Conversion of units

(Redirected from Unit 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:

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 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)
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 1×10−10 m ≡ 0.1 nm
astronomical unit au 149597870700 m
≈ Distance from Earth to Sun
149597870700 m 
attometre am 1×10−18 m 1×10−18 m
barleycorn (H)   = 13 in (see note above about rounding) = 8.46×10−3 m
bohr, atomic unit of length a0 = Bohr radius of hydrogen 5.2917721092(17)×10−11 m
cable length (imperial)   ≡ 608 ft ≈ 185.3184 m
cable length (International)   110 nmi ≡ 185.2 m
cable length (US)   ≡ 720 ft = 219.456 m
chain (Gunter's; Surveyor's) ch ≡ 66 ft (US) ≡ 4 rods 20.11684 m
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 1×10−15 m 1×10−15 m
fermi fm 1×10−15 m 1×10−15 m
finger   78 in = 0.022225 m
finger (cloth)   4+12 in = 0.1143 m
foot (Benoît) (H) ft (Ben) 0.304799735 m
foot (Cape) (H)   Legally defined as 1.033 English feet in 1859 0.314858 m
foot (Clarke's) (H) ft (Cla) 0.3047972654 m
foot (Indian) (H) ft Ind 0.304799514 m
foot, metric mf ≡ 300 mm ≡ 0.3 m
foot, metric (Mesures usuelles) (H) 13 m ≡ 0.3 m
foot (International) ft ≡ 0.3048 m ≡ 13 yd ≡ 12 inches ≡ 0.3048 m
foot (Sear's) (H) ft (Sear) 0.30479947 m
foot (US Survey) ft (US) 12003937 m  0.304800610 m
french; charriere F 13 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 ≡ 136 yd ≡ 112 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 4828 m
light-day   ≡ 24 light-hours 2.59020683712×1013 m
light-hour   ≡ 60 light-minutes 1.0792528488×1012 m
light-minute   ≡ 60 light-seconds 1.798754748×1010 m
light-second   ≡ Distance light travels in one second in vacuum 299792458 m
light-year ly ≡ Distance light travels in vacuum in 365.25 days  9.4607304725808×1015 m
line ln 112 in  = 0.002116 m
link (Gunter's; Surveyor's) lnk 1100 ch  ≡ 0.66 ft (US) ≡ 7.92 in 0.2011684 m
link (Ramsden's; Engineer's) lnk ≡ 1 ft  = 0.3048 m
metre (SI base unit)
(meter)
m ≡ Distance light travels in 1299792458 of a second in vacuum. (SI base unit)
mickey   1200 in = 1.27×10−4 m
micrometre (old: micron) μ; μm 1×10−6 m 1×10−6 m
mil; thou mil 1×10−3 in = 2.54×10−5 m
mil (Sweden and Norway) mil ≡ 10 km = 10000 m
mile (geographical) (H) 6082 ft = 1853.7936 m
mile (international) mi ≡ 80 chains ≡ 5280 ft1760 yd 1609.344 m
mile (tactical or data) 6000 ft 1828.8 m
mile (telegraph) (H) mi 6087 ft = 1855.3176 m
mile (US Survey) mi 5280 US Survey feet ≡ (5280 × 12003937) m 1609.347219 m
nail (cloth)   2+14 in  = 0.05715 m
nanometre nm 1×10−9 m 1×10−9 m
nautical league NL; nl ≡ 3 nmi  = 5556 m
nautical mile (international) NM; nmi 1852 m 1852 m
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.
648000/π au
30856775814913700 m
pica   ≡ 12 points Dependent on point measures.
picometre pm 1×10−12 m 1×10−12 m
point (American, English) pt 172.272 in 0.000351450 m
point (Didot; European)  pt 112 × 172 of pied du roi;

After 1878:
5133 cm
0.00037597 m;

After 1878:
0.00037593985 m
point (PostScript)  pt 172 in = 0.0003527 m
point (TeX)  pt 172.27 in = 0.0003514598 m
quarter   14 yd = 0.2286 m
rod; pole; perch (H) rd 16+12 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 1×1012 m
stick (H)   ≡ 2 in = 0.0508 m
toise (French, post 1667) (H) T ≡ 27000/13853 m ≈ 1.949 0363 m
twip twp 11440 in = 1.7638×10−5 m
x unit; siegbahn xu 1.0021×10−13 m 
yard (International) yd ≡ 0.9144 m  ≡ 3 ft ≡ 36 in ≡ 0.9144 m
yoctometre ym 1×10−24 m 1×10−24 m
zeptometre zm 1×10−21 m 1×10−21 m

