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 quantity will not change as long as it is multiplied by one.[2] Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.

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

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.

Tables of conversion factors

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

Legend
Symbol Definition
exactly equal
approximately equal to
digits indicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...)
(H) of chiefly historical interest

Length

Length
Name of unit Symbol Definition Relation to SI units
ångströmÅ 1×10−10 m ≡ 0.1 nm
astronomical unitAU 149597870700 m
≈ Distance from Earth to Sun
149597870700 m [4]
attometream 1×10−18 m 1×10−18 m
barleycorn (H)  = 13 in (see note above about rounding) ≈ 8.46×103 m
bohr, atomic unit of lengtha0 = Bohr radius of hydrogen 5.2917721092(17)×10−11 m[5]
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 [6] 20.11684 m
cubit (H)  ≡ Distance from fingers to elbow ≈ 18 in ≈ 0.5 m
ell (H)ell ≡ 45 in [7] (In England usually) = 1.143 m
fathomftm ≡ 6 ft [7] = 1.8288 m
femtometrefm 1×10−15 m 1×10−15 m
fermifm 1×10−15 m[7] 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, metricmf ≡ 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 [8] 0.304800610 m
french; charriereF 13 mm = 0.3 ×103 m
furlongfur ≡ 10 chains = 660 ft = 220 yd [7] = 201.168 m
hand  ≡ 4 in [7] ≡ 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,[6] 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-yearly ≡ Distance light travels in vacuum in 365.25 days [9] 9.4607304725808×1015 m
lineln 112 in [10] = 0.002116 m
link (Gunter's; Surveyor's)lnk 1100 ch [7] ≡ 0.66 ft (US) ≡ 7.92 in 0.2011684 m
link (Ramsden's; Engineer's)lnk ≡ 1 ft [7] = 0.3048 m
metre (SI base unit)
(meter)
m ≡ Distance light travels in 1299792458 of a second in vacuum.[11]
110000000 of the distance from equator to pole.
≡ 1 m
mickey  1200 in = 1.27×10−4 m
micrometre (old: micron)μ; μm 1×10−6 m 1×10−6 m
mil; thoumil 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 [7] = 0.05715 m
nanometrenm 1×10−9 m 1×10−9 m
nautical leagueNL; nl ≡ 3 nmi [7] = 5556 m
nautical mile (Admiralty)NM (Adm); nmi (Adm) = 6080 ft = 1853.184 m
nautical mile (international)NM; nmi 1852 m[12] 1852 m
nautical mile (US pre 1954) ≡ 1853.248 m ≡ 1853.248 m
pace  ≡ 2.5 ft [7] = 0.762 m
palm  ≡ 3 in [7] = 0.0762 m
parsecpc Distant point with a parallax shift of one arc second from a base of one astronomical unit.
648000/π AU[13][14]
30856775814913700 m[15]
pica  ≡ 12 points Dependent on point measures.
picometrepm 1×10−12 m 1×10−12 m
point (American, English)[16][17]pt 172.272 in 0.000351450 m
point (Didot; European) [17][18]pt 112 × 172 of pied du roi;

After 1878:
5133 cm
0.00037597 m;

