board-foot fbm ? 144 cu in ?
bucket (imperial) bkt ? 4 gal (imp) =
bushel (imperial) bu (imp) ? 8 gal (imp) =
bushel (US dry heaped) bu (US) ? ​ bu (US lvl) =
bushel (US dry level) bu (US lvl) ? =
butt, pipe   ? 126 gal (US) (wine) =
coomb   ? 4 bu (imp) =
cord (firewood)   ? =
cord-foot   ? 16 cu ft =
cubic fathom cu fm ? 1 fm × 1 fm × 1 fm =
cubic foot ft3 ? 1 ft × 1 ft × 1 ft ?
cubic inch in3 ? 1 in × 1 in × 1 in ?
cubic metre (SI unit) m3 ? 1 m × 1 m × 1 m ? 1 m3
cubic mile cu mi ? 1 mi × 1 mi × 1 mi ?
cubic yard yd3 ? 27 cu ft ?
cup (breakfast)   ? 10 fl oz (imp) =
cup (Canadian) c (CA) ? 8 fl oz (imp) =
cup (metric) c ? ?
cup (US customary) c (US) ? 8 US fl oz ? ​ gal (US) =
cup (US food nutrition labeling) c (US) ? 240 mL =
dash (imperial)   ? ​ gi (imp) = ​ pinch (imp) = 369.961751302083×10-9 m3
dash (US)   ? ​ US fl oz = ​ US pinch =
dessertspoon (imperial)   ? ​ gi (imp) = 11.8387760416×10-6 m3
drop (imperial) gtt ? ​ fl oz (imp) = 98.6564670138×10-9 m3
drop (imperial) (alt) gtt ? ​ gi (imp) ?
drop (medical)   ? ​ ml = 83.03×10-9 m3
drop (medical)   ? ​ ml = 83.3×10-9 m3
drop (metric)   ? ​ mL =
drop (US) gtt ? ​ US fl oz = 82.14869322916×10-9 m3
drop (US) (alt) gtt ? ​ US fl oz ?
drop (US) (alt) gtt ? ​ US fl oz ?
fifth   ? ​ US gal =
firkin   ? 9 gal (imp) =
fluid drachm (imperial) fl dr ? ​ fl oz (imp) =
fluid dram (US); US fluidram fl dr ? ​ US fl oz =
fluid scruple (imperial) fl s ? ​ fl oz (imp) = 1.18387760416×10-6 m3
gallon (beer) beer gal ? 282 cu in =
gallon (imperial) gal (imp) ? ?
gallon (US dry) gal (US) ? ​ bu (US lvl) =
gallon (US fluid; Wine) gal (US) ? 231 cu in ?
gill (imperial); Noggin gi (imp); nog ? 5 fl oz (imp) =
gill (US) gi (US) ? 4 US fl oz =
hogshead (imperial) hhd (imp) ? 2 bl (imp) =
hogshead (US) hhd (US) ? 2 fl bl (US) =
jigger (bartending)   ? ​ US fl oz ?
kilderkin   ? 18 gal (imp) =
lambda ? ? 1 mm3 =
last   ? 80 bu (imp) =
litre
(liter)
L or l ? 1 dm3 ? 0.001 m3
load   ? 50 cu ft =
minim (imperial) min ? ​ fl oz (imp) = 1/60 fl dr (imp) = 59.1938802083×10-9 m3
minim (US) min ? ​ US fl oz = ​ US fl dr =
ounce (fluid imperial) fl oz (imp) ? ​ gal (imp) ?
ounce (fluid US customary) US fl oz ? ​ gal (US) ?
ounce (fluid US food nutrition labeling) US fl oz ? 30 mL ?
peck (imperial) pk ? 2 gal (imp) =
peck (US dry) pk ? ​ US lvl bu =
perch per ? =
pinch (imperial)   ? ​ gi (imp) = 1/16 tsp (imp) = 739.92350260416×10-9 m3
pinch (US)   ? ​ US fl oz = 1/16 US tsp =
pint (imperial) pt (imp) ? ​ gal (imp) =
pint (US dry) pt (US dry) ? ​ bu (US lvl) ? ​ gal (US dry) =
pint (US fluid) pt (US fl) ? ​ gal (US) =
pony   ? ​ US fl oz =
pottle; quartern   ? ​ gal (imp) = 80 fl oz (imp) =
quart (imperial) qt (imp) ? ​ gal (imp) =
quart (US dry) qt (US) ? ​ bu (US lvl) = ​ gal (US dry) =
quart (US fluid) qt (US) ? ​ gal (US fl) =
quarter; pail   ? 8 bu (imp) =
register ton   ? 100 cu ft =
sack (US)   ? 3 bu (US lvl) =
seam   ? 8 bu  =
shot (US)   usually 1.5 US fl oz ?
strike (imperial)   ? 2 bu (imp) =
strike (US)   ? 2 bu (US lvl) =
tablespoon (Australian metric)   ?
tablespoon (Canadian) tbsp ? ​ fl oz (imp) =
tablespoon (imperial) tbsp ? ​ fl oz (imp) =
tablespoon (metric)   ?
tablespoon (US customary) tbsp ? ​ US fl oz =
tablespoon (US food nutrition labeling) tbsp ? 15 mL =
teaspoon (Canadian) tsp ? ​ fl oz (imp) = 4.735510416×10-6 m3
teaspoon (imperial) tsp ? ​ gi (imp) = 5.91938802083×10-6 m3
teaspoon (metric)   ? ?
teaspoon (US customary) tsp ? ​ US fl oz =
teaspoon (US food nutrition labeling) tsp ? 5 mL =
timber foot   ? 1 cu ft =
ton (displacement)   ? 35 cu ft =
ton (freight)   ? 40 cu ft =
ton (water)   ? 28 bu (imp) =
tun   ? 252 gal (wine) =
wey (US)   ? 40 bu (US lvl) =

