Conversion of units

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Conversion of units refers to conversion factors between units of measurement.

Techniques

The simplest way to convert from one unit to another is to carry through the units themselves in the mathematical operation. To illustrate this process, consider the following examples.

You would like to convert 6 feet into metres. Consulting the table below and finding that one foot is exactly 0.3048 metre, you can now perform the mathematical conversion:

6 ft × 0.3048 m/ft = 1.8288 m

Notice that the "foot" units canceled out, leaving only metres, the desired result. (Since 0.3048 metre per foot have infinite precision, the precision of the answer is determined by the precision of the 6 ft figure; if, for example, you are defining the fathom, expressing it with 5 significant figures is correct. But if the 6 ft figure is a measurement, the result needs to be rounded appropriately.)

Say your height is 183 centimetres, and you wish to convert this into inches:

183 cm / (2.54 cm/in) = 72.0 in

To check our answer, we convert this result back into feet:

72 in / (12 in/ft) = 6.0 feet

which confirms the earlier result.

Multiple units can be manipulated in the same fashion:

7 mi/s × 1.609344 km/mi × 3600 s/h = 40,000 km/h

Thus, Earth escape velocity is about 7 miles per second, or 40,000 kilometres per hour. Notice that since the calculation started with one significant figure (the 7), the answer also has one significant figure (the 4 in 40,000).

Deciding whether to multiply or divide is determined by looking at the units and deciding which ones you want to "get rid" of. In the conversion just above, if we had divided by 3600 s/h instead of multiplying, the result would have come out in kilometre-hours per square second, clearly an incorrect and meaningless result.

Rounding of results

An important thing to remember is that the process of making a conversion cannot give you any more precise results than what you started with. While many of the conversion factors given in the tables below are exact, and others while not exact contain many significant digits, not all the numbers you get after performing calculations on a calculator or with pencil and paper are meaningful.

After using these conversion factors, be sure to round off the results appropriately.

Tables of conversion factors

Legend

Legend
≡ definition
= exactly equal to
≈ approximately equal to
(digits) indicates the digits repeat infinitely


Length

Length, l
Name of unit Symbol Definition Relation to SI units
angstrom Å ≡ 1.000 x 10-10 m = 0.1 nm
astronomical unit AU = 149 597 870.691 ± 0.030 km
atomic unit of length au ≡ a0 ≈ 5.291 772 083 x 10-11 ± 19 x 10-20 m
barley corn   ≡ 1/3 in ≈ 8.466 667 mm
Bohr radius a0; b ≡ α/(4πR∞) ≈ 5.291 772 083 x 10-11 ± 19 x 10-20 m
cable length (Imperial)   ≡ 608 ft = 185.3184 m
cable length (International)   ≡ 1/10 NM = 185.2 m
cable length (U.S.)   ≡ 720 ft = 219.456 m
calibre cal ≡ 1 in = 25.4 mm
chain (Gunter's; Surveyor's) ch ≡ 66 ft = 20.1168 m
chain (Ramsden's Engineer's) ch ≡ 100 ft = 30.48 m
cubit   ≡ 18 in = 0.4572 m
ell ell ≡ 45 in = 1.143 m
fathom fm ≡ 6 ft = 1.8288 m
≈ 1/1000 NM = 1.852 m
fermi fm ≡ 1.000 x 10-15 m = 1.000 x 10-15 m
finger   ≡ 7/8 in = 22.225 mm
finger (cloth)   ≡ 4 ½ in = 0.1143 m
foot (Benoît) ft (Ben) ≈ 0.304 799 735 m
foot (Clarke's; Cape) ft (Cla) ≈ 0.304 797 265 4 m
foot (Indian) ft Ind ≈ 0.304 799 514 m
foot (International) ft ≡ 1/3 yard = 0.3048 m
foot (Sear's) ft (Sear) ≈ 0.304 799 47 m
foot (U.S. Survey) ft (US) ≡ 1200/3937 m ≈ 0.304 800 610 m
furlong fur ≡ 660 ft = 201.168 m
geographical mile mi ≡ 6082 ft = 1853.7936 m
hand   ≡ 4 in = 0.1016 m
inch in ≡ 1/36 yd = 25.4 mm
league lea ≡ 3 mi = 4828.032 m
light-day   ≡ 24 light-hours = 2.590 206 837 12 x 1013 m
light-hour   ≡ 60 light-minutes = 1.079 252 848 8 x 1013 m
light-minute   ≡ 60 light-seconds = 1.798 754 748 x 1010 m
light-second   ≡ 2.997 924 58 x 108 m
light-year l.y. ≡ c0 × 86 400 × 365.25 = 9.460 730 472 580 8 x 1015 m
line ln ≡ 1/12 in (Klein 1988, 63) ≈ 2.116 667 mm
link (Gunter's; Surveyor's) lnk ≡ 1/100 ch = 0.201 168 m
link (Ramsden's; Engineer's) lnk ≡ 1 ft = 0.3048 m
metre (SI base unit) m ≡ 1 m = 1 m
mickey   ≡ 1/200 in = 1.27 x 10-4 m
micron µ ≡ 1.000 x 10-6 m
mil; thou mil ≡ 1.000 x 10-3 in = 2.54 x 10-5 m
mile mi ≡ 1760 yd = 5280 ft = 1609.344 m
mile (U.S. Survey) mi ≡ 5280 ft (US) = 5280 × 1200/3937 m ≈ 1609.347 219 m
nail (cloth)   ≡ 2 ¼ in = 57.15 mm
nautical league NL; nl ≡ 3 NM = 5556 m
nautical mile NM; nm ≡ 1852 m
nautical mile (Admiralty) NM (Adm); nm (Adm) ≡ 6080 ft = 1853.184 m
pace   ≡ 2.5 ft = 0.762 m
palm   ≡ 3 in = 76.2 mm
parsec pc ≈ 180 × 60 × 60/π AU

