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. 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[1] consists of a fraction in which the denominator is equal to the numerator, but they are in different units. Because of the identity property of multiplication, the value of a number will not change as long as it is multiplied by one.[2] Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.

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.

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. Conversion between units in the metric system can be discerned 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 ≡ 1×10−10 m ≡ 0.1 nm
astronomical unit AU ≡ 149597870700 m ≈ Distance from Earth to Sun ≡ 149597870700 m [3]
barleycorn (H)   =  1⁄3 in (see note above about rounding) ≈ 8.46×10−3 m
bohr, atomic unit of length a0 = Bohr radius of hydrogen ≈ 5.2917721092(17)×10−11 m[4]
cable length (imperial)   ≡ 608 ft ≈ 185.3184 m
cable length (International)   ≡  1⁄10 nmi ≡ 185.2 m
cable length (US)   ≡ 720 ft = 219.456 m
chain (Gunter's; Surveyor's) ch ≡ 66 ft (US) ≡ 4 rods [5] ≈ 20.11684 m
cubit (H)   ≡ Distance from fingers to elbow ≈ 18 in ≈ 0.5 m
ell (H) ell ≡ 45 in [6] (In England usually) = 1.143 m
fathom ftm ≡ 6 ft [6] = 1.8288 m
fermi fm ≡ 1×10−15 m[6] ≡ 1×10−15 m
finger   ≡  7⁄8 in = 0.022225 m
finger (cloth)   ≡  4 1⁄2 in = 0.1143 m
foot (Benoît) (H) ft (Ben) ≈ 0.304799735 m
foot (Cape) (H)   Legally defined as 1.033 English feet in 1859 ≈ 0.314858 m
foot (Clarke's) (H) ft (Cla) ≈ 0.3047972654 m
foot (Indian) (H) ft Ind ≈ 0.304799514 m
foot, metric mf ≡ √ 1⁄10 m ≈ 0.31622776602 m
foot, metric (long) lmf ≡  1⁄3 m ≈ 0.3 m
foot, metric (short) smf ≡ 0.30 m ≡ 0.30 m
foot (International) ft ≡ 0.3048 m ≡  1⁄3 yd ≡ 12 inches ≡ 0.3048 m
foot (Sear's) (H) ft (Sear) ≈ 0.30479947 m
foot (US Survey) ft (US) ≡  1200⁄3937 m [7] ≈ 0.304800610 m
french; charriere F ≡  1⁄3 mm = 0.3 ×10−3 m
furlong fur ≡ 10 chains = 660 ft = 220 yd [6] = 201.168 m
hand   ≡ 4 in [6] ≡ 0.1016 m
inch (International) in ≡ 2.54 cm ≡  1⁄36 yd ≡  1⁄12 ft ≡ 0.0254 m
league (land) lea ≈ 1 hour walk, Currently defined in US as 3 Statute miles,[5] 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 [8] = 9.4607304725808×1015 m
line ln ≡  1⁄12 in [9] = 0.002116 m
link (Gunter's; Surveyor's) lnk ≡  1⁄100 ch [6] ≡ 0.66 ft (US) ≡ 7.92 in ≈ 0.2011684 m
link (Ramsden's; Engineer's) lnk ≡ 1 ft [6] = 0.3048 m
metre (SI base unit)
(meter) 		m ≡ Distance light travels in  1⁄299792458 of a second in vacuum.[10]
≈  1⁄10000000 of the distance from equator to pole.		 ≡ 1 m
mickey   ≡  1⁄200 in = 1.27×10−4 m
micrometre (old: micron) µ ≡ 1×10−6 m
mil; thou mil ≡ 1×10−3 in ≡ 2.54×10−5 m
mil (Sweden and Norway) mil ≡ 10 km = 10000 m
mile (geographical) (H) ≡ 6082 ft = 1853.7936 m
mile (international) mi ≡ 80 chains ≡ 5280 ft ≡ 1760 yd ≡ 1609.344 m
mile (tactical or data) ≡ 6000 ft ≡ 1828.8 m
mile (telegraph) (H) mi ≡ 6087 ft = 1855.3176 m
mile (US Survey) mi ≡ 5280 US Survey feet ≡ (5280 ×  1200⁄3937) m ≈ 1609.347219 m
nail (cloth)   ≡  2 1⁄4 in [6] = 0.05715 m
nanometre nm ≡ 1×10−9 m ≡ 1×10−9 m
nautical league NL; nl ≡ 3 nmi [6] = 5556 m
nautical mile (Admiralty) NM (Adm); nmi (Adm) = 6080 ft = 1853.184 m
nautical mile (international) NM; nmi ≡ 1852 m[11] ≡ 1852 m
nautical mile (US pre 1954) ≡ 1853.248 m ≡ 1853.248 m
pace   ≡ 2.5 ft [6] = 0.762 m
palm   ≡ 3 in [6] = 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[12][13]		 ≈ 30856775814913700 m[14]
pica   ≡ 12 points Dependent on point measures.
point (American, English)[15][16] pt ≡  1⁄72.272 in ≈ 0.000351450 m
point (Didot; European) [16][17] pt ≡  1⁄12 ×  1⁄72 of pied du roi;