Area

Area
Name of unit Symbol Definition Relation to SI units
acre (international) ac 1 ch × 10 ch = 4840 sq yd 4046.8564224 m2
acre (US survey) ac ≡ 10 sq ch = 4840 sq yd, also 43560 sq ft 4046.873 m2
are a ≡ 100 m2 ≡ 100 m2
barn b ≡ 10−28 m2 ≡ 10−28 m2
barony   4000 ac 1.61874256896×107 m2
board bd 1 in × 1 ft 7.74192×10−3 m2
boiler horsepower equivalent direct radiation bhp EDR ≡ 1 ft2 × 1 bhp / (240 BTUIT/h) 12.958174 m2
circular inch circ in π4 sq in 5.067075×10−4 m2
circular mil; circular thou circ mil π4 mil2 5.067075×10−10 m2
cord   ≡ 192 bd 1.48644864 m2
cuerda (PR Survey) cda ≡ 1 cda x 1 cda = 0.971222 acre 3930.395625 m2
dunam   1000 m2 1000 m2
guntha (India)   ≡ 121 sq yd ≈ 101.17 m2
hectare ha 10000 m2 10000 m2
hide   ≈ 120 ac (variable) 5×105 m2
rood ro 14 ac = 1011.7141056 m2
ping 2011 m × 2011 m 3.306 m2
section 1 mi × 1 mi = 2.589988110336×106 m2
shed   ≡ 10−52 m2 = 10−52 m2
square (roofing) 10 ft × 10 ft = 9.290304 m2
square chain (international) sq ch 66 ft × 66 ft = 110 ac 404.68564224 m2
square chain (US Survey) sq ch 66 ft (US) × 66 ft (US) = 110 US survey acre 404.6873 m2
square foot sq ft 1 ft × 1 ft 9.290304×10−2 m2
square foot (US Survey) sq ft 1 ft (US) × 1 ft (US) 9.2903411613275×10−2 m2
square inch sq in 1 in × 1 in 6.4516×10−4 m2
square kilometre km2 ≡ 1 km × 1 km = 106 m2
square link (Gunter's)(International) sq lnk ≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft = 4.0468564224×10−2 m2
square link (Gunter's)(US Survey) sq lnk 1 lnk × 1 lnk0.66 ft (US) × 0.66 ft (US) 4.046872×10−2 m2
square link (Ramsden's) sq lnk ≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft = 0.09290304 m2
square metre (SI unit) m2 ≡ 1 m × 1 m = 1 m2
square mil; square thou sq mil ≡ 1 mil × 1 mil = 6.4516×10−10 m2
square mile sq mi ≡ 1 mi × 1 mi 2.589988110336×106 m2
square mile (US Survey) sq mi ≡ 1 mi (US) × 1 mi (US) 2.58999847×106 m2
square rod/pole/perch sq rd ≡ 1 rd × 1 rd = 25.29285264 m2
square yard (International) sq yd ≡ 1 yd × 1 yd 0.83612736 m2
stremma   1000 m2 = 1000 m2
township   ≡ 36 sq mi (US) 9.323994×107 m2
yardland   ≈ 30 ac 1.2×105 m2