≈ 206 264.806 25 AU
= 3.261 563 776 9 ± 6 x 10-10 light-years

= 3.085 677 581 3 x 1016 ± 6 x 106 m
point (ATA) pt ≡ 0.013837 in = 0.351 459 8 mm
point (Didot; European) pt ≡ 0.376 065 mm
point (metric) pt ≡ 3/8 mm = 0.375 mm
point (PostScript) pt ≡ 1/72 in ≈ 0.352 778 mm
quarter   ≡ ¼ yd = 0.2286 m
rod; pole; perch rd ≡ 16 ½ ft = 5.0292 m
rope rope ≡ 20 ft = 6.096 m
span   ≡ 6 in = 0.1524 m
span (cloth)   ≡ 9 in = 0.2286 m
spatTemplate:Citation needed S ≡ 1012 m = 1 Tm
stick   ≡ 2 in = 50.8 mm
stigma; pm   ≡ 1.000 x 10-12 m ≡ 1.000 x 10-12 m
telegraph mile mi ≡ 6087 ft = 1855.3176 m
twip twp ≡ 1/1440 in ≈ 1.763 889 x 10-5 m
x unit; siegbahn xu ≈ 1.0021 x 10-13 m
yard (International) yd ≡3 ft ≡ 0.9144 m = 0.9144 m

Area

Area, A
Name of unit Symbol Definition Relation to SI units
acre ac ≡ 10 sq ch = 4840 sq yd = 4046.856 422 4 m²
are a ≡ 100 m²
barn b ≡ 10−28 m²
barony   ≡ 4000 ac = 1.618 742 568 96 x 107 m²
board bd ≡ 1 in × 1 ft = 7.741 92 x 10-3 m²
boiler horsepower equivalent direct radiation bhp EDR ≡ (1 ft²) (1 bhp) / (240 BTUIT/h) ≈ 12.958 174 m²
circular inch circ in ≡ π/4 in² ≈ 5.067 075 x 10-4 m²
circular mil; circular thou circ mil ≡ π/4 mil² ≈ 5.067 075 x 10-10 m²
cord   ≡ 192 bd = 1.486 448 64 m²
dunam   ≡ 1000 m² = 1000 m²
hectare ha ≡ 10 000 m² = 0.01 km²
hide   ≡ 100 ac = 4.046 856 422 4 x 105 m²
rood ro ≡ ¼ ac = 1011.714 105 6 m²
square chain sq ch ≡ 1 ch² = 404.685 642 24 m²
square foot sq ft ≡ 1 ft² = 9.290 304 x 10-2 m²
square inch sq in ≡ 1 in² = 6.4516 x 10-4 m²
square kilometre km² ≡ 1 km² = 106 m²
square link sq lnk ≡ 1 lnk² = 4.046 856 422 4 x 10-2 m²
square metre (SI unit) m² ≡ 1 m × 1 m = 1 m²
square mil; square thou sq mil ≡ 1 mil² = 6.4516 x 10-10 m²
square mile; section sq mi ≡ 1 mi² = 2.589 988 110 336 x 106 m²
square rod/pole/perch sq rd ≡ 1 rd² = 25.292 852 64 m²
square U.S. Survey mile sq mi ≡ 1 mi (US)² ≈ 2.589 998 x 106 m²
square yard sq yd ≡ 1 yd² = 0.836 127 36 m²
township   ≡ 36 sq mi (US) ≈ 9.323 994 x 107 m²
yardland   ≡ 30 ac = 1.214 056 926 72 x 105 m²