After 1878:
0.00037593985 m
point (PostScript) [16]pt 172 in = 0.0003527 m
point (TeX) [16]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 [7] = 6.096 m
shaku (Japan) ≡ 10/33 m ≈ 0.303 0303 m
span (H)   ≡ 9 in [7] = 0.2286 m
spat [19] 1×1012 m
stick (H)  ≡ 2 in = 0.0508 m
toise (French, post 1667) (H)T ≡ 27000/13853 m ≈ 1.949 0363 m
twiptwp 11440 in = 1.7638×10−5 m
x unit; siegbahnxu 1.0021×10−13 m [7]
yard (International)yd ≡ 0.9144 m [8] ≡ 3 ft ≡ 36 in ≡ 0.9144 m
yoctometreym 1×10−24 m 1×10−24 m
zeptometrezm 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[20]
area ≡ 100 m2 ≡ 100 m2
barnb ≡ 10−28 m2 ≡ 10−28 m2
barony  4000 ac 1.61874256896×107 m2
boardbd 1 in × 1 ft 7.74192×10−3 m2
boiler horsepower equivalent direct radiationbhp EDR ≡ 1 ft2 × 1 bhp / (240 BTUIT/h) 12.958174 m2
circular inchcirc in π4 sq in 5.067075×10−4 m2
circular mil; circular thoucirc 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
hectareha 10000 m2 10000 m2
hide  ≈ 120 ac (variable) 5×105 m2
roodro 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 footsq 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 inchsq in 1 in × 1 in 6.4516×10−4 m2
square kilometrekm2 ≡ 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 thousq mil ≡ 1 mil × 1 mil = 6.4516×10−10 m2
square milesq 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/perchsq 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-footac 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-barrelbl; 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-footfbm ≡ 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 (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 fathomcu fm ≡ 1 fm × 1 fm × 1 fm = 6.116438863872 m3
cubic footft3 ≡ 1 ft × 1 ft × 1 ft 0.028316846592 m3
cubic inchin3 ≡ 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 milecu mi ≡ 1 mi × 1 mi × 1 mi 4168181825.440579584 m3
cubic yardyd3 ≡ 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[21] = 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)  0.996412 ml = 83.03×10−9 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 fluidramfl 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); Noggingi (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
lambdaλ ≡ 1 mm3 = 1×10−9 m3
last  ≡ 80 bu (imp) = 2.9094976 m3
litre
(liter)
L or l ≡ 1 dm3 [22] ≡ 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[21] 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
perchper 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 [19] = 0.29095 m3
shot (US)  usually 1.5 US fl oz[19] 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)  15.0×10−6 m3
tablespoon (US customary)tbsp 12 US fl oz = 14.78676478125×10−6 m3
tablespoon (US food nutrition labeling)tbsp ≡ 15 mL[21] = 1.5×10−5 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[21] = 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
NATO mil(various) 6400 rad 0.981748×10−3 rad
Swedish streck 6300 rad 0.997302×10−3 rad
milliradianmrad 11000 rad 1×10−3 rad
Warsaw Pact mil 6000 rad 1.047167×10−3 rad
arcminute; MOA' 60 0.290888×10−3 rad
arcsecond" 3600 4.848137×10−6 rad
centesimal minute of arc' 1100 grad 0.157080×10−3 rad
centesimal second of arc" 110000 grad 1.570796×10−6 rad
degree (of arc)° 1360 of a revolution ≡ π180 rad 17.453293×10−3 rad
grad; gradian; gongrad 1400 of a revolution ≡ π200 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
spat ≡ 4π sr[19] – The solid angle subtended by a sphere at its centre. 12.56637 sr
square degreedeg2; 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.[19]

= 1 sr

Mass

Notes:

  • See Weight for detail of mass/weight distinction and conversion.
  • Avoirdupois is a system of mass based on a pound of 16 ounces, while Troy weight is the system of mass where 12 troy ounces equals one troy pound.
  • In this table, the unit gee is used to denote standard gravity in order to avoid confusion with the "g" symbol for grams.
Mass
Name of unit Symbol Definition Relation to SI units
atomic mass unit, unifiedu; AMU Same as dalton (see below) 1.660539040(20)×10−27 kg[6]
atomic unit of mass, electron rest massme 9.10938291(40)×10−31 kg[23]
bag (coffee)  ≡ 60 kg = 60 kg
bag (Portland cement)  ≡ 94 lb av = 42.63768278 kg
barge  22 12 short ton = 20411.65665 kg
caratkt 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
daltonDa 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[6]
dram (apothecary; troy)dr t ≡ 60 gr = 3.8879346 g
dram (avoirdupois)dr av 27 1132 gr = 1.7718451953125 g
electronvolteV ≡ 1 eV (energy unit) / c2 = 1.78266184(45)×10−36 kg[6]
gammaγ ≡ 1 μg = 1 μg
graingr 17000 lb av 64.79891 mg
gravegv. grave was the original name of the kilogram ≡ 1 kg
hundredweight (long)long cwt or cwt ≡ 112 lb av = 50.80234544 kg
hundredweight (short); centalsh cwt ≡ 100 lb av = 45.359237 kg
kilogram
(kilogramme)
kg ≡ mass of the prototype near Paris
≈ mass of 1 litre of water
≡ 1 kg (SI base unit)[11]
kipkip 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[21] = 28 g
pennyweightdwt; 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; hylslug ≡ 1 ɡ0 × 1 lb av × 1 s2/ft 14.593903 kg
stonest ≡ 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, longlong tn or ton 2240 lb = 1016.0469088 kg
ton, shortsh tn 2000 lb = 907.18474 kg
tonne (mts unit)t 1000 kg = 1000 kg
wey  ≡ 252 lb = 18 st = 114.30527724 kg (variants exist)
ZentnerZtr. Definitions vary.[19][24]