### Plane angle

Plane angle
Name of unit Symbol Definition Relation to SI units
NATO mil (various) ? ​ rad ?
Swedish streck ? ​ rad ?
Warsaw Pact mil ? ​ rad ?
arcminute; MOA ' ? ​ ?
arcsecond " ? ​ ?
centesimal minute of arc ' ? ​ grad ?
centesimal second of arc " ? ​ grad ?
degree (of arc) ° ? ​ of a revolution ? ​ rad ?
octant   ? 45° ?
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 2? radians.
sextant   ? 60° ?
sign   ? 30° ?

### Solid angle

Solid angle
Name of unit Symbol Definition Relation to SI units
spat  - The solid angle subtended by a sphere at its centre.
square degree deg2; sq.deg.; (°)2
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 4? sr.
= 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 unit gee is used to denote standard gravity in order to avoid confusion with the "g" symbol for grams.
Mass
Name of unit Symbol Definition Relation to SI units
atomic mass unit, unified u; AMU Same as dalton (see below) ? 
atomic unit of mass, electron rest mass me ? 
bag (coffee)   ? 60 kg = 60 kg
bag (Portland cement)   ? 94 lb av =
barge   ? ​ short ton =
carat kt ? ​ gr = 3 mg
carat (metric) ct ? 200 mg = 200 mg
clove   ? 8 lb av =
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
? 
dram (apothecary; troy) dr t ? 60 gr =
dram (avoirdupois) dr av ? ​ gr =
electronvolt eV ? 1 eV (energy unit) / c2 = 
gamma ? ? 1 ?g = 1 ?g
grain gr ? ​ lb av ?
grave gv. grave was the original name of the kilogram ? 1 kg
hundredweight (long) long cwt or cwt ? 112 lb av =
hundredweight (short); cental sh cwt ? 100 lb av =
kilogram
(kilogramme)
kg ? mass of the prototype near Paris
? mass of 1 litre of water
? 1 kg (SI base unit)
kip kip ? av =
mark   ? 8 oz t =
mite   ? ​ gr =
mite (metric)   ? ​ g = 50 mg
ounce (apothecary; troy) oz t ? ​ lb t =
ounce (avoirdupois) oz av ? ​ lb =
ounce (US food nutrition labelling) oz ? 28 g = 28 g
pennyweight dwt; pwt ? ​ oz t =
point   ? ​ ct = 2 mg
pound (avoirdupois) lb av ? = grains ?
pound (metric)   ? 500 g = 500 g
pound (troy) lb t ? grains =
quarter (imperial)   ? ​ long cwt = 2 st = 28 lb av =
quarter (informal)   ? ​ short ton =
quarter, long (informal)   ? ​ long ton =
quintal (metric) q ? 100 kg = 100 kg
scruple (apothecary) s ap ? 20 gr =
sheet   ? ​ lb av = 647.9891 mg
slug; geepound; hyl slug ? 1 ɡ0 × 1 lb av × 1 s2/ft ?
stone st ? 14 lb av =
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 ? =
ton, short sh tn ? =
tonne (mts unit) t ? =
wey   ? 252 lb = 18 st = (variants exist)
Zentner Ztr. Definitions vary.