Volume

Volume, V
Name of unit Symbol Definition Relation to SI units
cubic metre (SI unit) m³ ≡ 1 m × 1 m × 1 m
litre L ≡ 1 dm³
lambda λ ≡ 1 mm³ = 1 μL
drop (metric)   ≡ 1/20 mL = 0.05 mL
minim (Imperial) min ≡ 1/480 fl oz (Imp) = 1/60 fl dr (Imp) ≈ 0.059 193 880 208 333 mL
minim (U.S.) min ≡ 1/480 US fl oz = 1/60 US fl dr = 0.061 611 519 921 875 mL
drop (U.S.) (alt) gtt ≡ 1/456 US fl oz ≈ 0.064 854 231 mL
drop (Imperial) (alt) gtt ≡ 1/1824 gi (Imp) ≈ 0.077 886 684 mL
drop (U.S.) gtt ≡ 1/360 US fl oz = 0.082 148 693 229 1(6) mL
drop (medical)   ≡ 1/12 mL = 0.08(3) mL
drop (Imperial) gtt ≡ 1/288 fl oz (Imp) = 0.098 656 467 013 (8) mL
dash (U.S.)   ≡ 1/96 US fl oz = ½ US pinch = 0.308 057 599 609 375 mL
dash (Imperial)   ≡ 1/384 gi (Imp) = ½ pinch (Imp) = 0.369 961 751 302 08(3) mL
pinch (U.S.)   ≡ 1/48 US fl oz = 1/8 US tsp = 0.616 115 199 218 75 mL
pinch (Imperial)   ≡ 1/192 gi (Imp) = 1/8 tsp (Imp) = 0.739 923 502 604 1(6) mL
fluid scruple (Imperial) fl s ≡ 1/24 fl oz (Imp) = 1.183 877 604 1(6) mL
fluid drachm (Imperial) fl dr ≡ 1/8 fl oz (Imp) = 3.551 632 812 5 mL
fluid dram (U.S.); U.S. fluidram fl dr ≡ 1/8 US fl oz = 3.696 691 195 312 5 mL
teaspoon (Canadian) tsp ≡ 1/6 fl oz (Imp) ≈ 4.735 510 416 667 mL
teaspoon (U.S.) tsp ≡ 1/6 US fl oz = 4.928 921 595 mL
teaspoon (metric)   ≡ 5 mL
teaspoon (Imperial) tsp ≡ 1/24 gi (Imp) = 5.919 388 020 8(3) mL
dessertspoon (Imperial)   ≡ 1/12 gi (Imp) = 11.838 776 041 (6) mL
tablespoon (Canadian) tbsp ≡ ½ fl oz (Imp) = 14.206 531 25 mL
tablespoon (U.S.) tbsp ≡ ½ US fl oz = 14.786 764 782 5 mL
tablespoon (metric)   ≡ 15 mL
cubic inch cu in ≡ 1 in³ = 16.387 064 mL
tablespoon (Imperial) tbsp ≡ 5/8 fl oz (Imp) = 17.758 164 062 5 mL
pony   ≡ 3/4 US fl oz = 22.180 147 171 875 mL
fluid ounce (Imperial) fl oz (Imp) ≡ 1/160 gal (Imp) = 28.413 062 5 mL
fluid ounce (U.S.) fl oz (US) ≡ 1/128 gal (US) = 29.573 529 562 5 mL
shot   ≡ 1 US fl oz = 29.573 529 562 5 mL
jigger   ≡ 1 ½ US fl oz = 44.360 294 343 75 mL
gill (U.S.) gi (US) ≡ 4 US fl oz = 118.294 118 25 mL
gill (Imperial); Noggin gi (Imp); nog ≡ 5 fl oz (Imp) = 142.065 312 5 mL
cup (Canadian) c (CA) ≡ 8 fl oz (Imp) = 227.3045 mL
cup (U.S.) c (US) ≡8 US fl oz ≡ 1/16 gal (US) = 236.588 236 5 mL
cup (metric) c ≡ 250 mL
breakfast cup   ≡ 10 fl oz (Imp) = 284.130 625 mL
pint (U.S. fluid) pt (US fl) ≡ 1/8 gal (US) = 473.176 473 mL
pint (U.S. dry) pt (US dry) ≡ 1/4 bu (US lvl) = 0.550 610 471 357 5 L
pint (Imperial) pt (Imp) ≡ 1/8 gal (Imp) = 0.568 261 25 L
fifth   ≡ 1/5 US gal = 0.757 082 356 8 L
quart (U.S. fluid) qt (US) ≡ 1/4 gal (US fl) = 0.946 352 946 L