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 timeau 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]
Centuryc ≡ 100 years (100 a) = 3.1556952 Gs[note 2][note 3]
Dayd = 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
Decadedec ≡ 10 years (10 a) = 315.569520 Ms[note 2][note 3]
Fortnightfn ≡ 2 wk = 1.2096 Ms[note 3]
Helek 11080 h = 3.3 s
Hipparchic cycle  ≡ 4 Callippic cycles - 1 d = 9.593424 Gs
Hourh ≡ 60 min = 3.6 ks[note 3]
Jiffyj 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]
Millidaymd 11000 d = 86.4 s
Minutemin ≡ 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[25] = 2.592×106 s[note 3]
Month (Greg. av.)mo = 30.436875 d 2.6297 Ms[note 3]
Month (hollow)mo ≡ 29 d[25] = 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)[26][27] = 8 a of 365.25 d = 2922 d = 252.4608 Ms[note 3]
Planck time  ≡ (Gc5)12 5.39116×10−44 s[28]
Seconds 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[11] (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
SvedbergS ≡ 10−13 s = 100 fs
Weekwk ≡ 7 d = 168 h = 10080 min = 604.8 ks[note 3]
Year (common)a, y, or yr365 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 yr366 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. 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 minuteAPM ≡ 1/60 Hz 0.0167 Hz
Cycle per secondcps ≡ 1 Hz = 1 cps = 1 Hz
degree per seconddeg/s ≡ 1 °/s 0.00278 Hz
hertz (SI unit)Hz ≡ Number of cycles per second = 1 Hz = 1/s
Radian per secondrad/s ≡ 1/2π Hz 0.159155 Hz
revolutions per minuterpm ≡ 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 hourfph ≡ 1 ft/h = 8.46×10−5 m/s
foot per minutefpm ≡ 1 ft/min = 5.08×10−3 m/s
foot per secondfps ≡ 1 ft/s = 3.048×10−1 m/s
furlong per fortnight  ≡ furlong/fortnight 1.663095×10−4 m/s
inch per houriph ≡ 1 in/h = 7.05×10−6 m/s
inch per minuteipm ≡ 1 in/min = 4.23×10−4 m/s
inch per secondips ≡ 1 in/s = 2.54×10−2 m/s
kilometre per hourkm/h ≡ 1 km/h = 2.7×10−1 m/s
knotkn ≡ 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 numberM 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 hourmph ≡ 1 mi/h = 0.44704 m/s
mile per minutempm ≡ 1 mi/min = 26.8224 m/s
mile per secondmps ≡ 1 mi/s = 1609.344 m/s
speed of light in vacuumc 299792458 m/s = 299792458 m/s
speed of sound in airs 1225 to 1062 km/h (761–660 mph or 661–574 kn)[note 1] 340 to 295 m/s
Note
  1. 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).[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 = 2.7311773×107 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 = 4.381263638×108 m3/s
gallon (US fluid) per hour GPH ≡ 1 gal/h = 1.051503273×106 m3/s
gallon (US fluid) per minute GPM ≡ 1 gal/min = 6.30901964×10−5 m3/s
litre per minute l/min or L/min ≡ 1 L/min = 1.6×105 m3/s

