Conversion of units

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

Contents

Techniques

Process overview

The process of conversion depends on the specific situation and the intended purpose. This may be governed by regulation, contract, technical specifications or other published standards. Engineering judgment may include such factors as:

Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement. This is sometimes called soft conversion. It does not involve changing the physical configuration of the item being measured.

By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system. It sometimes involves a slightly different configuration, or size substitution, of the item.[ clarification needed ] Nominal values are sometimes allowed and used.

Conversion factors

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

Calculation involving non-SI Units

In the cases where non-SI units are used, the numerical calculation of a formula can be done by first working out the pre-factor, and then plug in the numerical values of the given/known quantities.

For example, in the study of Bose–Einstein condensate, [4] atomic mass m is usually given in daltons, instead of kilograms, and chemical potential μ is often given in Boltzmann constant times nanokelvin. The condensate's healing length is given by:

For a 23Na condensate with chemical potential of (Boltzmann constant times) 128 nK, the calculation of healing length (in microns) can be done in two steps:

Calculate the pre-factor

Assume that this gives

which is our pre-factor.

Calculate the numbers

Now, make use of the fact that . With , .

This method is especially useful for programming and/or making a worksheet, where input quantities are taking multiple different values; For example, with the pre-factor calculated above, it's very easy to see that the healing length of 174Yb with chemical potential 20.3 nK is .

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
SymbolDefinition
exactly equal
approximately equal to
digitsindicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...)
(H)of chiefly historical interest

Length

Length
Name of unitSymbolDefinitionRelation to SI units
ångström Å1×10−10 m≡ 0.1 nm
astronomical unit au149597870700 m
≈ Distance from Earth to Sun
149597870700 m [5]
attometre am1×10−18 m1×10−18 m
barleycorn (H) = 13 in (see note above about rounding)≈ 8.46×103 m
bohr, atomic unit of length a0= Bohr radius of hydrogen5.2917721092(17)×10−11 m [6]
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 [7] 20.11684 m
cubit (H) ≡ Distance from fingers to elbow ≈ 18 in≈ 0.5 m
ell (H)ell≡ 45 in [8] (In England usually)= 1.143 m
fathom ftm≡ 6 ft [8] = 1.8288 m
femtometre fm1×10−15 m1×10−15 m
fermi fm1×10−15 m [8] 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 18590.314858 m
foot (Clarke's) (H)ft (Cla)0.3047972654 m
foot (Indian) (H)ft Ind0.304799514 m
foot, metric mf≡ 300 mm≡ 0.3 m
foot, metric (Mesures usuelles) (H)13 m≡ 0.3 m
foot (International)ft≡ 0.3048 m ≡ 13 yd ≡ 12 inches≡ 0.3048 m
foot (Sear's) (H)ft (Sear)0.30479947 m
foot (US Survey)ft (US)12003937 m [9] 0.304800610 m
french; charriereF13 mm= 0.3×103 m
furlong fur≡ 10 chains = 660 ft = 220 yd [8] = 201.168 m
hand  ≡ 4 in [8] ≡ 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, [7] but historically varied from 2 to 9 km4828 m
light-day  ≡ 24 light-hours2.59020683712×1013 m
light-hour  ≡ 60 light-minutes1.0792528488×1012 m
light-minute  ≡ 60 light-seconds1.798754748×1010 m
light-second  ≡ Distance light travels in one second in vacuum299792458 m
light-year ly≡ Distance light travels in vacuum in 365.25 days [10] 9.4607304725808×1015 m
line ln112 in [11] = 0.002116 m
link (Gunter's; Surveyor's)lnk1100 ch [8] ≡ 0.66 ft (US) ≡ 7.92 in0.2011684 m
link (Ramsden's; Engineer's)lnk≡ 1 ft [8] = 0.3048 m
metre (SI base unit)
(meter)
m≡ Distance light travels in 1299792458 of a second in vacuum. [12]
110000000 of the distance from equator to pole.
(SI base unit)
mickey 1200 in= 1.27×10−4 m
micrometre (old: micron)μ; μm1×10−6 m1×10−6 m
mil; thou mil1×10−3 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 yd1609.344 m
mile (tactical or data)6000 ft1828.8 m
mile (telegraph) (H)mi6087 ft= 1855.3176 m
mile (US Survey)mi5280 US Survey feet ≡ (5280 × 12003937) m1609.347219 m
nail (cloth) 2 14 in [8] = 0.05715 m
nanometre nm1×10−9 m1×10−9 m
nautical leagueNL; nl≡ 3 nmi [8] = 5556 m
nautical mile (Admiralty)NM (Adm); nmi (Adm)= 6080 ft= 1853.184 m
nautical mile (international)NM; nmi1852 m [13] 1852 m
nautical mile (US pre 1954)≡ 1853.248 m≡ 1853.248 m
pace ≡ 2.5 ft [8] = 0.762 m
palm  ≡ 3 in [8] = 0.0762 m
parsec pcDistant point with a parallax shift of one arc second from a base of one astronomical unit.
648000/π AU [14] [15]
30856775814913700 m [16]
pica  ≡ 12 pointsDependent on point measures.
picometre pm1×10−12 m1×10−12 m
point (American, English) [17] [18] pt172.272 in 0.000351450 m
point (Didot; European) [18] [19] pt112 × 172 of pied du roi;