quart (U.S. dry) qt (US) ≡ 1/32 bu (US lvl) = ¼ gal (US dry) = 1.101 220 942 715 L
quart (Imperial) qt (Imp) ≡ ¼ gal (Imp) = 1.136 522 5 L
pottle; quartern   ≡ ½ gal (Imp) = 80 fl oz (Imp) = 2.273 045 L
board-foot fbm ≡ 144 cu in = 2.359 737 216 L
gallon (U.S. fluid; Wine) gal (US) ≡ 231 cu in = 3.785 411 784 L
gallon (U.S. dry) gal (US) ≡ 1/8 bu (US lvl) = 4.404 883 770 86 L
gallon (Imperial) gal (Imp) ≡ = 4.546 09 L
beer gallon beer gal ≡ 282 cu in = 4.621 152 048 L
peck (U.S. dry) pk ≡ ¼ US lvl bu = 8.809 767 541 72 L
peck (Imperial) pk ≡ 2 gal (Imp) = 9.092 18 L
bucket (Imperial) bkt ≡ 4 gal (Imp) = 18.184 36 L
timber foot   ≡ 1 cu ft = 28.316 846 592 L
cubic foot cu ft ≡ 1 ft × 1 ft × 1 ft = 28.316 846 592 L
firkin   ≡ 9 gal (US) = 34.068 706 056 L
bushel (U.S. dry level) bu (US lvl) ≡ 2150.42 cu in = 35.239 070 166 88 L
bushel (Imperial) bu (Imp) ≡ 8 gal (Imp) = 36.368 72 L
bushel (U.S. dry heaped) bu (US) ≡ 1 ¼ bu (US lvl) = 44.048 837 708 6 L
strike (U.S.)   ≡ 2 bu (US lvl) = 70.478 140 333 76 L
strike (Imperial)   ≡ 2 bu (Imp) = 72.737 44 L
kilderkin   ≡ 18 gal (Imp) = 81.829 62 L
sack (U.S.)   ≡ 3 bu (US lvl) = 105.717 210 500 64 L
sack (Imperial); bag   ≡ 3 bu (Imp) = 109.106 16 L
barrel (U.S. dry) bl (US) ≡ 105 qt (US) = 105/32 bu (US lvl) = 115.628 198 985 075 L
barrel (U.S. fluid) fl bl (US) ≡ 31 ½ gal (US) = 119.240 471 196 L
coomb   ≡ 4 bu (Imp) = 145.474 88 L
barrel (petroleum) bl ≡ 42 gal (US) = 158.987 294 928 L
barrel (Imperial) bl (Imp) ≡ 36 gal (Imp) = 163.659 24 L
hogshead (U.S.) hhd (US) ≡ 2 fl bl (US) = 238.480 942 392 L
seam   ≡ 8 bu (US lvl) = 281.912 561 335 04 L
quarter; pail   ≡ 8 bu (Imp) = 290.949 76 L
hogshead (Imperial) hhd (Imp) ≡ 2 bl (Imp) = 327.318 48 L
cord-foot   ≡ 16 cu ft = 0.453 069 545 472 m³
butt, pipe   ≡ 126 gal (wine) = 0.476 961 884 784 m³
perch per ≡ 16 ½ ft × 1 1/2 ft × 1 ft = 0.700 841 953 152 m³
cubic yard cu yd ≡ 27 cu ft = 0.764 554 857 984 m³
tun   ≡ 252 gal (wine) = 0.953 923 769 568 m³
displacement ton   ≡ 35 cu ft = 0.991 089 630 72 m³
water ton   ≡ 28 bu (Imp) = 1.018 324 16 m³
freight ton   ≡ 40 cu ft = 1.132 673 863 68 m³
wey (U.S.)   ≡ 40 bu (US lvl) = 1.409 562 806 675 2 m³
load   ≡ 50 cu ft = 1.415 842 329 6 m³
register ton   ≡ 100 cu ft = 2.831 684 659 2 m³
last   ≡ 80 bu (Imp) = 2.909 497 6 m³
cord (firewood)   ≡ 8 ft × 4 ft × 4 ft = 3.624 556 363 776 m³
cubic fathom cu fm ≡ 1 fm × 1 fm × 1 fm = 6.116 438 863 872 m³
acre-inch   ≡ 1 ac × 1 in = 102.790 153 128 96 m³
acre-foot   ≡ 1 ac × 1 ft = 1233.481 837 547 52 m³
cubic mile cu mi ≡ 1 mi³ = 4.168 181 825 440 579 584 km³