Acceleration

Acceleration
Name of unit Symbol Definition Relation to SI units
foot per hour per secondfph/s ≡ 1 ft/(h·s) = 8.46×10−5 m/s2
foot per minute per secondfpm/s ≡ 1 ft/(min·s) = 5.08×10−3 m/s2
foot per second squaredfps2 ≡ 1 ft/s2 = 3.048×10−1 m/s2
gal; galileoGal ≡ 1 cm/s2 = 10−2 m/s2
inch per minute per secondipm/s ≡ 1 in/(min·s) = 4.23×10−4 m/s2
inch per second squaredips2 ≡ 1 in/s2 = 2.54×10−2 m/s2
knot per secondkn/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 secondmph/s ≡ 1 mi/(h·s) = 4.4704×10−1 m/s2
mile per minute per secondmpm/s ≡ 1 mi/(min·s) = 26.8224 m/s2
mile per second squaredmps2 ≡ 1 mi/s2 = 1.609344×103 m/s2
standard gravityɡ0 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·c2a0 8.23872206×10−8 N[32]
dyne (cgs unit)dyn ≡ g·cm/s2 = 10−5 N
kilogram-force; kilopond; grave-forcekgf; kp; Gf ɡ0 × 1 kg = 9.80665 N
kip; kip-forcekip; kipf; klbf ɡ0 × 1000 lb = 4.4482216152605×103 N
milligrave-force, gravet-forcemGf; gf ɡ0 × 1 g = 9.80665 mN
long ton-forcetnf ɡ0 × 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.[33] = 1 N = 1 kg·m/s2
ounce-forceozf ɡ0 × 1 oz = 0.27801385095378125 N
pound-forcelbf ɡ0 × 1 lb = 4.4482216152605 N
poundalpdl ≡ 1 lb·ft/s2 = 0.138254954376 N
short ton-forcetnf 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]
barbar 100000 Pa ≡ 105 Pa
barye (cgs unit)  ≡ 1 dyn/cm2 = 0.1 Pa
centimetre of mercurycmHg 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 millimetrekgf/mm2 ≡ 1 kgf/mm2 = 9.80665×106 Pa[34]
kip per square inchksi ≡ 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 mercuryμmHg 13595.1 kg/m3 × 1 μm × ɡ0 ≈ 0.001 torr 0.1333224 Pa[34]
millimetre of mercurymmHg 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 footpsf ≡ 1 lbf/ft2 47.88026 Pa[34]
pound per square inchpsi ≡ 1 lbf/in2 6.894757×103 Pa[34]
poundal per square footpdl/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
torrtorr 101325760 Pa 133.3224 Pa[34]

Torque or moment of force

Torque
Name of unit Symbol Definition Relation to SI units
pound-force-footlbf•ft ɡ0 × 1 lb × 1 ft = 1.3558179483314004 N⋅m
poundal-ftpdl•ft ≡ 1 lb·ft2/s2 = 4.21401100938048×10−2 N⋅m
pound force-inchlbf•in ɡ0 × 1 lb × 1 in = 0.1129848290276167 N⋅m
kilogram force-meterkgf•m 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 equivalentboe 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 centimetrecc atm; scc ≡ 1 atm × 1 cm3 = 0.101325 J
cubic foot of atmosphere; standard cubic footcu 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 yardcu yd atm; scy ≡ 1 atm × 1 yd3 = 77.4685209852288×103 J
electronvolteV e × 1 V 1.602176565(35)×10−19 J
erg (cgs unit)erg ≡ 1 g·cm2/s2 = 10−7 J
foot-pound forceft lbf ɡ0 × 1 lb × 1 ft = 1.3558179483314004 J
foot-poundalft 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 energyEh ≡ me·α2·c2 (= 2 Ry) 4.359744×10−18 J
horsepower-hourhp·h ≡ 1 hp × 1 h = 2.684519537696172792×106 J
inch-pound forcein 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 caloriekcal; Cal 1000 calIT = 4.1868×103 J
kilowatt-hour; Board of Trade UnitkW·h; B.O.T.U. ≡ 1 kW × 1 h = 3.6×106 J
litre-atmospherel atm; sl ≡ 1 atm × 1 L = 101.325 J
quad  ≡ 1015 BTUIT = 1.05505585262×1018 J
rydbergRy R··c 2.179872×10−18 J
therm (E.C.)  100000 BTUIT = 105.505585262×106 J
therm (US)  100000 BTU59 °F = 105.4804×106 J
thermieth ≡ 1 McalIT = 4.1868×106 J
ton of coal equivalentTCE ≡ 7 Gcalth = 29.288×109 J
tonne of oil equivalenttoe ≡ 10 GcalIT = 41.868×109 J
ton of TNTtTNT ≡ 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 minuteatm ccm ≡ 1 atm × 1 cm3/min = 1.68875×10−3 W
atmosphere-cubic centimetre per secondatm ccs ≡ 1 atm × 1 cm3/s = 0.101325 W
atmosphere-cubic foot per houratm cfh ≡ 1 atm × 1 cu ft/h = 0.79700124704 W
atmosphere-cubic foot per minuteatm cfm ≡ 1 atm × 1 cu ft/min = 47.82007468224 W
atmosphere-cubic foot per secondatm cfs ≡ 1 atm × 1 cu ft/s = 2.8692044809344×103 W
BTU (International Table) per hourBTUIT/h ≡ 1 BTUIT/h 0.293071 W
BTU (International Table) per minuteBTUIT/min ≡ 1 BTUIT/min 17.584264 W
BTU (International Table) per secondBTUIT/s ≡ 1 BTUIT/s = 1.05505585262×103 W
calorie (International Table) per secondcalIT/s ≡ 1 calIT/s = 4.1868 W
erg per seconderg/s ≡ 1 erg/s = 10−7 W
foot-pound-force per hourft·lbf/h ≡ 1 ft lbf/h 3.766161×10−4 W
foot-pound-force per minuteft·lbf/min ≡ 1 ft lbf/min = 2.259696580552334×10−2 W
foot-pound-force per secondft·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 minuteL·atm/min ≡ 1 atm × 1 L/min = 1.68875 W
litre-atmosphere per secondL·atm/s ≡ 1 atm × 1 L/s = 101.325 W
luseclusec ≡ 1 L·µmHg/s [19] 1.333×10−4 W
ponceletp ≡ 100 m·kgf/s = 980.665 W
square foot equivalent direct radiationsq 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 actionau 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 hourlb/(ft·h) ≡ 1 lb/(ft·h) 4.133789×10−4 Pa·s
pound per foot secondlb/(ft·s) ≡ 1 lb/(ft·s) 1.488164 Pa·s
pound-force second per square footlbf·s/ft2 ≡ 1 lbf·s/ft2 47.88026 Pa·s
pound-force second per square inchlbf·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 secondft2/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 ×107 newton per metre between two straight parallel conductors of infinite length and negligible circular cross-section placed one metre apart in a vacuum.[11] = 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/sc 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 chargeau e 1.602176462×10−19 C
coulombC ≡ The amount of electricity carried in one second of time by one ampere of current.[33] = 1 C = 1 A·s
faradayF ≡ 1 mol × NA·e 96485.3383 C
milliampere hourmA·h ≡ 0.001 A × 1 h = 3.6 C
statcoulomb; franklin; electrostatic unit (cgs unit)statC; Fr; esu 0.1 A·mc 3.335641×10−10 C