After 1878:
≡  5⁄133 cm		 ≈ 0.00037597 m;

After 1878:
≈ 0.00037593985 m
point (PostScript) [15] pt ≡  1⁄72 in = 0.0003527 m
point (TeX) [15] pt ≡  1⁄72.27 in = 0.0003514598 m
quarter   ≡  1⁄4 yd = 0.2286 m
rod; pole; perch (H) rd ≡  16 1⁄2 ft = 5.0292 m
rope (H) rope ≡ 20 ft [6] = 6.096 m
shaku (Japan) ≡ 10/33 m ≈ 0.303 0303 m
smoot   ≡ Height of Oliver R. Smoot.
≡ 5 ft 7 in		 ≡ 1.7018 m
span (H)  　 ≡ 9 in [6] = 0.2286 m
spat [18] ≡ 1×1012 m
stick (H)   ≡ 2 in = 0.0508 m
picometre (old: bicron, stigma) pm ≡ 1×10−12 m
twip twp ≡  1⁄1440 in = 1.7638×10−5 m
x unit; siegbahn xu ≈ 1.0021×10−13 m [6]
yard (International) yd ≡ 0.9144 m [7] ≡ 3 ft ≡ 36 in ≡ 0.9144 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[19]
are a ≡ 100 m2 = 100 m2
barn b ≡ 10−28 m2 = 10−28 m2
barony   ≡ 4000 ac ≈ 1.618742×107 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 ≡  π⁄4 sq in ≈ 5.067075×10−4 m2
circular mil; circular thou circ mil ≡  π⁄4 mil2 ≈ 5.067075×10−10 m2
cord   ≡ 192 bd = 1.48644864 m2
cuerda (PR Survey) cda ≡ 1 cda x 1 cda = 0.971222 acre ≡ 3930.395625 m2
dunam   ≡ 1000 m2 = 1000 m2
guntha (India)   ≡ 121 sq yd ≈ 101.17 m2
hectare ha ≡ 10000 m2 ≡ 10000 m2
hide   ≈ 120 ac (variable) ≈ 5×105 m2
rood ro ≡  1⁄4 ac = 1011.7141056 m2
ping ≡  20⁄11 m ×  20⁄11 m ≈ 3.306 m2
section ≡ 1 mi × 1 mi = 2.589988110336×106 m2
shed   ≡ 10−52 m2 = 10−52 m2
square (roofing) ≡ 10 ft × 10 ft = 9.290304 m2
square chain (international) sq ch ≡ 66 ft × 66 ft =  1⁄10 ac ≡ 404.68564224 m2
square chain (US Survey) sq ch ≡ 66 ft (US) × 66 ft (US) =  1⁄10 US survey acre ≈ 404.6873 m2
square foot sq ft ≡ 1 ft × 1 ft ≡ 9.290304×10−2 m2
square foot (US Survey) sq ft ≡ 1 ft (US) × 1 ft (US) ≈ 9.2903411613275×10−2 m2
square inch sq in ≡ 1 in × 1 in ≡ 6.4516×10−4 m2
square kilometre km2 ≡ 1 km × 1 km = 106 m2
square link (Gunter's)(International) sq lnk ≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft = 4.0468564224×10−2 m2
square link (Gunter's)(US Survey) sq lnk ≡ 1 lnk × 1 lnk ≡ 0.66 ft (US) × 0.66 ft (US) ≈ 4.046872×10−2 m2
square link (Ramsden's) sq lnk ≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft = 0.09290304 m2
square metre (SI unit) m2 ≡ 1 m × 1 m = 1 m2
square mil; square thou sq mil ≡ 1 mil × 1 mil = 6.4516×10−10 m2
square mile sq mi ≡ 1 mi × 1 mi = 2.589988110336×106 m2
square mile (US Survey) sq mi ≡ 1 mi (US) × 1 mi (US) ≈ 2.58999847×106 m2
square rod/pole/perch sq rd ≡ 1 rd × 1 rd = 25.29285264 m2
square yard (International) sq yd ≡ 1 yd × 1 yd ≡ 0.83612736 m2
stremma   ≡ 1000 m2 = 1000 m2
township   ≡ 36 sq mi (US) ≈ 9.323994×107 m2
yardland   ≈ 30 ac ≈ 1.2×105 m2