### Density

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

### Time

Time
Name of unit Symbol Definition Relation to SI units
Atomic unit of time au ? a0/(??c) ?
Callippic cycle   ? 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d = or [note 1]
Century c ? 100 years (100 a) [note 2][note 3]
Day d = 24 h = min = [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) ?
Decade dec ? 10 years (10 a) = [note 2][note 3]
Fortnight fn ? 2 wk = [note 3]
Helek ? ​ h = 3.3 s
Hipparchic cycle   ? 4 Callippic cycles - 1 d =
Hour h ? 60 min = [note 3]
Jiffy j ? ​ s = 16.6 ms
Jiffy (alternative) ja ? ​ s = 10 ms
Ke (quarter of an hour)   ? ​ h = ​ d = 15 min = 900 s
Ke (traditional)   ? ​ d = 14.4 min = 864 s
Lustre; Lustrum   ? 5 a of 365 d[note 4] =
Metonic cycle; enneadecaeteris   ? 110 mo (hollow) + 125 mo (full) = 6940 d ? 19 a =
Millennium   ? years [note 2][note 3]
Milliday md ? ​ 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 = [note 3]
Month (Greg. av.) mo = ? [note 3]
Month (hollow) mo ? 29 d = [note 3]
Month (synodic) mo Cycle time of moon phases ? (average) ?
Octaeteris   = 48 mo (full) + 48 mo (hollow) + 3 mo (full) = 8 a of 365.25 d = 2922 d = [note 3]
Planck time   ? (​) ? 
Second s ? Time of 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 (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of metres. (SI base unit)
Shake   ? 10-8 s = 10 ns
Sigma   ? 10-6 s = 1 ?s
Sothic cycle   ? a of 365 d =
Svedberg S ? 10-13 s = 100 fs
Week wk ? 7 d = 168 h = = [note 3]
Year (common) 365 d = [note 3][note 3]
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. = [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 =
Year (leap) a, y, or yr 366 d = [note 3]
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 d, each day being SI seconds ?
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 ?
Notes:
1. ^ see Callippic cycle for explanation of the differences
2. ^ a b c This is based on the average Gregorian year. See above for definition of year lengths.
3. 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.
4. ^ 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 ?
Cycle per second cps ? 1 Hz = 1 cps = 1 Hz
degree per second deg/s ? 1 °/s ? 1/360 Hz = 7 Hz
hertz (SI unit) Hz ? One cycle per second = 1 Hz = 1/s
revolutions per minute rpm ? One unit rpm equals one rotation completed around a fixed axis in one minute of time. ?

### Speed or velocity

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 =
foot per second fps ? 1 ft/s =
furlong per fortnight   ? furlong/fortnight ?
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 =
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 = [] = 3 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 =
mile per minute mpm ? 1 mi/min =
mile per second mps ? 1 mi/s =
speed of light in vacuum c ? =
speed of sound in air s to (761-660 mph or 661-574 kn)[note 1] ?
Note
1. ^ a b The speed of sound varies especially with temperature and pressure from about (1,225 km/h or 761 mph or 661 kn)
in air at sea level to about (1,062 km/h or 660 mph or 573 kn) at jet altitudes (12200 m or 40000 ft).

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 CFM[] ? 1 ft3/min =
cubic foot per second ft3/s ? 1 ft3/s =
cubic inch per minute in3/min ? 1 in3/min = 3×10-7 m3/s
cubic inch per second in3/s ? 1 in3/s =
cubic metre per second (SI unit) m3/s ? 1 m3/s = 1 m3/s
gallon (US fluid) per day GPD[] ? 1 gal/d = 8×10-8 m3/s
gallon (US fluid) per hour GPH[] ? 1 gal/h = 3×10-6 m3/s
gallon (US fluid) per minute GPM[] ? 1 gal/min =
litre per minute l/min or L/min ? 1 L/min = 1.6×10-5 m3/s