After 1878:
5133 cm
0.00037597 m;

After 1878:
0.00037593985 m
point (PostScript) [17] pt172 in = 0.0003527 m
point (TeX) [17] pt172.27 in = 0.0003514598 m
quarter 14 yd= 0.2286 m
rod; pole; perch (H)rd16 12 ft= 5.0292 m
rope (H)rope≡ 20 ft [8] = 6.096 m
shaku (Japan)≡ 10/33 m≈ 0.303 0303 m
span (H) ≡ 9 in [8] = 0.2286 m
spat [20] 1×1012 m
stick (H) ≡ 2 in= 0.0508 m
toise (French, post 1667) (H)T≡ 27000/13853 m≈ 1.949 0363 m
twip twp11440 in= 1.7638×10−5 m
x unit; siegbahnxu1.0021×10−13 m [8]
yard (International)yd≡ 0.9144 m [9] ≡ 3 ft ≡ 36 in≡ 0.9144 m
yoctometre ym1×10−24 m1×10−24 m
zeptometre zm1×10−21 m1×10−21 m

Area

Area
Name of unitSymbolDefinitionRelation to SI units
acre (international)ac1 ch × 10 ch = 4840 sq yd4046.8564224 m2
acre (US survey)ac≡ 10 sq ch = 4840 sq yd, also 43560 sq ft4046.873 m2 [21]
are a≡ 100 m2≡ 100 m2
barn b≡ 10−28 m2≡ 10−28 m2
barony 4000 ac1.61874256896×107 m2
boardbd1 in × 1 ft7.74192×10−3 m2
boiler horsepower equivalent direct radiationbhp EDR≡ 1 ft2 × 1 bhp / (240 BTUIT/h)12.958174 m2
circular inch circ inπ4 sq in5.067075×10−4 m2
circular mil; circular thoucirc milπ4 mil25.067075×10−10 m2
cord ≡ 192 bd1.48644864 m2
cuerda (PR Survey)cda≡ 1 cda x 1 cda = 0.971222 acre3930.395625 m2
dunam  1000 m21000 m2
guntha (India) ≡ 121 sq yd≈ 101.17 m2
hectare ha10000 m210000 m2
hide  ≈ 120 ac (variable)5×105 m2
roodro14 ac= 1011.7141056 m2
ping 2011 m × 2011 m3.306 m2
section1 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 ch66 ft × 66 ft = 110 ac404.68564224 m2
square chain (US Survey)sq ch66 ft (US) × 66 ft (US) = 110 US survey acre404.6873 m2
square foot sq ft1 ft × 1 ft9.290304×10−2 m2
square foot (US Survey)sq ft1 ft (US) × 1 ft (US)9.2903411613275×10−2 m2
square inch sq in1 in × 1 in6.4516×10−4 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 lnk1 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 mile sq mi≡ 1 mi × 1 mi2.589988110336×106 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 yd0.83612736 m2
stremma  1000 m2= 1000 m2
township  ≡ 36 sq mi (US)9.323994×107 m2
yardland  ≈ 30 ac1.2×105 m2