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 1⁄2 gal (US) = 0.119240471196 m3
board-foot fbm ≡ 144 cu in ≡ 2.359737216×10−3 m3
bucket (imperial) bkt ≡ 4 gal (imp) = 0.01818436 m3
bushel (imperial) bu (imp) ≡ 8 gal (imp) = 0.03636872 m3
bushel (US dry heaped) bu (US) ≡  1 1⁄4 bu (US lvl) = 0.0440488377086 m3
bushel (US dry level) bu (US lvl) ≡ 2150.42 cu in = 0.03523907016688 m3
butt, pipe   ≡ 126 gal (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 cu ft ≡ 1 ft × 1 ft × 1 ft ≡ 0.028316846592 m3
cubic inch cu in ≡ 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 cu yd ≡ 27 cu ft ≡ 0.764554857984 m3
cup (breakfast)   ≡ 10 fl oz (imp) = 284.130625×10−6 m3
cup (Canadian) c (CA) ≡ 8 fl oz (imp) = 227.3045×10−6 m3
cup (metric) c ≡ 250.0×10−6 m3 = 250.0×10−6 m3
cup (US customary) c (US) ≡ 8 US fl oz ≡  1⁄16 gal (US) = 236.5882365×10−6 m3
cup (US food nutrition labeling) c (US) ≡ 240 mL[20] = 2.4×10−4 m3
dash (imperial)   ≡  1⁄384 gi (imp) =  1⁄2 pinch (imp) = 369.961751302083×10−9 m3
dash (US)   ≡  1⁄96 US fl oz =  1⁄2 US pinch = 308.057599609375×10−9 m3
dessertspoon (imperial)   ≡  1⁄12 gi (imp) = 11.8387760416×10−6 m3
drop (imperial) gtt ≡  1⁄288 fl oz (imp) = 98.6564670138×10−9 m3
drop (imperial) (alt) gtt ≡  1⁄1824 gi (imp) ≈ 77.886684×10−9 m3
drop (medical)   ≡  0.9964⁄12 ml = 83.03×10−9 m3
drop (medical)   ≡  1⁄12 ml = 83.3×10−9 m3
drop (metric)   ≡  1⁄20 mL = 50.0×10−9 m3
drop (US) gtt ≡  1⁄360 US fl oz = 82.14869322916×10−9 m3
drop (US) (alt) gtt ≡  1⁄456 US fl oz ≈ 64.85423149671×10−9 m3
drop (US) (alt) gtt ≡  1⁄576 US fl oz ≈ 51.34293326823×10−9 m3
fifth   ≡  1⁄5 US gal = 757.0823568×10−6 m3
firkin   ≡ 9 gal (imp) = 0.04091481 m3
fluid drachm (imperial) fl dr ≡  1⁄8 fl oz (imp) = 3.5516328125×10−6 m3
fluid dram (US); US fluidram fl dr ≡  1⁄8 US fl oz = 3.6966911953125×10−6 m3
fluid scruple (imperial) fl s ≡  1⁄24 fl oz (imp) = 1.18387760416×10−6 m3
gallon (beer) beer gal ≡ 282 cu in = 4.621152048×10−3 m3
gallon (imperial) gal (imp) ≡ 4.54609 L ≡ 4.54609×10−3 m3
gallon (US dry) gal (US) ≡  1⁄8 bu (US lvl) = 4.40488377086×10−3 m3
gallon (US fluid; Wine) gal (US) ≡ 231 cu in ≡ 3.785411784×10−3 m3
gill (imperial); Noggin gi (imp); nog ≡ 5 fl oz (imp) = 142.0653125×10−6 m3
gill (US) gi (US) ≡ 4 US fl oz = 118.29411825×10−6 m3
hogshead (imperial) hhd (imp) ≡ 2 bl (imp) = 0.32731848 m3
hogshead (US) hhd (US) ≡ 2 fl bl (US) = 0.238480942392 m3
jigger (bartending)   ≡  1 1⁄2 US fl oz ≈ 44.36×10−6 m3
kilderkin   ≡ 18 gal (imp) = 0.08182962 m3
lambda λ ≡ 1 mm3 = 1×10−9 m3
last   ≡ 80 bu (imp) = 2.9094976 m3
litre
(liter) 		L ≡ 1 dm3 [21] ≡ 0.001 m3
load   ≡ 50 cu ft = 1.4158423296 m3
minim (imperial) min ≡  1⁄480 fl oz (imp) = 1/60 fl dr (imp) = 59.1938802083×10−9 m3
minim (US) min ≡  1⁄480 US fl oz =  1⁄60 US fl dr = 61.611519921875×10−9 m3