### Acceleration

Acceleration
Name of unit Symbol Definition Relation to SI units
foot per hour per second fph/s ? 1 ft/(h?s) = 8.46×10-5 m/s2
foot per minute per second fpm/s ? 1 ft/(min?s) =
foot per second squared fps2 ? 1 ft/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 =
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) =
mile per minute per second mpm/s ? 1 mi/(min?s) = 26.8224 m/s2
mile per second squared mps2 ? 1 mi/s2 =
standard gravity ɡ0 ? =

### Force

Force
Name of unit Symbol Definition Relation to SI units
atomic unit of force ? ​ ? 
dyne (cgs unit) dyn ? g?cm/s2 = 10-5 N
kilogram-force; kilopond; grave-force kgf; kp; Gf ? ɡ0 × 1 kg =
kip; kip-force kip; kipf; klbf ? ɡ0 × =
milligrave-force, gravet-force mGf; gf ? ɡ0 × 1 g =
long ton-force tnf[] ? ɡ0 × 1 long ton =
newton (SI unit) N A force capable of giving a mass of one kilogram an acceleration of one metre per second per second. = 1 N = 1 kg?m/s2
ounce-force ozf ? ɡ0 × 1 oz =
pound-force lbf ? ɡ0 × 1 lb =
poundal pdl ? 1 lb?ft/s2 =
short ton-force tnf[] ? ɡ0 × 1 short ton =
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 ? 
atmosphere (technical) at ? 1 kgf/cm2 = 
bar bar ?  Pa ? 105 Pa
barye (cgs unit)   ? 1 dyn/cm2 = 0.1 Pa
centimetre of mercury cmHg ? × 1 cm × ɡ0 ? 
centimetre of water (4 °C) cmH2O ? 999.972 kg/m3 × 1 cm × ɡ0 ? 
foot of mercury (conventional) ftHg ? × 1 ft × ɡ0 ? 
foot of water (39.2 °F) ftH2O ? 999.972 kg/m3 × 1 ft × ɡ0 ? 
inch of mercury (conventional) inHg ? × 1 in × ɡ0 ? 
inch of water (39.2 °F) inH2O ? 999.972 kg/m3 × 1 in × ɡ0 ? 
kilogram-force per square millimetre kgf/mm2 ? 1 kgf/mm2 = 
kip per square inch ksi ? 1 kipf/sq in ? 
long ton per square foot   ? 1 long ton × ɡ0 / 1 sq ft ?
micrometre of mercury μmHg ? × 1 μm × ɡ0 ? 0.001 torr ? 
millimetre of mercury mmHg ? × 1 mm × ɡ0 ? 1 torr ? 
millimetre of water (3.98 °C) mmH2O ? 999.972 kg/m3 × 1 mm × ɡ0 = =
pascal (SI unit) Pa ? N/m2 = kg/(m?s2) = 1 Pa
pièze (mts unit) pz ? = = 1 kPa
pound per square foot psf ? 1 lbf/ft2 ? 
pound per square inch psi ? 1 lbf/in2 ? 
poundal per square foot pdl/sq ft ? 1 pdl/sq ft ? 
short ton per square foot   ? 1 short ton × ɡ0 / 1 sq ft ?
torr torr ? ​ Pa ? 

### Torque or moment of force

Torque
Name of unit Symbol Definition Relation to SI units
pound-force-foot lbfoft ? ɡ0 × 1 lb × 1 ft =
poundal-ft pdloft ? 1 lb?ft2/s2 =
pound force-inch lbfoin ? ɡ0 × 1 lb × 1 in =
kilogram force-meter kgfom ? ɡ0 × N × m =
Newton metre (SI unit) N?m ? N × m = kg?m2/s2 =