Volume

Volume
Name of unitSymbolDefinitionRelation 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-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-foot bdft≡ 144 cu in2.359737216×10−3 m3
bucket (imperial)bkt≡ 4 gal (imp)= 0.01818436 m3
bushel (imperial)bu (imp)≡ 8 gal (imp)= 0.03636872 m3
bushel (US dry heaped)bu (US)1 14 bu (US lvl)= 0.0440488377086 m3
bushel (US dry level)bu (US lvl)2150.42 cu in= 0.03523907016688 m3
butt, pipe ≡ 126 gal (US) (wine)= 0.476961884784 m3
coomb  ≡ 4 bu (imp)= 0.14547488 m3
cord (firewood) 8 ft × 4 ft × 4 ft= 3.624556363776 m3
cord-foot ≡ 16 cu ft= 0.453069545472 m3
cubic fathom cu fm≡ 1 fm × 1 fm × 1 fm= 6.116438863872 m3
cubic foot ft3≡ 1 ft × 1 ft × 1 ft0.028316846592 m3
cubic inch in3≡ 1 in × 1 in × 1 in16.387064×10−6 m3
cubic metre (SI unit)m3≡ 1 m × 1 m × 1 m≡ 1 m3
cubic mile cu mi≡ 1 mi × 1 mi × 1 mi4168181825.440579584 m3
cubic yard yd3≡ 27 cu ft0.764554857984 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)c250.0×10−6 m3250.0×10−6 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 [22] = 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)gtt1288 fl oz (imp)= 98.6564670138×10−9 m3
drop (imperial) (alt)gtt11824 gi (imp)77.886684×10−9 m3
drop (medical) 112 mL= 83.3×10−9 m3
drop (metric) 120 mL= 50.0×10−9 m3
drop (US)gtt1360 US fl oz= 82.14869322916×10−9 m3
drop (US) (alt)gtt1456 US fl oz64.85423149671×10−9 m3
drop (US) (alt)gtt1576 US fl oz51.34293326823×10−9 m3
fifth 15 US gal= 757.0823568×10−6 m3
firkin  ≡ 9 gal (imp)= 0.04091481 m3
fluid drachm (imperial)fl dr18 fl oz (imp)= 3.5516328125×10−6 m3
fluid dram (US); US fluidramfl dr18 US fl oz= 3.6966911953125×10−6 m3
fluid scruple (imperial)fl s124 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 L4.54609×10−3 m3
gallon (US dry)gal (US)18 bu (US lvl)= 4.40488377086×10−3 m3
gallon (US fluid; Wine)gal (US)≡ 231 cu in3.785411784×10−3 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 oz44.36×10−6 m3
kilderkin  ≡ 18 gal (imp)= 0.08182962 m3
lambda λ≡ 1 mm3= 1×10−9 m3
last  ≡ 80 bu (imp)= 2.9094976 m3
litre
(liter)
L or l≡ 1 dm3 [23] ≡ 0.001 m3
load ≡ 50 cu ft= 1.4158423296 m3
minim (imperial)min1480 fl oz (imp) = 1/60 fl dr (imp)= 59.1938802083×10−9 m3
minim (US)min1480 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 oz1128 gal (US)29.5735295625×10−6 m3
ounce (fluid US food nutrition labeling)US fl oz≡ 30 mL [22] 3×10−5 m3
peck (imperial)pk≡ 2 gal (imp)= 9.09218×10−3 m3
peck (US dry)pk14 US lvl bu= 8.80976754172×10−3 m3
perch per16 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 [20] = 0.29095 m3
shot (US) usually 1.5 US fl oz [20] 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)tbsp12 fl oz (imp)= 14.20653125×10−6 m3
tablespoon (imperial)tbsp58 fl oz (imp)= 17.7581640625×10−6 m3
tablespoon (metric) 15×10−6 m3
tablespoon (US customary)tbsp12 US fl oz= 14.78676478125×10−6 m3
tablespoon (US food nutrition labeling)tbsp≡ 15 mL [22] = 15×10−6 m3
teaspoon (Canadian)tsp16 fl oz (imp)= 4.735510416×10−6 m3
teaspoon (imperial)tsp124 gi (imp)= 5.91938802083×10−6 m3
teaspoon (metric) 5.0×10−6 m35.0×10−6 m3
teaspoon (US customary)tsp16 US fl oz= 4.92892159375×10−6 m3
teaspoon (US food nutrition labeling)tsp≡ 5 mL [22] = 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 unitSymbolDefinitionRelation to SI units
NATO mil (various)6400 rad0.981748×10−3 rad
Swedish streck 6300 rad0.997302×10−3 rad
milliradian mrad11000 rad1×10−3 rad
Warsaw Pact mil 6000 rad1.047167×10−3 rad
arcminute; MOA'600.290888×10−3 rad
arcsecond "36004.848137×10−6 rad
centesimal minute of arc '1100 grad0.157080×10−3 rad
centesimal second of arc "110000 grad1.570796×10−6 rad
degree (of arc) °1360 of a revolution ≡ π180 rad17.453293×10−3 rad
grad; gradian; gongrad1400 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)radThe 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 unitSymbolDefinitionRelation to SI units
spat ≡ 4π sr [20] – The solid angle subtended by a sphere at its centre.12.56637 sr
square degree deg2; sq.deg.; (°)2≡ (π180)2 sr0.30462×10−3 sr
steradian (SI unit)srThe 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. [20]
= 1 sr

Mass

Notes:

Mass
Name of unitSymbolDefinitionRelation to SI units
atomic mass unit, unified u; AMUSame as dalton (see below)1.660539040(20)×10−27 kg [7]
atomic unit of mass, electron rest massme9.10938291(40)×10−31 kg [24]
bag (coffee) ≡ 60 kg= 60 kg
bag (Portland cement) ≡ 94 lb av= 42.63768278 kg
barge 22 12 short ton= 20411.65665 kg
carat kt3 16 gr= 205.1965483 mg
carat (metric)ct≡ 200 mg= 200 mg
clove  ≡ 8 lb av= 3.62873896 kg
crith ≡ mass of 1 L of hydrogen gas at STP ≈ 89.9349 mg
dalton Da1/12 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 [7]
dram (apothecary; troy)dr t≡ 60 gr= 3.8879346 g
dram (avoirdupois)dr av27 1132 gr= 1.7718451953125 g
electronvolt eV≡ 1 eV (energy unit) / c 2= 1.78266184(45)×10−36 kg [7]
gammaγ≡ 1 μg= 1 μg
grain gr17000 lb av64.79891 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); centalsh cwt≡ 100 lb av= 45.359237 kg
kilogram
(kilogramme)
kg≈ mass of the prototype near Paris
≈ mass of 1 litre of water
(SI base unit) [12]
kip kip1000 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 t112 lb t= 31.1034768 g
ounce (avoirdupois)oz av116 lb= 28.349523125 g
ounce (US food nutrition labelling)oz≡ 28 g [22] = 28 g
pennyweight dwt; pwt120 oz t= 1.55517384 g
point  1100 ct= 2 mg
pound (avoirdupois) lb av0.45359237 kg = 7000 grains0.45359237 kg
pound (metric)  ≡ 500 g= 500 g
pound (troy) lb t5760 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/ft14.593903 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 ton2240 lb= 1016.0469088 kg
ton, short sh tn2000 lb= 907.18474 kg
tonne (mts unit)t1000 kg= 1000 kg
wey  ≡ 252 lb = 18 st= 114.30527724 kg (variants exist)
ZentnerZtr.Definitions vary. [20] [25]