ounce (fluid imperial) fl oz (imp) ≡  1⁄160 gal (imp) ≡ 28.4130625×10−6 m3
ounce (fluid US customary) US fl oz ≡  1⁄128 gal (US) ≡ 29.5735295625×10−6 m3
ounce (fluid US food nutrition labeling) US fl oz ≡ 30 mL[20] ≡ 3×10−5 m3
peck (imperial) pk ≡ 2 gal (imp) = 9.09218×10−3 m3
peck (US dry) pk ≡  1⁄4 US lvl bu = 8.80976754172×10−3 m3
perch per ≡  16 1⁄2 ft ×  1 1⁄2 ft × 1 ft = 0.700841953152 m3
pinch (imperial)   ≡  1⁄192 gi (imp) = 1/16 tsp (imp) = 739.92350260416×10−9 m3
pinch (US)   ≡  1⁄48 US fl oz = 1/16 US tsp = 616.11519921875×10−9 m3
pint (imperial) pt (imp) ≡  1⁄8 gal (imp) = 568.26125×10−6 m3
pint (US dry) pt (US dry) ≡  1⁄64 bu (US lvl) ≡  1⁄8 gal (US dry) = 550.6104713575×10−6 m3
pint (US fluid) pt (US fl) ≡  1⁄8 gal (US) = 473.176473×10−6 m3
pony   ≡  3⁄4 US fl oz = 22.180147171875×10−6 m3
pottle; quartern   ≡  1⁄2 gal (imp) = 80 fl oz (imp) = 2.273045×10−3 m3
quart (imperial) qt (imp) ≡  1⁄4 gal (imp) = 1.1365225×10−3 m3
quart (US dry) qt (US) ≡  1⁄32 bu (US lvl) =  1⁄4 gal (US dry) = 1.101220942715×10−3 m3
quart (US fluid) qt (US) ≡  1⁄4 gal (US fl) = 946.352946×10−6 m3
quarter; pail   ≡ 8 bu (imp) = 0.29094976 m3
register ton   ≡ 100 cu ft = 2.8316846592 m3
sack (imperial); bag   ≡ 3 bu (imp) = 0.10910616 m3
sack (US)   ≡ 3 bu (US lvl) = 0.10571721050064 m3
seam   ≡ 8 bu (US lvl) = 0.28191256133504 m3
shot (US)   usually 1.5 US fl oz[18] ≈ 44×10−6 m3
strike (imperial)   ≡ 2 bu (imp) = 0.07273744 m3
strike (US)   ≡ 2 bu (US lvl) = 0.07047814033376 m3
tablespoon (Australian metric)   ≡ 20.0×10−6 m3
tablespoon (Canadian) tbsp ≡  1⁄2 fl oz (imp) = 14.20653125×10−6 m3
tablespoon (imperial) tbsp ≡  5⁄8 fl oz (imp) = 17.7581640625×10−6 m3
tablespoon (metric)   ≡ 15.0×10−6 m3
tablespoon (US customary) tbsp ≡  1⁄2 US fl oz = 14.78676478125×10−6 m3
tablespoon (US food nutrition labeling) tbsp ≡ 15 mL[20] = 1.5×10−5 m3
teaspoon (Canadian) tsp ≡  1⁄6 fl oz (imp) = 4.735510416×10−6 m3
teaspoon (imperial) tsp ≡  1⁄24 gi (imp) = 5.91938802083×10−6 m3
teaspoon (metric)   ≡ 5.0×10−6 m3 = 5.0×10−6 m3
teaspoon (US customary) tsp ≡  1⁄6 US fl oz = 4.92892159375×10−6 m3
teaspoon (US food nutrition labeling) tsp ≡ 5 mL[20] = 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
angular mil µ ≡  2π⁄6400 rad ≈ 0.981748×10−3 rad
arcminute; MOA ' ≡  1°⁄60 ≈ 0.290888×10−3 rad
arcsecond " ≡  1°⁄3600 ≈ 4.848137×10−6 rad
centesimal minute of arc ' ≡  1⁄100 grad ≈ 0.157080×10−3 rad
centesimal second of arc " ≡  1⁄10000 grad ≈ 1.570796×10−6 rad
degree (of arc) ° ≡  1⁄360 of a revolution ≡  π⁄180 rad ≈ 17.453293×10−3 rad
grad; gradian; gon grad ≡  1⁄400 of a revolution ≡  π⁄200 rad ≡ 0.9° ≈ 15.707963×10−3 rad
octant   ≡ 45° ≈ 0.785398 rad
quadrant   ≡ 90° ≈ 1.570796 rad
radian (SI unit) rad The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians. = 1 rad
sextant   ≡ 60° ≈ 1.047198 rad
sign   ≡ 30° ≈ 0.523599 rad