### Energy

Energy
Name of unit Symbol Definition Relation to SI units
barrel of oil equivalent boe ? ?
British thermal unit (ISO) BTUISO ? =
British thermal unit (International Table) BTUIT =
British thermal unit (mean) BTUmean ?
British thermal unit (thermochemical) BTUth ?
British thermal unit (39 °F) BTU39 °F ?
British thermal unit (59 °F) BTU59 °F ? =
British thermal unit (60 °F) BTU60 °F ?
British thermal unit (63 °F) BTU63 °F ?
calorie (International Table) calIT ? =
calorie (mean) calmean ​ of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm ?
calorie (thermochemical) calth ? 4.184 J =
Calorie (US; FDA) Cal ? 1 kcal = =
calorie (3.98 °C) cal3.98 °C ?
calorie (15 °C) cal15 °C ? 4.1855 J =
calorie (20 °C) cal20 °C ?
Celsius heat unit (International Table) CHUIT ? 1 BTUIT × 1 K/°R =
cubic centimetre of atmosphere; standard cubic centimetre cc atm; scc ? 1 atm × 1 cm3 =
cubic foot of atmosphere; standard cubic foot cu ft atm; scf ? 1 atm × 1 ft3 =
cubic foot of natural gas   ? =
cubic yard of atmosphere; standard cubic yard cu yd atm; scy ? 1 atm × 1 yd3 =
electronvolt eV ? e × 1 V ?
erg (cgs unit) erg ? 1 g?cm2/s2 = 10-7 J
foot-pound force ft lbf ? ɡ0 × 1 lb × 1 ft =
foot-poundal ft pdl ? 1 lb?ft2/s2 =
gallon-atmosphere (imperial) imp gal atm ? 1 atm × 1 gal (imp) =
gallon-atmosphere (US) US gal atm ? 1 atm × 1 gal (US) =
hartree, atomic unit of energy Eh ? me??2?c2 (= 2 Ry) ?
horsepower-hour hp?h ? 1 hp × 1 h =
inch-pound force in lbf ? ɡ0 × 1 lb × 1 in =
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. = 1 J = 1 m?N = 1 kg?m2/s2 = 1 C?V = 1 W?s
kilocalorie; large calorie kcal; Cal ? =
kilowatt-hour; Board of Trade Unit kW?h; B.O.T.U. ? 1 kW × 1 h =
litre-atmosphere l atm; sl ? 1 atm × 1 L =
rydberg Ry ? R??h?c ?
therm (E.C.)   ? =
therm (US)   ? =
thermie th ? 1 McalIT =
tonne of coal equivalent TCE ? 7 Gcalth =
tonne of oil equivalent toe ? 10 GcalIT =
ton of TNT tTNT ? 1 Gcalth =
watt hour W?h ? 1 W × 1 h =
watt second W?s ? 1 J =

### Power or heat flow rate

Power
Name of unit Symbol Definition Relation to SI units
atmosphere-cubic centimetre per minute atm ccm[] ? 1 atm × 1 cm3/min =
atmosphere-cubic centimetre per second atm ccs[] ? 1 atm × 1 cm3/s =
atmosphere-cubic foot per hour atm cfh[] ? 1 atm × 1 cu ft/h =
atmosphere-cubic foot per minute atm cfm[] ? 1 atm × 1 cu ft/min =
atmosphere-cubic foot per second atm cfs[] ? 1 atm × 1 cu ft/s =
BTU (International Table) per hour BTUIT/h ? 1 BTUIT/h ?
BTU (International Table) per minute BTUIT/min ? 1 BTUIT/min ?
BTU (International Table) per second BTUIT/s ? 1 BTUIT/s =
calorie (International Table) per second calIT/s ? 1 calIT/s =
erg per second erg/s ? 1 erg/s =
foot-pound-force per hour ft?lbf/h ? 1 ft lbf/h ?
foot-pound-force per minute ft?lbf/min ? 1 ft lbf/min =
foot-pound-force per second ft?lbf/s ? 1 ft lbf/s =
horsepower (boiler) hp ? 34.5 lb/h × 970.3 BTUIT/lb ? 
horsepower (European electrical) hp ? 75 kp?m/s = []
horsepower (electrical) hp ? 746 W = 
horsepower (mechanical) hp ? 550 ft?lbf/s =
horsepower (metric) hp or PS ? 75 m?kgf/s = 
litre-atmosphere per minute L·atm/min ? 1 atm × 1 L/min =
litre-atmosphere per second L·atm/s ? 1 atm × 1 L/s =
lusec lusec ? 1 L·µmHg/s  ?
poncelet p ? 100 m?kgf/s =
square foot equivalent direct radiation sq ft EDR ? 240 BTUIT/h ?
ton of air conditioning   ? of ice melted / 24 h ?
ton of refrigeration (imperial)   ? × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg?°F ?
ton of refrigeration (IT)   ? × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg?°F ?
watt (SI unit) W The power which in one second of time gives rise to one joule of energy. = = 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 ? ? ? ​ ? 