Density

Density
Name of unitSymbolDefinitionRelation to SI units
gram per millilitreg/mL≡ g/mL= 1000 kg/m3
kilogram per cubic metre (SI unit)kg/m3≡ kg/m3= 1 kg/m3
kilogram per litrekg/L≡ kg/L= 1000 kg/m3
ounce (avoirdupois) per cubic footoz/ft3≡ oz/ft31.001153961 kg/m3
ounce (avoirdupois) per cubic inchoz/in3≡ oz/in31.729994044×103 kg/m3
ounce (avoirdupois) per gallon (imperial)oz/gal≡ oz/gal6.236023291 kg/m3
ounce (avoirdupois) per gallon (US fluid)oz/gal≡ oz/gal7.489151707 kg/m3
pound (avoirdupois) per cubic footlb/ft3≡ lb/ft316.01846337 kg/m3
pound (avoirdupois) per cubic inchlb/in3≡ lb/in32.767990471×104 kg/m3
pound (avoirdupois) per gallon (imperial)lb/gal≡ lb/gal99.77637266 kg/m3
pound (avoirdupois) per gallon (US fluid)lb/gal≡ lb/gal119.8264273 kg/m3
slug per cubic footslug/ft3≡ slug/ft3515.3788184 kg/m3

Time

Time
Name of unitSymbolDefinitionRelation to SI units
Atomic unit of time aua0/(αc)2.418884254×10−17 s
Callippic cycle  ≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d= 2.396736 Gs or 2.3983776 Gs [note 1]
Century c≡ 100 years (100 a)= 3.1556952 Gs [note 2] [note 3]
Day d= 24 h = 1440 min= 86.4 ks [note 3]
Day (sidereal)d≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame)86.1641 ks
Decade dec≡ 10 years (10 a)= 315.569520 Ms [note 2] [note 3]
Fortnight fn≡ 2 wk= 1.2096 Ms [note 3]
Helek 11080 h= 3.3 s
Hipparchic cycle  ≡ 4 Callippic cycles - 1 d= 9.593424 Gs
Hour h≡ 60 min= 3.6 ks [note 3]
Jiffy j160 s= 16.6 ms
Jiffy (alternative)ja1100 s= 10 ms
Ke (quarter of an hour) 14 h = 196 d = 15 min= 900 s
Ke (traditional) 1100 d = 14.4 min= 864 s
Lustre; Lustrum ≡ 5 a of 365 d [note 4] = 157.68 Ms
Metonic cycle; enneadecaeteris ≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a= 599.616 Ms
Millennium  1000 years (1000 a)= 31.556952 Gs [note 2] [note 3]
Milliday md11000 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 d2.6297 Ms [note 3]
Month (hollow)mo≡ 29 d [26] = 2.5056 Ms [note 3]
Month (synodic)moCycle 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  ≡ ( G c 5)125.39116×10−44 s [29]
Second (SI base unit)s≡ Time of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0 K [12] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of 299792458 metres.(SI base unit)
Shake  ≡ 10−8 s= 10 ns
Sigma ≡ 10−6 s= 1 μs
Sothic cycle  1461 a of 365 d= 46.074096 Gs
Svedberg S≡ 10−13 s= 100 fs
Week wk≡ 7 d = 168 h = 10080 min= 604.8 ks [note 3]
Year (common)a, y, or yr365 d= 31.536 Ms [note 3] [30]
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] [30]
Year (mean tropical) a, y, or yrConceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, [Converter 1] approximately 365.24219 d, each day being 86400 SI seconds [31] 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 d31.5581497632 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 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 unitSymbolDefinitionRelation to SI units
Actions per minuteAPM≡ 1/60 Hz0.0167 Hz
Cycle per second cps≡ 1 Hz= 1 cps = 1 Hz
degree per seconddeg/s≡ 1 °/s ≡ 1/360 Hz= 0.0027 Hz
hertz (SI unit)Hz≡ One cycle per second= 1 Hz = 1/s
Radian per second rad/s≡ 1/(2π) Hz0.159155 Hz
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 unitSymbolDefinitionRelation 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/fortnight1.663095×10−4 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 [32] = 0.514773 m/s
mach number MRatio of the speed to the speed of sound [note 1] in the medium (unitless).≈ 340 m/s in air at sea level
≈ 295 m/s in air at jet altitudes
metre per second (SI unit)m/s≡ 1 m/s= 1 m/s
mile per hour mph≡ 1 mi/h= 0.44704 m/s
mile per minute mpm≡ 1 mi/min= 26.8224 m/s
mile per second mps≡ 1 mi/s= 1609.344 m/s
speed of light in vacuumc299792458 m/s= 299792458 m/s
speed of sound in airs1225 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 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). [33]