Volume

Volume
Name of unit Symbol Definition Relation to SI units
acre-foot ac ft ≡ 1 ac x 1 ft = 43560 cu ft = 1233.48183754752 m3
acre-inch   ≡ 1 ac × 1 in = 102.79015312896 m3
barrel (imperial) bl (imp) ≡ 36 gal (imp) = 0.16365924 m3
barrel (petroleum); archaic blue-barrel bl; bbl ≡ 42 gal (US) = 0.158987294928 m3
barrel (US dry) bl (US) ≡ 105 qt (US) = 105/32 bu (US lvl) = 0.115628198985075 m3
barrel (US fluid) fl bl (US) 31+12 gal (US) = 0.119240471196 m3
board-foot bdft ≡ 144 cu in 2.359737216×10−3 m3
bucket (imperial) bkt ≡ 4 gal (imp) = 0.01818436 m3
bushel (imperial) bu (imp) ≡ 8 gal (imp) = 0.03636872 m3
bushel (US dry heaped) bu (US) 1+14 bu (US lvl) = 0.0440488377086 m3
bushel (US dry level) bu (US lvl) 2150.42 cu in = 0.03523907016688 m3
butt, pipe   ≡ 126 gal (US) (wine) = 0.476961884784 m3
coomb   ≡ 4 bu (imp) = 0.14547488 m3
cord (firewood)   8 ft × 4 ft × 4 ft = 3.624556363776 m3
cord-foot   ≡ 16 cu ft = 0.453069545472 m3
cubic fathom cu fm ≡ 1 fm × 1 fm × 1 fm = 6.116438863872 m3
cubic foot ft3 ≡ 1 ft × 1 ft × 1 ft 0.028316846592 m3
cubic inch in3 ≡ 1 in × 1 in × 1 in 16.387064×10−6 m3
cubic metre (SI unit) m3 ≡ 1 m × 1 m × 1 m ≡ 1 m3
cubic mile cu mi ≡ 1 mi × 1 mi × 1 mi 4168181825.440579584 m3
cubic yard yd3 ≡ 27 cu ft 0.764554857984 m3
cup (breakfast)   ≡ 10 fl oz (imp) = 284.130625×10−6 m3
cup (Canadian) c (CA) ≡ 8 fl oz (imp) = 227.3045×10−6 m3
cup (metric) c 250.0×10−6 m3 250.0×10−6 m3
cup (US customary) c (US) ≡ 8 US fl oz ≡ 116 gal (US) = 236.5882365×10−6 m3
cup (US food nutrition labeling) c (US) ≡ 240 mL = 2.4×10−4 m3
dash (imperial)   1384 gi (imp) = 12 pinch (imp) = 369.961751302083×10−9 m3
dash (US)   196 US fl oz = 12 US pinch = 308.057599609375×10−9 m3
dessertspoon (imperial)   112 gi (imp) = 11.8387760416×10−6 m3
drop (imperial) gtt 1288 fl oz (imp) = 98.6564670138×10−9 m3
drop (imperial) (alt) gtt 11824 gi (imp) 77.886684×10−9 m3
drop (medical)   112 mL = 83.3×10−9 m3
drop (metric)   120 mL = 50.0×10−9 m3
drop (US) gtt 1360 US fl oz = 82.14869322916×10−9 m3
drop (US) (alt) gtt 1456 US fl oz 64.85423149671×10−9 m3
drop (US) (alt) gtt 1576 US fl oz 51.34293326823×10−9 m3
fifth   15 US gal = 757.0823568×10−6 m3
firkin   ≡ 9 gal (imp) = 0.04091481 m3
fluid drachm (imperial) fl dr 18 fl oz (imp) = 3.5516328125×10−6 m3
fluid dram (US); US fluidram fl dr 18 US fl oz = 3.6966911953125×10−6 m3
fluid scruple (imperial) fl s 124 fl oz (imp) = 1.18387760416×10−6 m3
gallon (beer) beer gal ≡ 282 cu in = 4.621152048×10−3 m3
gallon (imperial) gal (imp) 4.54609 L 4.54609×10−3 m3
gallon (US dry) gal (US) 18 bu (US lvl) = 4.40488377086×10−3 m3
gallon (US fluid; Wine) gal (US) ≡ 231 cu in 3.785411784×10−3 m3
gill (imperial); Noggin gi (imp); nog ≡ 5 fl oz (imp) = 142.0653125×10−6 m3
gill (US) gi (US) ≡ 4 US fl oz = 118.29411825×10−6 m3
hogshead (imperial) hhd (imp) ≡ 2 bl (imp) = 0.32731848 m3
hogshead (US) hhd (US) ≡ 2 fl bl (US) = 0.238480942392 m3
jigger (bartending)   1+12 US fl oz 44.36×10−6 m3
kilderkin   ≡ 18 gal (imp) = 0.08182962 m3
lambda λ ≡ 1 mm3 = 1×10−9 m3
last   ≡ 80 bu (imp) = 2.9094976 m3
litre
(liter)
L or l ≡ 1 dm3  ≡ 0.001 m3
load   ≡ 50 cu ft = 1.4158423296 m3
minim (imperial) min 1480 fl oz (imp) = 1/60 fl dr (imp) = 59.1938802083×10−9 m3
minim (US) min 1480 US fl oz = 160 US fl dr = 61.611519921875×10−9 m3
ounce (fluid imperial) fl oz (imp) 1160 gal (imp) 28.4130625×10−6 m3
ounce (fluid US customary) US fl oz 1128 gal (US) 29.5735295625×10−6 m3
ounce (fluid US food nutrition labeling) US fl oz ≡ 30 mL 3×10−5 m3
peck (imperial) pk ≡ 2 gal (imp) = 9.09218×10−3 m3
peck (US dry) pk 14 US lvl bu = 8.80976754172×10−3 m3
perch per 16+12 ft × 1+12 ft × 1 ft = 0.700841953152 m3
pinch (imperial)   1192 gi (imp) = 1/16 tsp (imp) = 739.92350260416×10−9 m3
pinch (US)   148 US fl oz = 1/16 US tsp = 616.11519921875×10−9 m3
pint (imperial) pt (imp) 18 gal (imp) = 568.26125×10−6 m3
pint (US dry) pt (US dry) 164 bu (US lvl) ≡ 18 gal (US dry) = 550.6104713575×10−6 m3
pint (US fluid) pt (US fl) 18 gal (US) = 473.176473×10−6 m3
pony   34 US fl oz = 22.180147171875×10−6 m3
pottle; quartern   12 gal (imp) = 80 fl oz (imp) = 2.273045×10−3 m3
quart (imperial) qt (imp) 14 gal (imp) = 1.1365225×10−3 m3
quart (US dry) qt (US) 132 bu (US lvl) = 14 gal (US dry) = 1.101220942715×10−3 m3
quart (US fluid) qt (US) 14 gal (US fl) = 946.352946×10−6 m3
quarter; pail   ≡ 8 bu (imp) = 0.29094976 m3
register ton   ≡ 100 cu ft = 2.8316846592 m3
sack (US)   ≡ 3 bu (US lvl) = 0.10571721050064 m3
seam   ≡ 8 bu  = 0.29095 m3
shot (US)   usually 1.5 US fl oz 44.4×10−6 m3
strike (imperial)   ≡ 2 bu (imp) = 0.07273744 m3
strike (US)   ≡ 2 bu (US lvl) = 0.07047814033376 m3
tablespoon (Australian metric)   20.0×10−6 m3
tablespoon (Canadian) tbsp 12 fl oz (imp) = 14.20653125×10−6 m3
tablespoon (imperial) tbsp 58 fl oz (imp) = 17.7581640625×10−6 m3
tablespoon (metric)   15×10−6 m3
tablespoon (US customary) tbsp 12 US fl oz = 14.78676478125×10−6 m3
tablespoon (US food nutrition labeling) tbsp ≡ 15 mL = 15×10−6 m3
teaspoon (Canadian) tsp 16 fl oz (imp) = 4.735510416×10−6 m3
teaspoon (imperial) tsp 124 gi (imp) = 5.91938802083×10−6 m3
teaspoon (metric)   5.0×10−6 m3 5.0×10−6 m3
teaspoon (US customary) tsp 16 US fl oz = 4.92892159375×10−6 m3
teaspoon (US food nutrition labeling) tsp ≡ 5 mL = 5×10−6 m3
timber foot   ≡ 1 cu ft = 0.028316846592 m3
ton (displacement)   ≡ 35 cu ft = 0.99108963072 m3
ton (freight)   ≡ 40 cu ft = 1.13267386368 m3
ton (water)   ≡ 28 bu (imp) = 1.01832416 m3
tun   ≡ 252 gal (wine) = 0.953923769568 m3
wey (US)   ≡ 40 bu (US lvl) = 1.4095628066752 m3

Plane angle

Plane angle
Name of unit Symbol Definition Relation to SI units
arcminute; MOA ' 60 0.290888×10−3 rad
degree (of arc) ° 1360 of a revolution ≡ π180 rad 17.453293×10−3 rad
radian (SI unit) rad The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius.
One full revolution encompasses 2π radians.