Angle

Angle
Name of unit Symbol Definition Relation to SI units
radian (SI unit) rad ≡ 1 rad
centesimal second of arc " ≡ 1 gr/10000 ≈ 1.570 796 µrad
arcsecond " ≡ 1°/3600 ≈ 4.848 137 µrad
centesimal minute of arc ' ≡ 1 gr/100 ≈ 0.157 080 mrad
minute of arc ' ≡ 1°/60 ≈ 0.290 888 mrad
angular mil µ ≡ 2π/6400 rad ≈ 0.981 748 mrad
grad; gradian; gon gr ≡ 2π/400 rad = 0.9° ≈ 15.707 963 mrad
degree (of arc) ° ≡ π/180 rad ≈ 17.453 293 mrad
sign   ≡ 30° ≈ 0.523 599 rad
octant   ≡ 45° ≈ 0.785 398 rad
sextant   ≡ 60° ≈ 1.047 198 rad
quadrant   ≡ 90° ≈ 1.570 796 rad

Solid angle

Solid angle
Name of unit Symbol Definition Relation to SI units
steradian sr (SI derived unit)

Mass

Mass, m
Name of unit Symbol Definition Relation to SI units
kilogram kg (SI base unit)
electron rest mass me ≈ 9.109 381 88 x 10-31 ± 72 x 10-39 kg
atomic unit of mass au ≡ me ≈ 9.109 381 88 x 10-31 ± 72 x 10-39 kg
unified atomic mass unit amu ≈ 1.660 538 73 x 10-27 ± 13 x 10-35 kg
dalton Da ≈ 1.660 902 10 x 10-27 ± 13 x 10-35 kg
gamma γ ≡ 1 μg
point   ≡ 1/100 kt (metric) = 2 mg
mite   ≡ 1/20 gr = 3.239 945 5 mg
mite (metric)   ≡ 1/20 g = 50 mg
grain gr ≡ 64.798 91 mg
crith   ≈ 89.9349 mg
carat (metric) kt ≡ 200 mg
carat kt ≡ 3 1/6 gr ≈ 205.196 548 333 mg
sheet   ≡ 1/700 lb av = 647.9891 mg
scruple (avoirdupois) s av ≡ 20 gr = 1.295 978 2 g
pennyweight dwt; pwt ≡ 1/20 oz t = 1.555 173 84 g
dram (avoirdupois) dr av ≡ 27 11/32 gr = 1.771 845 195 312 5 g
dram (apothecary; troy) dr t ≡ 60 gr = 3.887 934 6 g
hyl (CGS unit)   ≡ 1 gee × 1 g × 1 s²/m = 9.806 65 g
ounce (avoirdupois) oz av ≡ 1/16 lb = 28.349 523 125 g
assay ton (short) AT ≡ 1 mg × 1 sh tn ÷ 1 oz t ≈ 29.166 667 g
ounce (apothecary; troy) oz t ≡ 1/12 lb t = 31.103 476 8 g
assay ton (long) AT ≡ 1 mg × 1 long tn ÷ 1 oz t ≈ 32.666 667 g
mark   ≡ 8 oz t = 248.827 814 4 g
pound (troy) lb t ≡ 5760 grains = 0.373 241 721 6 kg
pound (avoirdupois) lb av ≡ 7000 grains = 0.453 592 37 kg
pound (metric)   ≡ 500 g
clove   ≡ 8 lb av = 3.628 738 96 kg
stone st ≡ 14 lb av = 6.350 293 18 kg
hyl (MKS unit)   ≡ 1 gee × 1 kg × 1 s²/m = 9.806 65 kg
quarter (Imperial)   ≡ 1/4 long cwt = 2 st = 28 lb av = 12.700 586 36 kg
slug; geepound slug ≡ 1 gee × 1 lb av × 1 s²/ft ≈ 14.593 903 kg
bag (Portland cement)   ≡ 94 lb av = 42.637 682 78 kg
short hundredweight; cental sh cwt ≡ 100 lb av = 45.359 237 kg
long hundredweight long cwt or cwt ≡ 112 lb av = 50.802 345 44 kg
bag (coffee) ≡ 60 kg = 60 kg
quintal (metric) q ≡ 100 kg
wey   ≡ 252 lb = 18 st = 114.305 277 24 kg (variants exist)
long quarter   ≡ ¼ long tn = 254.011 727 2 kg
kip kip ≡ 1000 lb av = 453.592 37 kg
short ton sh tn ≡ 2000 lb = 907.184 74 kg
tonne (mts unit) t ≡ 1000 kg
long ton long tn or ton ≡ 2240 lb = 1016.046 908 8 kg
barge   ≡ 22 ½ sh tn = 20,411.656 65 kg
Zentner Ztr. Definitions vary; see: The Swiss Federal Office for Metrology gives Zentner on a German language web page[1] and quintal on the English translation of that page[2]; the unit is marked "spécifiquement suisse !" and Rowlett, Russ. A Dictionary of Units of Measurement. Viewed October 14, 2006 at http://www.unc.edu/~rowlett/units/dictZ.html. See also discussion at Talk:Conversion of units#Zentner