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 unitSymbolDefinitionRelation to SI units
cubic foot per minuteCFM[ citation needed ]≡ 1 ft3/min= 4.719474432×10−4 m3/s
cubic foot per secondft3/s≡ 1 ft3/s= 0.028316846592 m3/s
cubic inch per minutein3/min≡ 1 in3/min= 2.7311773×107 m3/s
cubic inch per secondin3/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 dayGPD[ citation needed ]≡ 1 gal/d= 4.381263638×108 m3/s
gallon (US fluid) per hourGPH[ citation needed ]≡ 1 gal/h= 1.051503273×106 m3/s
gallon (US fluid) per minuteGPM[ citation needed ]≡ 1 gal/min= 6.30901964×10−5 m3/s
litre per minutel/min or L/min≡ 1 L/min= 1.6×105 m3/s

Acceleration

Acceleration
Name of unitSymbolDefinitionRelation 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 squaredfps2≡ 1 ft/s2= 3.048×10−1 m/s2
gal; galileoGal≡ 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 squaredips2≡ 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 squaredmps2≡ 1 mi/s2= 1.609344×103 m/s2
standard gravity ɡ09.80665 m/s2= 9.80665 m/s2

Force

Force
Name of unitSymbolDefinitionRelation to SI units
atomic unit of force meα 2c 2 a0 8.23872206×10−8 N [34]
dyne (cgs unit)dyn≡ g⋅cm/s2= 10−5 N
kilogram-force; kilopond; grave-forcekgf; kp; Gfɡ0 × 1 kg= 9.80665 N
kip; kip-forcekip; kipf; klbfɡ0 × 1000 lb= 4.4482216152605×103 N
milligrave-force, gravet-forcemGf; gfɡ0 × 1 g= 9.80665 mN
long ton-forcetnf[ citation needed ]ɡ0 × 1 long ton= 9.96401641818352×103 N
newton (SI unit)NA force capable of giving a mass of one kilogram an acceleration of one metre per second per second. [35] = 1 N = 1 kg⋅m/s2
ounce-force ozfɡ0 × 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-forcetnf[ citation needed ]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 unitSymbolDefinitionRelation to SI units
atmosphere (standard)atm101325 Pa [36]
atmosphere (technical)at≡ 1 kgf/cm2= 9.80665×104 Pa [36]
bar bar100000 Pa≡ 105 Pa
barye (cgs unit) ≡ 1 dyn/cm2= 0.1 Pa
centimetre of mercurycmHg13595.1 kg/m3 × 1 cm × ɡ0 1.33322×103 Pa [36]
centimetre of water (4 °C)cmH2O≈ 999.972 kg/m3 × 1 cm × ɡ098.0638 Pa [36]
foot of mercury (conventional)ftHg13595.1 kg/m3 × 1 ft × ɡ04.063666×104 Pa [36]
foot of water (39.2 °F)ftH2O≈ 999.972 kg/m3 × 1 ft × ɡ02.98898×103 Pa [36]
inch of mercury (conventional)inHg13595.1 kg/m3 × 1 in × ɡ03.386389×103 Pa [36]
inch of water (39.2 °F)inH2O≈ 999.972 kg/m3 × 1 in × ɡ0249.082 Pa [36]
kilogram-force per square millimetrekgf/mm2≡ 1 kgf/mm2= 9.80665×106 Pa [36]
kip per square inch ksi≡ 1 kipf/sq in6.894757×106 Pa [36]
long ton per square foot  ≡ 1 long ton × ɡ0 / 1 sq ft1.0725178011595×105 Pa
micrometre of mercuryμmHg13595.1 kg/m3 × 1 μm × ɡ0 ≈ 0.001 torr0.1333224 Pa [36]
millimetre of mercury mmHg 13595.1 kg/m3 × 1 mm × ɡ0 ≈ 1 torr133.3224 Pa [36]
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 [37]
pièze (mts unit)pz1000 kg/m⋅s2= 103 Pa = 1 kPa
pound per square foot psf≡ 1 lbf/ft247.88026 Pa [36]
pound per square inch psi≡ 1 lbf/in26.894757×103 Pa [36]
poundal per square foot pdl/sq ft≡ 1 pdl/sq ft1.488164 Pa [36]
short ton per square foot  ≡ 1 short ton × ɡ0 / 1 sq ft9.5760518×104 Pa
torr torr101325760 Pa133.3224 Pa [36]

Torque or moment of force

Torque
Name of unitSymbolDefinitionRelation to SI units
pound-force-footlbf•ftɡ0 × 1 lb × 1 ft= 1.3558179483314004 N⋅m
poundal-ftpdl•ft≡ 1 lb⋅ft2/s2= 4.21401100938048×10−2 N⋅m
pound force-inch lbf•inɡ0 × 1 lb × 1 in= 0.1129848290276167 N⋅m
kilogram force-meter kgf•mɡ0 × N × m= 9.80665 N⋅m
Newton metre (SI unit)N⋅m≡ N × m = kg⋅m2/s2= 1 N⋅m