Solid angle

Solid angle
Name of unit Symbol Definition Relation to SI units
spat ≡ 4π sr – The solid angle subtended by a sphere at its centre. 12.56637 sr
square degree deg2; sq.deg.; (°)2 ≡ (π180)2 sr 0.30462×10−3 sr
steradian (SI unit) sr The solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r2.
A sphere subtends 4π sr.
= 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 g0 is used to denote standard gravity in order to avoid confusion with the (upright) g symbol for gram.
Mass
Name of unit Symbol Definition Relation to SI units
atomic mass unit, unified u; AMU Same as dalton (see below) 1.660539040(20)×10−27 kg
atomic unit of mass, electron rest mass me 9.10938291(40)×10−31 kg
bag (coffee)   ≡ 60 kg = 60 kg
bag (Portland cement)   ≡ 94 lb av = 42.63768278 kg
barge   22+12 short ton = 20411.65665 kg
carat kt 3+16 gr = 205.1965483 mg
carat (metric) ct ≡ 200 mg = 200 mg
clove   ≡ 8 lb av = 3.62873896 kg
crith   ≡ mass of 1 L of hydrogen gas at STP ≈ 89.9349 mg
dalton Da 1/12 the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest 1.660538921(73)×10−27 kg
dram (apothecary; troy) dr t ≡ 60 gr = 3.8879346 g
dram (avoirdupois) dr av 27+1132 gr = 1.7718451953125 g
electronvolt eV ≡ 1 eV (energy unit) / c2 = 1.78266184(45)×10−36 kg
gamma γ ≡ 1 μg = 1 μg
grain gr 17000 lb av 64.79891 mg
grave gv grave was the original name of the kilogram ≡ 1 kg
hundredweight (long) long cwt or cwt ≡ 112 lb av = 50.80234544 kg
hundredweight (short); cental sh cwt ≡ 100 lb av = 45.359237 kg
kilogram
(kilogramme)
kg ≈ mass of the prototype near Paris
≈ mass of 1 litre of water
(SI base unit)
kip kip 1000 lb av = 453.59237 kg
mark   ≡ 8 oz t = 248.8278144 g
mite   120 gr = 3.2399455 mg
mite (metric)   120 g = 50 mg
ounce (apothecary; troy) oz t 112 lb t = 31.1034768 g
ounce (avoirdupois) oz av 116 lb = 28.349523125 g
ounce (US food nutrition labelling) oz ≡ 28 g = 28 g
pennyweight dwt; pwt 120 oz t = 1.55517384 g
point   1100 ct = 2 mg
pound (avoirdupois) lb av 0.45359237 kg = 7000 grains 0.45359237 kg
pound (metric)   ≡ 500 g = 500 g
pound (troy) lb t 5760 grains = 0.3732417216 kg
quarter (imperial)   14 long cwt = 2 st = 28 lb av = 12.70058636 kg
quarter (informal)   14 short ton = 226.796185 kg
quarter, long (informal)   14 long ton = 254.0117272 kg
quintal (metric) q ≡ 100 kg = 100 kg
scruple (apothecary) s ap ≡ 20 gr = 1.2959782 g
sheet   1700 lb av = 647.9891 mg
slug; geepound; hyl slug g0 × 1 lb av × 1 s2/ft 14.593903 kg
stone st ≡ 14 lb av = 6.35029318 kg
ton, assay (long) AT ≡ 1 mg × 1 long ton ÷ 1 oz t = 32.6 g
ton, assay (short) AT ≡ 1 mg × 1 short ton ÷ 1 oz t = 29.16 g
ton, long long tn or ton 2240 lb = 1016.0469088 kg
ton, short sh tn 2000 lb = 907.18474 kg
tonne (mts unit) t 1000 kg = 1000 kg
wey   ≡ 252 lb = 18 st = 114.30527724 kg (variants exist)
Zentner Ztr. Definitions vary.

Density

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

Time

Time
Name of unit Symbol Definition Relation to SI units
Atomic unit of time au a0/(αc) 2.418884254×10−17 s
Callippic cycle   ≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d = 2.396736 Gs or 2.3983776 Gs[note 1]
Century c ≡ 100 years (100 a) 3.1556952 Gs[note 2][note 3]
Day d = 24 h = 1440 min = 86.4 ks[note 3]
Day (sidereal) d ≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame) 86.1641 ks
Decade dec ≡ 10 years (10 a) = 315.569520 Ms[note 2][note 3]
Fortnight fn ≡ 2 wk = 1.2096 Ms[note 3]
Helek 11080 h = 3.3 s
Hipparchic cycle   ≡ 4 Callippic cycles - 1 d = 9.593424 Gs
Hour h ≡ 60 min = 3.6 ks[note 3]
Jiffy j 160 s = 16.6 ms
Jiffy (alternative) ja 1100 s = 10 ms
Ke (quarter of an hour)   14 h = 196 d = 15 min = 900 s
Ke (traditional)   1100 d = 14.4 min = 864 s
Lustre; Lustrum   ≡ 5 a of 365 d[note 4] = 157.68 Ms
Metonic cycle; enneadecaeteris   ≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a = 599.616 Ms
Millennium   1000 years (1000 a) 31.556952 Gs[note 2][note 3]
Milliday md 11000 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 = 2.592×106 s[note 3]
Month (Greg. av.) mo = 30.436875 d 2.6297 Ms[note 3]
Month (hollow) mo ≡ 29 d = 2.5056 Ms[note 3]
Month (synodic) mo Cycle time of moon phases ≈ 29.530589 d (average) 2.551 Ms
Octaeteris   = 48 mo (full) + 48 mo (hollow) + 3 mo (full) = 8 a of 365.25 d = 2922 d = 252.4608 Ms[note 3]
Planck time   ≡ (c5)12 5.39116×10−44 s
Second (SI base unit) s ≡ Time of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0 K (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of 299792458 metres. (SI base unit)
Shake   ≡ 10−8 s = 10 ns
Sigma   ≡ 10−6 s = 1 μs
Sothic cycle   1461 a of 365 d = 46.074096 Gs
Svedberg S ≡ 10−13 s = 100 fs
Week wk ≡ 7 d = 168 h = 10080 min = 604.8 ks[note 3]
Year (common) a, y, or yr 365 d = 31.536 Ms[note 3]
Year (Gregorian) a, y, or yr = 365.2425 d average, calculated from common years (365 d) plus leap years (366 d) on most years divisible by 4. See leap year for details. = 31.556952 Ms[note 3]
Year (Julian) a, y, or yr = 365.25 d average, calculated from common years (365 d) plus one leap year (366 d) every four years = 31.5576 Ms
Year (leap) a, y, or yr 366 d = 31.6224 Ms[note 3]
Year (mean tropical) a, y, or yr Conceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, [Converter 1] approximately 365.24219 d, each day being 86400 SI seconds 31.556925 Ms
Year (sidereal) a, y, or yr ≡ Time taken for Sun to return to the same position with respect to the stars of the celestial sphere, approximately 365.256363 d 31.5581497632 Ms
Notes:
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 0.0167 Hz
Cycle per second cps ≡ 1 Hz = 1 cps = 1 Hz
degree per second deg/s ≡ 1 °/s ≡ 1/360 Hz = 0.0027 Hz
hertz (SI unit) Hz ≡ One cycle per second = 1 Hz = 1/s
revolutions per minute rpm ≡ One unit rpm equals one rotation completed around a fixed axis in one minute of time. 0.104719755 rad/s