Solid angle

Solid angle
Name of unit Symbol Definition Relation to SI units
square degree deg2; sq.deg.; (°)2 ≡ ( π⁄180)2 sr ≈ 0.30462×10−3 sr
steradian (SI unit) sr The solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r2. A sphere encompasses 4π sr.[18] = 1 sr

Mass

Notes:

Mass
Name of unit Symbol Definition Relation to SI units
atomic mass unit, unified u; AMU ≈ 1.660538921(73)×10−27 kg[22]
atomic unit of mass, electron rest mass me ≈ 9.10938291(40)×10−31 kg[23]
bag (coffee)   ≡ 60 kg = 60 kg
bag (Portland cement)   ≡ 94 lb av = 42.63768278 kg
barge   ≡  22 1⁄2 short ton = 20411.65665 kg
carat kt ≡  3 1⁄6 gr = 205.1965483 mg
carat (metric) ct ≡ 200 mg = 200 mg
clove   ≡ 8 lb av = 3.62873896 kg
crith   ≡ mass of 1 L of hydrogen gas at STP ≈ 89.9349 mg
dalton Da ≈ 1.660538921(73)×10−27 kg[22]
dram (apothecary; troy) dr t ≡ 60 gr = 3.8879346 g
dram (avoirdupois) dr av ≡  27 11⁄32 gr = 1.7718451953125 g
electronvolt eV ≡ 1 eV (energy unit) / c2 = 1.78266184(45)×10−36 kg[24]
gamma γ ≡ 1 μg = 1 μg
grain gr ≡  1⁄7000 lb av ≡ 64.79891 mg
grave gv. grave was the original name of the kilogram ≡ 1 kg
hundredweight (long) long cwt or cwt ≡ 112 lb av = 50.80234544 kg
hundredweight (short); cental sh cwt ≡ 100 lb av = 45.359237 kg
kilogram
(kilogramme)		 kg ≡ mass of the prototype near Paris (≈ mass of 1 L of water) ≡ 1 kg (SI base unit)[10]
kip kip ≡ 1000 lb av = 453.59237 kg
mark   ≡ 8 oz t = 248.8278144 g
mite   ≡  1⁄20 gr = 3.2399455 mg
mite (metric)   ≡  1⁄20 g = 50 mg
ounce (apothecary; troy) oz t ≡  1⁄12 lb t = 31.1034768 g
ounce (avoirdupois) oz av ≡  1⁄16 lb = 28.349523125 g
ounce (US food nutrition labelling) oz ≡ 28 g[20] = 28 g
pennyweight dwt; pwt ≡  1⁄20 oz t = 1.55517384 g
point   ≡  1⁄100 ct = 2 mg
pound (avoirdupois) lb av ≡ 0.45359237 kg = 7000 grains ≡ 0.45359237 kg
pound (metric)   ≡ 500 g = 500 g
pound (troy) lb t ≡ 5760 grains = 0.3732417216 kg
quarter (imperial)   ≡  1⁄4 long cwt = 2 st = 28 lb av = 12.70058636 kg
quarter (informal)   ≡  1⁄4 short ton = 226.796185 kg
quarter, long (informal)   ≡  1⁄4 long ton = 254.0117272 kg
quintal (metric) q ≡ 100 kg = 100 kg
scruple (apothecary) s ap ≡ 20 gr = 1.2959782 g
sheet   ≡  1⁄700 lb av = 647.9891 mg
slug; geepound; hyl slug ≡ 1 ɡ0 × 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.[18][25]

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/(α·c) ≈ 2.418884254×10−17 s
Callippic cycle   ≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d = 2.396736 Gs or 2.3983776 Gs[note 1]
century c ≡ 100 years (100 a) = 3.1556952 Gs[note 2][note 3]
day d = 24 h = 1440 min = 86.4 ks[note 3]
day (sidereal) d ≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame) ≈ 86.1641 ks
decade dec ≡ 10 years (10 a) = 315.569520 Ms[note 2][note 3]
fortnight fn ≡ 2 wk = 1.2096 Ms[note 3]
helek ≡  1⁄1080 h = 3.3 s
Hipparchic cycle   ≡ 4 Callippic cycles - 1 d = 9.593424 Gs
hour h ≡ 60 min = 3.6 ks[note 3]
jiffy j ≡  1⁄60 s = 16.6 ms
jiffy (alternative) ja ≡  1⁄100 s = 10 ms
ke (quarter of an hour)   ≡  1⁄4 h =  1⁄96 d = 15 min = 900 s
ke (traditional)   ≡  1⁄100 d = 14.4 min = 864 s
lustre; lustrum   ≡ 5 a of 365 d = 157.68 Ms
Metonic cycle; enneadecaeteris   ≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a = 599.616 Ms
millennium   ≡ 1000 years (1000 a) = 31.556952 Gs[note 2][note 3]
milliday md ≡  1⁄1000 d = 86.4 s
minute min ≡ 60 s, due to leap seconds sometimes 59 s or 61 s, = 60 s[note 3]
moment   ≡ 90 s = 90 s
month (full) mo ≡ 30 d[26] = 2.592×106 s[note 3]
month (Greg. av.) mo = 30.436875 d ≈ 2.6297 Ms[note 3]
month (hollow) mo ≡ 29 d[26] = 2.5056 Ms[note 3]
month (synodic) mo Cycle time of moon phases ≈ 29.530589 d (average) ≈ 2.551 Ms
octaeteris   = 48 mo (full) + 48 mo (hollow) + 3 mo (full)[27][28] = 8 a of 365.25 d = 2922 d = 252.4608 Ms[note 3]
Planck time   ≡ ( Gℏ⁄c5) 1⁄2 ≈ 1.351211868×10−43 s
second 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[10] (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 = 460.74096 Ts
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][note 3][29]
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][29]
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[30] ≈ 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. 1 2 3 This is based on the average Gregorian year. See above for definition of year lengths.
  3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Where UTC is observed, the length this unit may increase or decrease depending on the number of leap seconds which occur during the time interval in question.