Energy

Energy
Name of unitSymbolDefinitionRelation to SI units
barrel of oil equivalent boe5.8×106 BTU59 °F6.12×109 J
British thermal unit (ISO)BTUISO1.0545×103 J= 1.0545×103 J
British thermal unit (International Table)BTUIT= 1.05505585262×103 J
British thermal unit (mean)BTUmean1.05587×103 J
British thermal unit (thermochemical)BTUth1.054350×103 J
British thermal unit (39 °F)BTU39 °F1.05967×103 J
British thermal unit (59 °F)BTU59 °F1.054804×103 J= 1.054804×103 J
British thermal unit (60 °F)BTU60 °F1.05468×103 J
British thermal unit (63 °F)BTU63 °F1.0546×103 J
calorie (International Table)calIT4.1868 J= 4.1868 J
calorie (mean)calmean1100 of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm4.19002 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 °C4.2045 J
calorie (15 °C)cal15 °C≡ 4.1855 J= 4.1855 J
calorie (20 °C)cal20 °C4.1819 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
electronvolt eVe × 1 V1.602176565(35)×10−19 J
erg (cgs unit)erg≡ 1 g⋅cm2/s2= 10−7 J
foot-pound force ft lbfɡ0 × 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 energy Eh≡ meα 2c 2 (= 2 Ry)4.359744×10−18 J
horsepower-hour hp⋅h≡ 1 hp × 1 h= 2.684519537696172792×106 J
inch-pound force in lbfɡ0 × 1 lb × 1 in= 0.1129848290276167 J
joule (SI unit)JThe 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. [35] = 1 J = 1 m⋅N = 1 kg⋅m2/s2 = 1 C⋅V = 1 W⋅s
kilocalorie; large calorie kcal; Cal1000 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-atmosphere l atm; sl≡ 1 atm × 1 L= 101.325 J
quad  ≡ 1015 BTUIT= 1.05505585262×1018 J
rydberg Ry 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
tonne of coal equivalent TCE≡ 7 Gcalth= 29.288×109 J
tonne of oil equivalent toe≡ 10 GcalIT= 41.868×109 J
ton of TNT tTNT≡ 1 Gcalth= 4.184×109 J
watt hour W⋅h≡ 1 W × 1 h= 3.6×103 J
watt second W⋅s≡ 1 J= 1×100 J

Power or heat flow rate

Power
Name of unitSymbolDefinitionRelation to SI units
atmosphere-cubic centimetre per minute atm ccm[ citation needed ]≡ 1 atm × 1 cm3/min= 1.68875×10−3 W
atmosphere-cubic centimetre per second atm ccs[ citation needed ]≡ 1 atm × 1 cm3/s= 0.101325 W
atmosphere-cubic foot per hour atm cfh[ citation needed ]≡ 1 atm × 1 cu ft/h= 0.79700124704 W
atmosphere-cubic foot per minuteatm cfm[ citation needed ]≡ 1 atm × 1 cu ft/min= 47.82007468224 W
atmosphere-cubic foot per secondatm cfs[ citation needed ]≡ 1 atm × 1 cu ft/s= 2.8692044809344×103 W
BTU (International Table) per hourBTUIT/h≡ 1 BTUIT/h0.293071 W
BTU (International Table) per minuteBTUIT/min≡ 1 BTUIT/min17.584264 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/h3.766161×10−4 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/lb9809.5 W [38]
horsepower (European electrical)hp≡ 75 kp⋅m/s= 736 W[ citation needed ]
horsepower (electrical)hp≡ 746 W= 746 W [38]
horsepower (mechanical)hp≡ 550 ft⋅lbf/s [38] = 745.69987158227022 W
horsepower (metric)hp or PS≡ 75 m⋅kgf/s= 735.49875 W [38]
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 [20] 1.333×10−4 W
poncelet p≡ 100 m⋅kgf/s= 980.665 W
square foot equivalent direct radiationsq ft EDR≡ 240 BTUIT/h70.337057 W
ton of air conditioning 2000 lb of ice melted / 24 h3504 W
ton of refrigeration (imperial) 2240 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F3.938875×103 W
ton of refrigeration (IT) 2000 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F3.516853×103 W
watt (SI unit)WThe power which in one second of time gives rise to one joule of energy. [35] = 1 W = 1 J/s = 1 N⋅m/s = 1 kg⋅m2/s3

Action

Action
Name of unitSymbolDefinitionRelation to SI units
atomic unit of action au 2π 1.05457168×10−34 J⋅s [39]

Dynamic viscosity

Dynamic viscosity
Name of unitSymbolDefinitionRelation 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/ft247.88026 Pa⋅s
pound-force second per square inchlbf⋅s/in2≡ 1 lbf⋅s/in26894.757 Pa⋅s

Kinematic viscosity

Kinematic viscosity
Name of unitSymbolDefinitionRelation 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 unitSymbolDefinitionRelation to SI units
ampere (SI base unit)A≡ one coulomb of charge going past a given point per second. [40] (SI base unit)
electromagnetic unit; abampere (cgs unit)abamp≡ 10 A= 10 A
esu per second; statampere (cgs unit)esu/s0.1 A⋅m/s c 3.335641×10−10 A