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

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

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) = 5.08×10−3 m/s2
foot per second squared fps2 ≡ 1 ft/s2 = 3.048×10−1 m/s2
gal; galileo Gal ≡ 1 cm/s2 = 10−2 m/s2
inch per minute per second ipm/s ≡ 1 in/(min⋅s) = 4.23×10−4 m/s2
inch per second squared ips2 ≡ 1 in/s2 = 2.54×10−2 m/s2
knot per second kn/s ≡ 1 kn/s ≈ 5.14×10−1 m/s2
metre per second squared (SI unit) m/s2 ≡ 1 m/s2 = 1 m/s2
mile per hour per second mph/s ≡ 1 mi/(h⋅s) = 4.4704×10−1 m/s2
mile per minute per second mpm/s ≡ 1 mi/(min⋅s) = 26.8224 m/s2
mile per second squared mps2 ≡ 1 mi/s2 = 1.609344×103 m/s2
standard gravity g0 9.80665 m/s2 = 9.80665 m/s2

Force

Force
Name of unit Symbol Definition Relation to SI units
atomic unit of force meα2c2a0 8.23872206×10−8 N
dyne (CGS unit) dyn ≡ g⋅cm/s2 = 10−5 N
kilogram-force; kilopond; grave-force kgf; kp; gvf g0 × 1 kg = 9.80665 N
kip; kip-force kip; kipf; klbf g0 × 1000 lb = 4.4482216152605×103 N
milligrave-force, gravet-force mgvf; gvtf g0 × 1 g = 9.80665 mN
long ton-force tnf[citation needed] g0 × 1 long ton = 9.96401641818352×103 N
newton (SI unit) N A force capable of giving a mass of one kilogram an acceleration of one metre per second per second. = 1 N = 1 kg⋅m/s2
ounce-force ozf g0 × 1 oz = 0.27801385095378125 N
pound-force lbf g0 × 1 lb = 4.4482216152605 N
poundal pdl ≡ 1 lb⋅ft/s2 = 0.138254954376 N
short ton-force tnf[citation needed] g0 × 1 short ton = 8.896443230521×103 N
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 101325 Pa
atmosphere (technical) at ≡ 1 kgf/cm2 = 9.80665×104 Pa
bar bar 100000 Pa ≡ 105 Pa
barye (CGS unit)   ≡ 1 dyn/cm2 = 0.1 Pa
centimetre of mercury cmHg 13595.1 kg/m3 × 1 cm × g0 1.33322×103 Pa
centimetre of water (4 °C) cmH2O ≈ 999.972 kg/m3 × 1 cm × g0 98.0638 Pa
foot of mercury (conventional) ftHg 13595.1 kg/m3 × 1 ft × g0 4.063666×104 Pa
foot of water (39.2 °F) ftH2O ≈ 999.972 kg/m3 × 1 ft × g0 2.98898×103 Pa
inch of mercury (conventional) inHg 13595.1 kg/m3 × 1 in × g0 3.386389×103 Pa
inch of water (39.2 °F) inH2O ≈ 999.972 kg/m3 × 1 in × g0 249.082 Pa
kilogram-force per square millimetre kgf/mm2 ≡ 1 kgf/mm2 = 9.80665×106 Pa
kip per square inch ksi ≡ 1 kipf/sq in 6.894757×106 Pa
long ton per square foot   ≡ 1 long ton × g0 / 1 sq ft 1.0725178011595×105 Pa
micrometre of mercury μmHg 13595.1 kg/m3 × 1 μm × g0 ≈ 0.001 torr 0.1333224 Pa
millimetre of mercury mmHg 13595.1 kg/m3 × 1 mm × g0 ≈ 1 torr 133.3224 Pa
millimetre of water (3.98 °C) mmH2O ≈ 999.972 kg/m3 × 1 mm × g0 = 0.999972 kgf/m2 = 9.80638 Pa
pascal (SI unit) Pa ≡ N/m2 = kg/(m⋅s2) = 1 Pa
pièze (mts unit) pz 1000 kg/m⋅s2 = 103 Pa = 1 kPa
pound per square foot psf ≡ 1 lbf/ft2 47.88026 Pa
pound per square inch psi ≡ 1 lbf/in2 6.894757×103 Pa
poundal per square foot pdl/sq ft ≡ 1 pdl/sq ft 1.488164 Pa
short ton per square foot   ≡ 1 short ton × g0 / 1 sq ft 9.5760518×104 Pa
torr torr 101325760 Pa 133.3224 Pa