Frequency

Frequency
Name of unit Symbol Definition Relation to SI units
hertz (SI unit) Hz ≡ Number of cycles 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 to 295 m/s
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. 1 2 The speed of sound varies especially with temperature and pressure from about 1225 km/h (761 mph or 661 kn) in air at sea level to about 1062 km/h (660 mph or 570 kn) at jet altitudes (12200 m or 40000 ft).[31]

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 = 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 ≡ 1 gal/d = 4.381263638×10−8 m3/s
gallon (US fluid) per hour GPH ≡ 1 gal/h = 1.051503273×10−6 m3/s
gallon (US fluid) per minute GPM ≡ 1 gal/min = 6.30901964×10−5 m3/s
litre per minute LPM ≡ 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 ɡ0 ≡ 9.80665 m/s2 = 9.80665 m/s2

Force

Force
Name of unit Symbol Definition Relation to SI units
atomic unit of force ≡  me·α2·c2⁄a0 ≈ 8.23872206×10−8 N[32]
dyne (cgs unit) dyn ≡ g·cm/s2 = 10−5 N
kilogram-force; kilopond; grave-force kgf; kp; Gf ≡ ɡ0 × 1 kg = 9.80665 N
kip; kip-force kip; kipf; klbf ≡ ɡ0 × 1000 lb = 4.4482216152605×103 N
milligrave-force, gravet-force mGf; gf ≡ ɡ0 × 1 g = 9.80665 mN
long ton-force tnf ≡ ɡ0 × 1 short 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.[33] = 1 N = 1 kg·m/s2
ounce-force ozf ≡ ɡ0 × 1 oz = 0.27801385095378125 N
pound-force lbf ≡ ɡ0 × 1 lb = 4.4482216152605 N
poundal pdl ≡ 1 lb·ft/s2 = 0.138254954376 N
short ton-force tnf ≡ ɡ0 × 1 short ton = 8.896443230521×103 N
sthene (mts unit) sn ≡ 1 t·m/s2 = 103 N

See also: Conversion between weight (force) and mass

Pressure or mechanical stress

Pressure
Name of unit Symbol Definition Relation to SI units
atmosphere (standard) atm ≡ 101325 Pa[34]
atmosphere (technical) at ≡ 1 kgf/cm2 = 9.80665×104 Pa[34]
bar bar ≡ 105 Pa
barye (cgs unit)   ≡ 1 dyn/cm2 = 0.1 Pa
centimetre of mercury cmHg ≡ 13595.1 kg/m3 × 1 cm × ɡ0 ≈ 1.33322×103 Pa[34]
centimetre of water (4 °C) cmH2O ≈ 999.972 kg/m3 × 1 cm × ɡ0 ≈ 98.0638 Pa[34]
foot of mercury (conventional) ftHg ≡ 13595.1 kg/m3 × 1 ft × ɡ0 ≈ 4.063666×104 Pa[34]
foot of water (39.2 °F) ftH2O ≈ 999.972 kg/m3 × 1 ft × ɡ0 ≈ 2.98898×103 Pa[34]
inch of mercury (conventional) inHg ≡ 13595.1 kg/m3 × 1 in × ɡ0 ≈ 3.386389×103 Pa[34]
inch of water (39.2 °F) inH2O ≈ 999.972 kg/m3 × 1 in × ɡ0 ≈ 249.082 Pa[34]
kilogram-force per square millimetre kgf/mm2 ≡ 1 kgf/mm2 = 9.80665×106 Pa[34]
kip per square inch ksi ≡ 1 kipf/sq in ≈ 6.894757×106 Pa[34]
long ton per square foot   ≡ 1 long ton × ɡ0 / 1 sq ft ≈ 1.0725178011595×105 Pa
micrometre of mercury mHg ≡ 13595.1 kg/m3 × 1 m × ɡ0 ≈ 0.001 torr ≈ 0.1333224 Pa[34]
millimetre of mercury mmHg ≡ 13595.1 kg/m3 × 1 mm × ɡ0 ≈ 1 torr ≈ 133.3224 Pa[34]
millimetre of water (3.98 °C) mmH2O ≈ 999.972 kg/m3 × 1 mm × ɡ0 = 0.999972 kgf/m2 = 9.80638 Pa
pascal (SI unit) Pa ≡ N/m2 = kg/(m·s2) = 1 Pa[35]
pièze (mts unit) pz ≡ 1000 kg/m·s2 = 103 Pa = 1 kPa
pound per square foot psf ≡ 1 lbf/ft2 ≈ 47.88026 Pa[34]
pound per square inch psi ≡ 1 lbf/in2 ≈ 6.894757×103 Pa[34]
poundal per square foot pdl/sq ft ≡ 1 pdl/sq ft ≈ 1.488164 Pa[34]
short ton per square foot   ≡ 1 short ton × ɡ0 / 1 sq ft ≈ 9.5760518×104 Pa
torr torr ≡  101325⁄760 Pa ≈ 133.3224 Pa[34]