Electric charge

Electric charge
Name of unitSymbolDefinitionRelation 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≡ charge of exactly 1/(1.602176634×10−19) elementary charges [40] = 1 C = 1 A⋅s
faraday F≡ 1 mol × NAe 96485.3383 C
milliampere hour mA⋅h≡ 0.001 A × 1 h= 3.6 C
statcoulomb; franklin; electrostatic unit (cgs unit)statC; Fr; esu0.1 A⋅m c 3.335641×10−10 C

Electric dipole

Electric dipole
Name of unitSymbolDefinitionRelation to SI units
atomic unit of electric dipole moment e a0  8.47835281×10−30 C⋅m [41]
coulomb meterC⋅m = 1 C × 1 m
debye D= 10−10 esu⋅Å= 3.33564095×10−30 C⋅m [42]

Electromotive force, electric potential difference

Voltage, electromotive force
Name of unitSymbolDefinitionRelation to SI units
abvolt (cgs unit)abV≡ 10−8 V= 10−8 V
statvolt (cgs unit)statVc⋅(1 μJ/A⋅m)= 299.792458 V
volt (SI unit)VThe 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. [35] = 1 V = 1 W/A = 1 kg⋅m2/(A⋅s3) = 1 J/C

Electrical resistance

Electrical resistance
Name of unitSymbolDefinitionRelation to SI units
ohm (SI unit)ΩThe 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. [35] = 1 Ω = 1 V/A = 1 kg⋅m2/(A2⋅s3)

Capacitance

Capacitor's ability to store charge
Name of unitSymbolDefinitionRelation to SI units
farad (SI unit)FThe capacitance between two parallel plates that results in one volt of potential difference when charged by one coulomb of electricity. [35] = 1 F = 1 C/V = 1 A2⋅s4/(kg⋅m2)

Magnetic flux

magnetic flux
Name of unitSymbolDefinitionRelation to SI units
maxwell (CGS unit)Mx≡ 10−8 Wb [38] = 10−8 Wb
weber (SI unit)WbMagnetic 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. [35] = 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 unitSymbolDefinitionRelation to SI units
gauss (CGS unit)GMx/cm2 = 10−4 T= 10−4 T [43]
tesla (SI unit)TWb/m2 = 1 T = 1 Wb/m2= 1 kg/(A⋅s2)

Inductance

Inductance
Name of unitSymbolDefinitionRelation to SI units
henry (SI unit)HThe 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. [35] = 1 H = 1 Wb/A = 1 kg⋅m2/(A⋅s)2

Temperature

Temperature
Name of unitSymbolDefinitionRelation to SI units
degree Celsius °C[°C] ≡ [K] − 273.15[K] ≡ [°C] + 273.15
degree Delisle °De[K] = 373.15 − [°De] × 23
degree Fahrenheit °F[°F] ≡ [°C] × 95 + 32[K] ≡ ([°F] + 459.67) × 59
degree Newton °N[K] = [°N] × 10033 + 273.15
degree Rankine °R;[°R] ≡ [K] × 95[K] ≡ [°R] × 5/9
degree Réaumur °Ré[K] = [°Ré] × 54 + 273.15
degree Rømer °Rø[K] = ([°Rø] − 7.5) × 4021 + 273.15
Regulo Gas Mark GM[°F] ≡ [GM] × 25 + 300[K] ≡ [GM] × 1259 + 422.038
kelvin (SI base unit)K≡ change in the thermodynamic temperature T that results in a change of thermal energy kT by 1.380 649×10−23 J. [44] (SI base unit)

Information entropy

Information entropy
Name of unitSymbolDefinitionRelation to SI unitsRelation to bits
natural unit of information; nip; nepitnat
shannon; bit Sh; bit; b≡ ln(2) × nat 0.693147  nat = 1 bit
hartley; banHart; ban≡ ln(10) × nat2.302585  nat
nibble ≡ 4 bits= 22 bit
byte B≡ 8 bits= 23 bit
kilobyte (decimal)kB1000 B= 8000 bit
kilobyte (kibibyte)KB; KiB1024 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 unitSymbolDefinitionRelation to SI units
candela (SI base unit); candlecdThe 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. [40] (SI base unit)
candlepower (new)cp≡ cd The use of candlepower as a unit is discouraged due to its ambiguity.= 1 cd
candlepower (old, pre-1948)cpVaries and is poorly reproducible. [45] Approximately 0.981 cd. [20] ≈ 0.981 cd

Luminance

Luminance
Name of unitSymbolDefinitionRelation to SI units
candela per square footcd/ft2≡ cd/ft210.763910417 cd/m2
candela per square inchcd/in2≡ cd/in21550.0031 cd/m2
candela per square metre (SI unit); nit (deprecated [20] )cd/m2≡ cd/m2= 1 cd/m2
footlambert fL≡ (1/π) cd/ft23.4262590996 cd/m2
lambert L≡ (104/π) cd/m23183.0988618 cd/m2
stilb (CGS unit)sb≡ 104 cd/m2= 104 cd/m2

Luminous flux

Luminous flux
Name of unitSymbolDefinitionRelation to SI units
lumen (SI unit)lmThe luminous flux of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant flux of 1/683 watt. [40] = 1 lm = 1 cd⋅sr