Torque or moment of force

Torque
Name of unit Symbol Definition Relation to SI units
pound-force-foot lbf⋅ft g0 × 1 lb × 1 ft = 1.3558179483314004 N⋅m
poundal-ft pdl⋅ft ≡ 1 lb⋅ft2/s2 = 4.21401100938048×10−2 N⋅m
pound force-inch lbf⋅in g0 × 1 lb × 1 in = 0.1129848290276167 N⋅m
kilogram force-meter kgf⋅m g0 × N × m = 9.80665 N⋅m
Newton metre (SI unit) N⋅m ≡ N × m = kg⋅m2/s2 = 1 N⋅m

Energy

Energy
Name of unit Symbol Definition Relation to SI units
barrel of oil equivalent boe 5.8×106 BTU59 °F 6.12×109 J
British thermal unit (ISO) BTUISO 1.0545×103 J = 1.0545×103 J
British thermal unit (International Table) BTUIT = 1.05505585262×103 J
British thermal unit (mean) BTUmean 1.05587×103 J
British thermal unit (thermochemical) BTUth 1.054350×103 J
British thermal unit (39 °F) BTU39 °F 1.05967×103 J
British thermal unit (59 °F) BTU59 °F 1.054804×103 J = 1.054804×103 J
British thermal unit (60 °F) BTU60 °F 1.05468×103 J
British thermal unit (63 °F) BTU63 °F 1.0546×103 J
calorie (International Table) calIT 4.1868 J = 4.1868 J
calorie (mean) calmean 1100 of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm 4.19002 J
calorie (thermochemical) calth ≡ 4.184 J = 4.184 J
Calorie (US; FDA) Cal ≡ 1 kcal = 1000 cal = 4184 J
calorie (3.98 °C) cal3.98 °C 4.2045 J
calorie (15 °C) cal15 °C ≡ 4.1855 J = 4.1855 J
calorie (20 °C) cal20 °C 4.1819 J
Celsius heat unit (International Table) CHUIT ≡ 1 BTUIT × 1 K/°R = 1.899100534716×103 J
cubic centimetre of atmosphere; standard cubic centimetre cc atm; scc ≡ 1 atm × 1 cm3 = 0.101325 J
cubic foot of atmosphere; standard cubic foot cu ft atm; scf ≡ 1 atm × 1 ft3 = 2.8692044809344×103 J
cubic foot of natural gas   1000 BTUIT = 1.05505585262×106 J
cubic yard of atmosphere; standard cubic yard cu yd atm; scy ≡ 1 atm × 1 yd3 = 77.4685209852288×103 J
electronvolt eV e × 1 V 1.602176634×10−19 J
erg (CGS unit) erg ≡ 1 g⋅cm2/s2 = 10−7 J
foot-pound force ft lbf g0 × 1 lb × 1 ft = 1.3558179483314004 J
foot-poundal ft pdl ≡ 1 lb⋅ft2/s2 = 4.21401100938048×10−2 J
gallon-atmosphere (imperial) imp gal atm ≡ 1 atm × 1 gal (imp) = 460.63256925 J
gallon-atmosphere (US) US gal atm ≡ 1 atm × 1 gal (US) = 383.5568490138 J
hartree, atomic unit of energy Eh ≡ meα2c2 (= 2 Ry) 4.359744×10−18 J
horsepower-hour hp⋅h ≡ 1 hp × 1 h = 2.684519537696172792×106 J
inch-pound force in lbf g0 × 1 lb × 1 in = 0.1129848290276167 J
joule (SI unit) J The work done when a force of one newton moves the point of its application a distance of one metre in the direction of the force. = 1 J = 1 m⋅N = 1 kg⋅m2/s2 = 1 C⋅V = 1 W⋅s
kilocalorie; large calorie kcal; Cal 1000 calIT = 4.1868×103 J
kilowatt-hour; Board of Trade Unit kW⋅h; B.O.T.U. ≡ 1 kW × 1 h = 3.6×106 J
litre-atmosphere l atm; sl ≡ 1 atm × 1 L = 101.325 J
quad   ≡ 1015 BTUIT = 1.05505585262×1018 J
rydberg Ry Rc 2.179872×10−18 J
therm (E.C.)   100000 BTUIT = 105.505585262×106 J
therm (US)   100000 BTU59 °F = 105.4804×106 J
thermie th ≡ 1 McalIT = 4.1868×106 J
tonne of coal equivalent TCE ≡ 7 Gcalth = 29.288×109 J
tonne of oil equivalent toe ≡ 10 GcalIT = 41.868×109 J
ton of TNT tTNT ≡ 1 Gcalth = 4.184×109 J
watt hour W⋅h ≡ 1 W × 1 h = 3.6×103 J
watt second W⋅s ≡ 1 J = 1×100 J