In physics, the pound of mass is sometimes written lbm to distinguish it from the pound-force (lbf). It should not be read as the mongrel unit "pound metre".

Time

Time, t
Name of unit Symbol Definition Relation to SI units
second s (SI base unit)
Planck time   ≡ √(Gℏ/c5) ≈ 1.351 211 818 x 10-43 s
atomic unit of time au ≡ a0/(α·c) ≈ 2.418 884 254 x 10-17 s
svedberg S ≡ 10−13 s = 100 fs
shake   ≡ 10−8 s = 10 ns
sigma   ≡ 10−6 s = 1 μs
jiffy   ≡ 1/60 s ≈ 16.666 667 ms
jiffy (alternate)   ≡ 1/100 s ≈ 10 ms
helek   ≡ 1/1080 h ≈ 3.333333 s
minute min ≡ 60 s
moment   ≡ 90 s ≡ 90 s
ke(traditional)   ≡ 1/100 d ≡ 864 s
quarter (of an h) ke ≡ 1/96 d ≡ 900 s
hour h ≡ 60 min = 3600 s
day d ≡ 24 h = 86 400 s
week wk ≡ 7 d = 604 800 s
fortnight   ≡ 2 wk = 1 209 600 s
month (hollow) mo ≡ 29 d = 2 505 600 s
month mo ≡ 30 d = 2 592 000 s
month (full) mo ≡ 31 d = 2 678 400 s
year (Calendar) a or y ≡ 365 d = 31 536 000 s
year (Gregorian) a or y ≡ 365.2425 d = 31 556 952 s
year (Julian) a or y ≡ 365.25 d = 31 557 600 s
sidereal year a or y ≡ 365.256363 d = 31 558 149.76 s
Olympiad   ≡ 4 a of 365 d = 1.2614 x 108 s
lustre; lustrum   ≡ 5 a of 365 d = 1.5768 x 108 s
octaeteris   ≡ 8 a of 365 d = 2.522 88 x 108 s
decade   ≡ 10 a of 365 d = 3.1536 x 108 s
enneadecaeteris; Metonic cycle   ≡ 110 mo (hollow) + 125 mo (full) = 19 a of 365 d = 5.996 16 x 108 s
Callippic cycle   ≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d = 2.398 377 6 x 108 s
century (Calendar)   ≡ 100 a of 365 d = 3.1536 x 108 s
century (Julian)   ≡ 100 a of 365.25 d = 3.155 76 x 109 s
Hipparchic cycle   ≡ 4 Callippic cycles - 1 d = 9.593 424 x 109 s
millennium (Calendar)   ≡ 1000 a of 365 d = 3.1536 x 108 s
millennium (Gregorian)   ≡ 1000 a of 365.2425 d = 3.155 695 2 x 1010 s
millennium (Julian)   ≡ 1000 a of 365.25 d = 3.155 76 x 1010 s
Sothic cycle   ≡ 1461 a of 365 d = 4.607 409 6 x 1010 s