### 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) ?
pound per foot second lb/(ft?s) ? 1 lb/(ft?s) ?
pound-force second per square foot lbf?s/ft2 ? 1 lbf?s/ft2 ?
pound-force second per square inch lbf?s/in2 ? 1 lbf?s/in2 ?

### Kinematic viscosity

Kinematic viscosity
Name of unit Symbol Definition Relation to SI units
square foot per second ft2/s ? 1 ft2/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 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. = 1 A = 1 C/s
electromagnetic unit; abampere (cgs unit) abamp ? 10 A = 10 A
esu per second; statampere (cgs unit) esu/s ? ​ ?

### 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 ?
coulomb C ? charge of exactly 1/ elementary charges = 1 C = 1 A?s
faraday F ? 1 mol × NA?e ?
milliampere hour mA?h ? 0.001 A × 1 h = 3.6 C
statcoulomb; franklin; electrostatic unit (cgs unit) statC; Fr; esu ? ​ ?

### Electric dipole

Electric dipole
Name of unit Symbol Definition Relation to SI units
atomic unit of electric dipole moment ea0   ? 
coulomb meter C?m   = 1 C × 1 m
debye D = 10-10 esu?Å = 

### 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 ?J/A?m) =
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. = 1 V = 1 W/A = 1 J/C

### Electrical resistance

Electrical resistance
Name of unit Symbol Definition Relation to SI units
ohm (SI unit) ? 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. = 1 ? = 1 V/A

### 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. = 1 F = 1 C/V

### Magnetic flux

magnetic flux
Name of unit Symbol Definition Relation to SI units
maxwell (CGS unit) Mx ? 10-8 Wb = 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. = 1 Wb = 1 V?s

### 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 
tesla (SI unit) T ? Wb/m2 = 1 T = 1 Wb/m2

### 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. = 1 H = 1 Wb/A

### Temperature

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] × ​
degree Fahrenheit °F [°F] ? [°C] × ​ + 32 [K] ? ([°F] + 459.67) × ​
degree Newton °N [K] = [°N] × ​ + 273.15
degree Rankine °R; [°R] ? [K] × ​ [K] ? [°R] × 5/9
degree Réaumur °Ré [K] = [°Ré] × ​ + 273.15
degree Rømer °Rø [K] = ([°Rø] - 7.5) × ​ + 273.15
Regulo Gas Mark GM [°F] ? [GM] × 25 + 300 [K] ? [GM] × ​ + 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. ? 1 K

### Information entropy

Information entropy
Name of unit Symbol Definition Relation to SI units Relation to bits
natural unit of information; nip; nepit nat
shannon; bit Sh; bit; b ? ln(2) × nat ? = 1 bit
hartley; ban Hart; ban ? ln(10) × nat ?
nibble ? 4 bits = 22 bit
byte B ? 8 bits = 23 bit
kilobyte (decimal) kB ? = bit
kilobyte (kibibyte) KB; KiB ? = 213 bit = 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); candle 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. = 1 cd
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. Approximately 0.981 cd. ? 0.981 cd

### Luminance

Luminance
Name of unit Symbol Definition Relation to SI units
candela per square foot cd/ft2 ? cd/ft2 ?
candela per square inch cd/in2 ? cd/in2 ?
candela per square metre (SI unit); nit (deprecated) cd/m2 ? cd/m2 = 1 cd/m2
footlambert fL ? (1/?) cd/ft2 ?
lambert L ? (104/?) cd/m2 ?
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 540×1012 hertz and that has a radiant flux of 1/683 watt. = 1 lm = 1 cd?sr

### Illuminance

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

Name of unit Symbol Definition Relation to SI units
becquerel (SI unit) Bq ? Number of disintegrations per second = 1 Bq = 1/s
curie Ci ?  =
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.

Name of unit Symbol Definition Relation to SI units
roentgen R 1 R ?  =

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

Name of unit Symbol Definition Relation to SI units
gray (SI unit) Gy ? 1 J/kg = 1 m2/s2 = 1 Gy

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 = 1 Sv

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.

## Notes and references

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Notes
1. ^ The technical definition of tropical year is the period of time for the ecliptic longitude of the Sun to increase 360 degrees. (Urban & Seidelmann 2013, Glossary, s.v. year, tropical)