Power or heat flow rate

Power
Name of unit Symbol Definition Relation to SI units
atmosphere-cubic centimetre per minute atm ccm[citation needed] ≡ 1 atm × 1 cm3/min = 1.68875×10−3 W
atmosphere-cubic centimetre per second atm ccs[citation needed] ≡ 1 atm × 1 cm3/s = 0.101325 W
atmosphere-cubic foot per hour atm cfh[citation needed] ≡ 1 atm × 1 cu ft/h = 0.79700124704 W
atmosphere-cubic foot per minute atm cfm[citation needed] ≡ 1 atm × 1 cu ft/min = 47.82007468224 W
atmosphere-cubic foot per second atm cfs[citation needed] ≡ 1 atm × 1 cu ft/s = 2.8692044809344×103 W
BTU (International Table) per hour BTUIT/h ≡ 1 BTUIT/h 0.293071 W
BTU (International Table) per minute BTUIT/min ≡ 1 BTUIT/min 17.584264 W
BTU (International Table) per second BTUIT/s ≡ 1 BTUIT/s = 1.05505585262×103 W
calorie (International Table) per second calIT/s ≡ 1 calIT/s = 4.1868 W
erg per second erg/s ≡ 1 erg/s = 10−7 W
foot-pound-force per hour ft⋅lbf/h ≡ 1 ft lbf/h 3.766161×10−4 W
foot-pound-force per minute ft⋅lbf/min ≡ 1 ft lbf/min = 2.259696580552334×10−2 W
foot-pound-force per second ft⋅lbf/s ≡ 1 ft lbf/s = 1.3558179483314004 W
horsepower (boiler) hp ≈ 34.5 lb/h × 970.3 BTUIT/lb 9809.5 W
horsepower (European electrical) hp ≡ 75 kp⋅m/s = 736 W[citation needed]
horsepower (electrical) hp ≡ 746 W = 746 W
horsepower (mechanical) hp ≡ 550 ft⋅lbf/s = 745.69987158227022 W
horsepower (metric) hp or PS ≡ 75 m⋅kgf/s = 735.49875 W
litre-atmosphere per minute L·atm/min ≡ 1 atm × 1 L/min = 1.68875 W
litre-atmosphere per second L·atm/s ≡ 1 atm × 1 L/s = 101.325 W
lusec lusec ≡ 1 L·µmHg/s  1.333×10−4 W
poncelet p ≡ 100 m⋅kgf/s = 980.665 W
square foot equivalent direct radiation sq ft EDR ≡ 240 BTUIT/h 70.337057 W
ton of air conditioning   2000 lb of ice melted / 24 h 3504 W
ton of refrigeration (imperial)   2240 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F 3.938875×103 W
ton of refrigeration (IT)   2000 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F 3.516853×103 W
watt (SI unit) W The power which in one second of time gives rise to one joule of energy. = 1 W = 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 2π 1.05457168×10−34 J⋅s

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) 4.133789×10−4 Pa⋅s
pound per foot second lb/(ft⋅s) ≡ 1 lb/(ft⋅s) 1.488164 Pa⋅s
pound-force second per square foot lbf⋅s/ft2 ≡ 1 lbf⋅s/ft2 47.88026 Pa⋅s
pound-force second per square inch lbf⋅s/in2 ≡ 1 lbf⋅s/in2 6894.757 Pa⋅s

Kinematic viscosity

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

Electric 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. (SI base unit)
electromagnetic unit; abampere (CGS unit) abamp ≘ 10 A = 10 A
esu per second; statampere (CGS unit) esu/s ≘ (10 A⋅cm/s) / c 3.335641×10−10 A

Electric 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 = 1.602176634×10−19 C
coulomb C ≡ charge of exactly 1/(1.602176634×10−19) elementary charges = 1 C = 1 A⋅s
faraday F ≡ 1 mol × NAe 96485.3383 C
milliampere hour mA⋅h ≡ 0.001 A × 1 h = 3.6 C
statcoulomb; franklin; electrostatic unit (CGS unit) statC; Fr; esu ≘ (10 A⋅cm) / c 3.335641×10−10 C

Electric dipole

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

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) = 299.792458 V
volt (SI unit) V The difference in electric potential across two points along a conducting wire carrying one ampere of constant current when the power dissipated between the points equals one watt. = 1 V = 1 W/A = 1 kg⋅m2/(A⋅s3) = 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. = 1 Ω = 1 V/A = 1 kg⋅m2/(A2⋅s3)

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 = 1 A2⋅s4/(kg⋅m2)

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 = 1 kg⋅m2/(A⋅s2)

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 = 1 kg/(A⋅s2)

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 = 1 kg⋅m2/(A⋅s)2

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] × 23
degree Fahrenheit °F [°F] ≡ [°C] × 95 + 32 [K] ≡ ([°F] + 459.67) × 59
degree Newton °N [K] = [°N] × 10033 + 273.15
degree Rankine °R; [°R] ≡ [K] × 95 [K] ≡ [°R] × 5/9
degree Réaumur °Ré [K] = [°Ré] × 54 + 273.15
degree Rømer °Rø [K] = ([°Rø] − 7.5) × 4021 + 273.15
Regulo Gas Mark GM [°F] ≡ [GM] × 25 + 250 [K] ≡ [GM] × 1259 + 394.26
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. (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 0.693147 nat = 1 bit
hartley; ban Hart; ban ≡ ln(10) × nat 2.302585 nat
bit bit; b = 1 bit
nibble ≡ 4 bits = 22 bit
byte B ≡ 8 bits = 23 bit
kilobyte (decimal) kB 1000 B = 8000 bit
kibibyte (kilobyte) KiB; KB 1024 B = 213 bit = 8192 bit

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

Luminous 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 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. (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. 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 10.763910417 cd/m2
candela per square inch cd/in2 ≡ cd/in2 1550.0031 cd/m2
candela per square metre (SI unit); nit (deprecated) cd/m2 ≡ cd/m2 = 1 cd/m2
footlambert fL ≡ (1/π) cd/ft2 3.4262590996 cd/m2
lambert L ≡ (104/π) cd/m2 3183.0988618 cd/m2
stilb (CGS unit) sb ≡ 104 cd/m2 = 104 cd/m2