Torque or moment of force

Torque
Name of unit Symbol Definition Relation to SI units
foot-pound force ft·lbf ≡ ɡ0 × 1 lb × 1 ft = 1.3558179483314004 N·m
foot-poundal ft·pdl ≡ 1 lb·ft2/s2 = 4.21401100938048×10−2 N·m
inch-pound force in·lbf ≡ ɡ0 × 1 lb × 1 in = 0.1129848290276167 N·m
metre kilogram-force m·kgf ≡ ɡ0 × 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  1⁄100 of the energy required to warm one gram of air-free water from 0 °C to 100 °C @ 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 ≈ 1.602176565(35)×10−19 J
erg (cgs unit) erg ≡ 1 g·cm2/s2 = 10−7 J
foot-pound force ft lbf ≡ ɡ0 × 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 ≡ me·α2·c2 (= 2 Ry) ≈ 4.359744×10−18 J
horsepower-hour hp·h ≡ 1 hp × 1 h = 2.684519537696172792×106 J
inch-pound force in lbf ≡ ɡ0 × 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.[33] = 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 ≡ R∞·ℎ·c ≈ 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
ton 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

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 = 1.68875×10−3 W
atmosphere-cubic centimetre per second atm ccs ≡ 1 atm × 1 cm3/s = 0.101325 W
atmosphere-cubic foot per hour atm cfh ≡ 1 atm × 1 cu ft/h = 0.79700124704 W
atmosphere-cubic foot per minute atm cfm ≡ 1 atm × 1 cu ft/min = 47.82007468224 W
atmosphere-cubic foot per second atm cfs ≡ 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[36]
horsepower (European electrical) hp ≡ 75 kp·m/s = 736 W
horsepower (electrical) hp ≡ 746 W = 746 W[36]
horsepower (mechanical) hp ≡ 550 ft·lbf/s[36] = 745.69987158227022 W
horsepower (metric) hp or PS ≡ 75 m·kgf/s = 735.49875 W[36]
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 [18] ≈ 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.[33] = 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 ≡ ℏ ≡  ℎ⁄2π ≈ 1.05457168×10−34 J·s[37]

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 ≡ The constant current needed to produce a force of 2 ×10−7 newton per metre between two straight parallel conductors of infinite length and negligible circular cross-section placed one metre apart in a vacuum.[10] = 1 A = 1 C/s
electromagnetic unit; abampere (cgs unit) abamp ≡ 10 A = 10 A
esu per second; statampere (cgs unit) esu/s ≡  0.1 A·m/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 ≈ 1.602176462×10−19 C
coulomb C ≡ The amount of electricity carried in one second of time by one ampere of current.[33] = 1 C = 1 A·s
faraday F ≡ 1 mol × NA·e ≈ 96485.3383 C
milliampere hour mA·h ≡ 0.001 A × 1 h = 3.6 C
statcoulomb; franklin; electrostatic unit (cgs unit) statC; Fr; esu ≡  0.1 A·m⁄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[38]
coulomb meter C·m   = 1 C · 1 m
debye D = 10−10 esu·Å = 3.33564095×10−30 C·m[39]

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.[33] = 1 V = 1 W/A = 1 kg·m2/(A·s3)

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.[33] = 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.[33] = 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[36] = 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.[33] = 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 [40]
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.[33] = 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] ×  2⁄3
degree Fahrenheit °F [°F] ≡ [°C] ×  9⁄5 + 32 [K] ≡ ([°F] + 459.67) ×  5⁄9
degree Newton °N [K] = [°N] ×  100⁄33 + 273.15
degree Rankine °R; [°R] ≡ [K] ×  9⁄5 [K] ≡ [°R] × 5/9
degree Réaumur °Ré [K] = [°Ré] ×  5⁄4 + 273.15
degree Rømer °Rø [K] = ([°Rø] − 7.5) ×  40⁄21 + 273.15
Regulo Gas Mark GM; [°F] ≡ [GM] × 25 + 300 [K] ≡ [GM] ×  125⁄9 + 422.038
kelvin (SI base unit) K ≡  1⁄273.16 of the thermodynamic temperature of the triple point of water.[10] ≡ 1 K

Information entropy

Information entropy
Name of unit Symbol Definition Relation to SI units Relation to bits
SI unit J/K ≡ J/K = 1 J/K
nat; nip; nepit nat ≡ kB = 1.3806505(23)×10−23 J/K
bit; shannon bit; b; Sh ≡ ln(2) × kB = 9.569940(16)×10−24 J/K = 1 bit
ban; hartley ban; Hart ≡ ln(10) × kB = 3.1790653(53)×10−23 J/K
nibble ≡ 4 bits = 3.8279760(64)×10−23 J/K = 22 bit
byte B ≡ 8 bits = 7.655952(13)×10−23 J/K = 23 bit
kilobyte (decimal) kB ≡ 1000 B = 7.655952(13)×10−20 J/K = 8000 bit
kilobyte (kibibyte) KB; KiB ≡ 1024 B = 7.839695(13)×10−20 J/K = 213 bit = 8192 bit

Often, information entropy is measured in shannons, 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. Other times the bit is used as a measure of information entropy and is thus a synonym of shannon.