Electric dipole

Electric dipole
Name of unit Symbol Definition Relation to SI units
atomic unit of electric dipole momentea0   8.47835281×10−30 C·m[38]
coulomb meterC·m   = 1 C · 1 m
debyeD = 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] × 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 MarkGM [°F] ≡ [GM] × 25 + 300 [K] ≡ [GM] × 1259 + 422.038
kelvin (SI base unit)K 1273.16 of the thermodynamic temperature of the triple point of water.[11] ≡ 1 K

Information entropy

Information entropy
Name of unit Symbol Definition Relation to SI units Relation to bits
natural unit of information; nip; nepitnat
shannon; bitSh; bit; b ≡ ln(2) × nat 0.693147 nat = 1 bit
hartley; banHart; ban ≡ ln(10) × nat 2.302585 nat
nibble ≡ 4 bits = 22 bit
byteB ≡ 8 bits = 23 bit
kilobyte (decimal)kB 1000 B = 8000 bit
kilobyte (kibibyte)KB; KiB 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); 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.[11] = 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.[19] ≈ 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[19]) 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
curieCi 3.7×1010 Bq[42] = 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.[43]

Radiation – exposure

Radiation - exposure
Name of unit Symbol Definition Relation to SI units
roentgenR 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
radrad ≡ 0.01 Gy[36] = 0.01 Gy

Radiation – equivalent dose

Radiation - equivalent dose
Name of unit Symbol Definition Relation to SI units
Röntgen equivalent manrem ≡ 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. David V. Chadderton (2004). Building Services Engineering. Taylor & Francis. pp. 33–. ISBN 978-0-415-31535-7.
  4. jobs (September 14, 2012). "The astronomical unit gets fixed : Nature News & Comment". Nature.com. doi:10.1038/nature.2012.11416. Retrieved August 31, 2013.
  5. "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.
  6. "NIST - National Institute of Standards and Technology". NIST.
  7. Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
  8. 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. 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. Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement. New York: Macmillan 0-312-37026-1. p. 152.
  17. 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. 142150.
  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. 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. 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" Archived 2006-04-10 at the Wayback Machine 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. Comité International des Poids et Mesures, Resolution 2, 1946, retrieved August 26, 2009
  34. 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. 5768.
  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. 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. 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)
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.