Luminous 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 = 10.763910417 lx
lumen per square inch lm/in2 ≡ lm/in2 1550.0031 lx
lux (SI unit) lx ≡ lm/m2 = 1 lx = 1 lm/m2
phot (CGS unit) ph ≡ lm/cm2 = 104 lx

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

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

Name of unit Symbol Definition Relation to SI units
roentgen R 1 R ≡ 2.58×10−4 C/kg = 2.58×10−4 C/kg

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 Gy = 1 J/kg = 1 m2⋅s2

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 = 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 = QD

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

1. ^ Béla Bodó; Colin Jones (26 June 2013). Introduction to Soil Mechanics. John Wiley & Sons. pp. 9–. ISBN 978-1-118-55388-6.
2. ^ "Identity property of multiplication". Retrieved 2015-09-09.
3. ^ David V. Chadderton (2004). Building Services Engineering. Taylor & Francis. pp. 33–. ISBN 978-0-415-31535-7.
4. ^ Foot, C. J. (2005). Atomic physics. Oxford University Press. ISBN 978-0-19-850695-9.
5. ^ jobs (September 14, 2012). "The astronomical unit gets fixed : Nature News & Comment". Nature.com. doi:10.1038/nature.2012.11416. S2CID 123424704. Retrieved August 31, 2013. Cite journal requires |journal= (help)
6. ^ "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.
7. Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
8. ^ a b 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.
9. ^ "International Astronomical Union - IAU". www.iau.org.
10. ^ Klein, Herbert Arthur. (1988). The Science of Measurement: a Historical Survey. Mineola, NY: Dover Publications 0-4862-5839-4.
11. ^ a b c The International System of Units, Section 2.1 (8 ed.), Bureau International des Poids et Mesures, 2006, archived from the original on October 1, 2009, retrieved August 26, 2009
12. ^ International System of Units, Archived August 21, 2008, at the Wayback Machine 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 8.
13. ^ Cox, Arthur N., ed. (2000). Allen's Astrophysical Quantities (4th ed.). New York: AIP Press / Springer. Bibcode:2000asqu.book.....C. ISBN 0387987460.
14. ^ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (2nd ed.). Princeton, NJ: Princeton University Press. Bibcode:2008gady.book.....B. ISBN 978-0-691-13026-2.
15. ^ P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
16. ^ a b c Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement. New York: Macmillan 0-312-37026-1. p. 152.
17. ^ a b 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.
18. ^ Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking. (1894). New York: Howard Lockwood. p. 521.
19. Rowlett, Russ (2005), How Many? A Dictionary of Units of Measurement
20. ^ 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.
21. US Code of Federal Regulations, Title 21, Section 101.9, Paragraph (b)(5)(viii), archived from the original on August 13, 2009, retrieved August 29, 2009
22. ^ 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".
23. ^ CODATA Value: atomic unit of mass. (2010). National Institute of Standards and Technology. Retrieved 29 May 2015.
24. ^ The Swiss Federal Office for Metrology gives Zentner on a German language web page "Archived copy". Archived from the original on 2006-09-28. Retrieved 2006-10-09.CS1 maint: archived copy as title (link) and quintal on the English translation of that page "Archived copy". Archived from the original on 2001-03-09. Retrieved 2006-10-09.CS1 maint: archived copy as title (link); the unit is marked "spécifiquement suisse !"
25. ^ a b 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.
26. ^ Richards, E.G. (1998), Mapping Time, Oxford University Press, pp. 94–95, ISBN 0-19-850413-6
27. ^ Steel, Duncan (2000), Marking Time, John Wiley & Sons, p. 46, ISBN 0-471-29827-1
28. ^ "CODATA Value: Planck time". physics.nist.gov. Retrieved 2018-06-20.
29. ^ a b 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.
30. ^ 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.
31. ^ Until 1970 the UK Admiralty (and until 1954 the US) used other definitions of the nautical mile and hence the knot. See also #Length
32. ^ Tom Benson. (2010.) "Mach Number" Archived 2006-04-10 at the Wayback Machine in Beginner's Guide to Aeronautics. NASA.
33. ^ CODATA Value: atomic unit of force. (2006). National Institute of Standards and Technology. Retrieved September 14, 2008.
34. Comité International des Poids et Mesures, Resolution 2, 1946, retrieved August 26, 2009
35. 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.
36. ^ 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.
37. NIST Guide to SI Units, Appendix B.9, retrieved August 27, 2009
38. ^ International System of Units, Archived July 16, 2012, at the Wayback Machine 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 7.
39. ^ a b c d "SI brochure (2019)" (PDF). SI Brochure. BIPM. p. 132. Retrieved May 23, 2019.
40. ^ The NIST Reference on Constants, Units, and Uncertainty, 2006, retrieved August 26, 2009
41. ^ Robert G. Mortimer Physical chemistry,Academic Press, 2000 ISBN 0-12-508345-9, page 677
42. ^ 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.
43. ^ "Mise en pratique" (PDF). BIPM.
44. ^ The NIST Reference on Constants, Units, and Uncertainty, retrieved August 28, 2009
45. ^ 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.
46. ^ a b The International System of Units, Section 2.2.2., Table 3 (8 ed.), Bureau International des Poids et Mesures, 2006, archived from the original on June 18, 2007, retrieved August 27, 2009
47. ^ The NIST Guide to the SI (Special Publication 811), section 5.2, 2008, retrieved August 27, 2009
48. ^ 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.
49. ^ Comité international des poids et mesures, 2002, Recommendation 2, retrieved August 27, 2009
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)