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.[10] = 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.[41] Approximately 0.981 cd.[18] ≈ 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[18]) 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 ≡ cd·sr = 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

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 ≡ 3.7×1010 Bq[42] = 3.7×1010 Bq
rutherford (H) rd ≡ 1 MBq = 106 Bq

Please note that although becquerel (Bq) and hertz (Hz) both ultimately refer to the same SI base unit (s−1), Hz is used only for periodic phenomena, and Bq is only used for stochastic processes associated with radioactivity.[43]

Radiation – exposure

Radiation - exposure
Name of unit Symbol Definition Relation to SI units
roentgen R 1 R ≡ 2.58×10−4 C/kg[36] = 2.58×10−4 C/kg

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 = 1 m2/s2 [45] = 1 Gy
rad rad ≡ 0.01 Gy[36] = 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

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.[46]

See also

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. ↑ jobs (September 14, 2012). "The astronomical unit gets fixed : Nature News & Comment". Nature.com. doi:10.1038/nature.2012.11416. Retrieved August 31, 2013.
  4. ↑ "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.
  5. 1 2 U.S. National Institute of Standards and Technology Handbook 44 Appendix C - General Tables of Units of Measurement 2013 Edition
  6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
  7. 1 2 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.
  8. ↑ The International Astronomical Union and Astronomical Units
  9. ↑ Klein, Herbert Arthur. (1988). The Science of Measurement: a Historical Survey. Mineola, NY: Dover Publications 0-4862-5839-4.
  10. 1 2 3 4 5 6 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
  11. ↑ 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.
  12. ↑ Cox, Arthur N., ed. (2000). Allen's Astrophysical Quantities (4th ed.). New York: AIP Press / Springer. Bibcode:2000asqu.book.....C. ISBN 0387987460.
  13. ↑ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (2nd ed.). Princeton, NJ: Princeton University Press. Bibcode:2008gady.book.....B. ISBN 978-0-691-13026-2.
  14. ↑ P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
  15. 1 2 3 Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement. New York: Macmillan 0-312-37026-1. p. 152.
  16. 1 2 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.
  17. ↑ Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking. (1894). New York: Howard Lockwood. p. 521.
  18. 1 2 3 4 5 6 7 Rowlett, Russ (2005), How Many? A Dictionary of Units of Measurement
  19. ↑ 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.
  20. 1 2 3 4 5 US Code of Federal Regulations, Title 21, Section 101.9, Paragraph (b)(5)(viii), retrieved August 29, 2009
  21. ↑ 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".
  22. 1 2
  23. ↑ CODATA Value: atomic unit of mass. (2010). National Institute of Standards and Technology. Retrieved 29 May 2015.
  24. ↑ http://physics.nist.gov/cgi-bin/cuu/Value?tevj%7Csearch_for=electronvolt
  25. ↑ The Swiss Federal Office for Metrology gives Zentner on a German language web page and quintal on the English translation of that page ; the unit is marked "spécifiquement suisse !"
  26. 1 2 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.
  27. ↑ Richards, E.G. (1998), Mapping Time, Oxford University Press, pp. 94–95, ISBN 0-19-850413-6
  28. ↑ Steel, Duncan (2000), Marking Time, John Wiley & Sons, p. 46, ISBN 0-471-29827-1
  29. 1 2 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. ↑ Tom Benson. (2010.) "Mach Number" in Beginner's Guide to Aeronautics. NASA.
  32. ↑ CODATA Value: atomic unit of force. (2006). National Institute of Standards and Technology. Retrieved September 14, 2008.
  33. 1 2 3 4 5 6 7 8 9 Comité International des Poids et Mesures, Resolution 2, 1946, retrieved August 26, 2009
  34. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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.
  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, p. 5.
  36. 1 2 3 4 5 6 7 NIST Guide to SI Units, Appendix B.9, retrieved August 27, 2009
  37. ↑ 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.
  38. ↑ The NIST Reference on Constants, Units, and Uncertainty, 2006, retrieved August 26, 2009
  39. ↑ Robert G. Mortimer Physical chemistry,Academic Press, 2000 ISBN 0-12-508345-9, page 677
  40. ↑ 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.
  41. ↑ The NIST Reference on Constants, Units, and Uncertainty, retrieved August 28, 2009
  42. ↑ 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. 1 2 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
  44. ↑ The NIST Guide to the SI (Special Publication 811), section 5.2, 2008, retrieved August 27, 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. 5.
  46. ↑ 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)
Wikibooks has a book on the topic of: FHSST Physics Units:How to Change Units
Wikivoyage has a travel guide for Metric and Imperial equivalents.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.