Illuminance

Illuminance
Name of unitSymbolDefinitionRelation to SI units
footcandle; lumen per square footfc≡ lm/ft2= 10.763910417 lx
lumen per square inchlm/in2≡ lm/in21550.0031 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 unitSymbolDefinitionRelation to SI units
becquerel (SI unit)Bq≡ Number of disintegrations per second= 1 Bq = 1/s
curie Ci3.7×1010 Bq [46] = 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. [47]

Radiation – exposure

Radiation - exposure
Name of unitSymbolDefinitionRelation to SI units
roentgen R1 R ≡ 2.58×10−4 C/kg [38] = 2.58×10−4 C/kg

The roentgen is not an SI unit and the NIST strongly discourages its continued use. [48]

Radiation – absorbed dose

Radiation - absorbed dose
Name of unitSymbolDefinitionRelation to SI units
gray (SI unit)Gy≡ 1 J/kg = 1 m2/s2 [49] = 1 Gy = 1 J/kg = 1 m2s2
rad rad≡ 0.01 Gy [38] = 0.01 Gy

Radiation – equivalent dose

Radiation - equivalent dose
Name of unitSymbolDefinitionRelation to SI units
Röntgen equivalent man rem≡ 0.01 Sv= 0.01 Sv
sievert (SI unit)Sv≡ 1 J/kg [47] = 1 Sv = 1 J/kg = 1 m2s2

Although the definitions for sievert (Sv) and gray (Gy) would seem to indicate that they measure the same quantities, this is not the case. The effect of receiving a certain dose of radiation (given as Gy) is variable and depends on many factors, thus a new unit was needed to denote the biological effectiveness of that dose on the body; this is known as the equivalent dose and is shown in Sv. The general relationship between absorbed dose and equivalent dose can be represented as

H = QD

where H is the equivalent dose, D is the absorbed dose, and Q is a dimensionless quality factor. Thus, for any quantity of D measured in Gy, the numerical value for H measured in Sv may be different. [50]

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. Foot, C. J. (2005). Atomic physics. Oxford University Press. ISBN   978-0-19-850695-9.
  5. jobs (September 14, 2012). "The astronomical unit gets fixed : Nature News & Comment". Nature.com. doi:10.1038/nature.2012.11416. S2CID   123424704 . Retrieved August 31, 2013.Cite journal requires |journal= (help)
  6. "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.
  7. 1 2 3 4 5 "NIST - National Institute of Standards and Technology". NIST.
  8. 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.
  9. 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.
  10. "International Astronomical Union - IAU". www.iau.org.
  11. Klein, Herbert Arthur. (1988). The Science of Measurement: a Historical Survey. Mineola, NY: Dover Publications 0-4862-5839-4.
  12. 1 2 3 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
  13. 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.
  14. Cox, Arthur N., ed. (2000). Allen's Astrophysical Quantities (4th ed.). New York: AIP Press / Springer. Bibcode:2000asqu.book.....C. ISBN   0387987460.
  15. Binney, James; Tremaine, Scott (2008). Galactic Dynamics (2nd ed.). Princeton, NJ: Princeton University Press. Bibcode:2008gady.book.....B. ISBN   978-0-691-13026-2.
  16. P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
  17. 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.
  18. 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. 142150.
  19. Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking. (1894). New York: Howard Lockwood. p. 521.
  20. 1 2 3 4 5 6 7 8 9 Rowlett, Russ (2005), How Many? A Dictionary of Units of Measurement
  21. 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.
  22. 1 2 3 4 5 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
  23. 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".
  24. CODATA Value: atomic unit of mass. (2010). National Institute of Standards and Technology. Retrieved 29 May 2015.
  25. 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 !"
  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. "CODATA Value: Planck time". physics.nist.gov. Retrieved 2018-06-20.
  30. 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.
  31. 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.
  32. Until 1970 the UK Admiralty (and until 1954 the US) used other definitions of the nautical mile and hence the knot. See also #Length above
  33. Tom Benson. (2010.) "Mach Number" Archived 2006-04-10 at the Wayback Machine in Beginner's Guide to Aeronautics. NASA.
  34. CODATA Value: atomic unit of force. (2006). National Institute of Standards and Technology. Retrieved September 14, 2008.
  35. 1 2 3 4 5 6 7 8 Comité International des Poids et Mesures, Resolution 2, 1946, retrieved August 26, 2009
  36. 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. 5768.
  37. 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.
  38. 1 2 3 4 5 6 7 NIST Guide to SI Units, Appendix B.9 , retrieved August 27, 2009
  39. 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.
  40. 1 2 3 4 "SI brochure (2019)" (PDF). SI Brochure. BIPM. p. 132. Retrieved May 23, 2019.
  41. The NIST Reference on Constants, Units, and Uncertainty, 2006, retrieved August 26, 2009
  42. Robert G. Mortimer Physical chemistry,Academic Press, 2000 ISBN   0-12-508345-9, page 677
  43. 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.
  44. "Mise en pratique" (PDF). BIPM.
  45. The NIST Reference on Constants, Units, and Uncertainty , retrieved August 28, 2009
  46. 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.
  47. 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
  48. The NIST Guide to the SI (Special Publication 811), section 5.2, 2008, retrieved August 27, 2009
  49. 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.
  50. 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)

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