Speed

Speed, v
Name of unit Symbol Definition Relation to SI units
metre per second (SI unit) m/s ≡ 1 m/s
foot per hour fph ≡ 1 ft/h ≈ 8.466 667 x 10-5 m/s
furlong per fortnight   ≡ ½ fur/wk ≈ 1.663 095 x 10-4 m/s
inch per minute ipm ≡ 1 in/min ≈ 4.23 333 x 10-4 m/s
foot per minute fpm ≡ 1 ft/min = 5.08 x 10-3 m/s
inch per second ips ≡ 1 in/s = 2.54 x 10-2 m/s
kilometre per hour km/h ≡ 1 km/h ≈ 2.777 778 x 10-1 m/s
foot per second fps ≡ 1 ft/s = 3.048 x 10-1 m/s
mile per hour mph ≡ 1 mi/h = 0.447 04 m/s
knot kn ≡ 1 NM/h = 1.852 km/h ≈ 0.514 444 m/s
knot (Admiralty) kn ≡ 1 NM (Adm)/h = 1.853 184 km/h ≈ 0.514 773 m/s
mile per minute mpm ≡ 1 mi/min = 26.8224 m/s
mile per second mps ≡ 1 mi/s = 1.609 344 km/s
speed of light in vacuum c ≡ 2.997 924 58 x 108 m/s

Acceleration

Acceleration, a
Name of unit Symbol Definition Relation to SI units
metre per second squared (SI unit) m/s² ≡ 1 m/s²
foot per hour per second fph/s ≡ 1 ft/h·s ≈ 8.466 667 x 10-5 m/s²
inch per minute per second ipm/s ≡ 1 in/min·s ≈ 4.233 333 x 10-4 m/s²
foot per minute per second fpm/s ≡ 1 ft/min·s = 5.08 x 10-3 m/s²
galileo Gal ≡ 1 cm/s² = 10−2 m/s²
inch per second squared ips² ≡ 1 in/s² = 2.54 x 10-2 m/s²
foot per second squared fps² ≡ 1 ft/s² = 3.048 x 10-1 m/s²
mile per hour per second mph/s ≡ 1 mi/h·s = 4.4704 x 10-1 m/s²
knot per second kn/s ≡ 1 kn/s ≈ 5.144 444 x 10-1 m/s²
standard gravity g ≡ 9.806 65 m/s²
mile per minute per second mpm/s ≡ 1 mi/min·s = 26.8224 m/s²
mile per second squared mps² ≡ 1 mi/s² = 1.609 344 x 103 m/s²

Force

Force, F
Name of unit Symbol Definition Relation to SI units
newton (SI unit) N ≡ kg·m/s²
atomic unit of force au ≡ me·α²·c²/a0 ≈ 8.238 722 241 x 10-8 N
dyne (cgs unit) dyn ≡ g·cm/s² ljm = 10−5 N
gravet   ≡ g × 1 g = 9.806 65 mN
poundal pdl ≡ 1 lb·ft/s² = 0.138 254 954 376 N
ounce-force ozf ≡ g × 1 oz = 0.278 013 850 953 781 2 N
pound-force lbf ≡ g × 1 lb = 4.448 221 615 260 5 N
kilogram-force; kilopond; grave kgf; kp ≡ g × 1 kg = 9.806 65 N
sthene (mts unit) sn ≡ 1 t·m/s² = 1 kN
kip; kip-force kip; kipf; klbf ≡ g × 1000 lb = 4.448 221 615 260 5 kN
ton-force tnf ≡ g × 1 sh tn = 8.896 443 230 521 kN

Pressure or mechanical stress

Pressure, p (lower case)
Name of unit Symbol Definition Relation to SI units
pascal (SI unit) Pa ≡ N/m² = kg/(m·s²)
barye (cgs unit)   ≡ 1 dyn/cm² = 0.1 Pa
poundal per square foot pdl/sq ft ≡ 1 pdl/sq ft ≈ 1.488 164 Pa
millimetre of water (3.98 °C) mmH2O ≈ 999.972 kg/m³ × 1 mm × g = 9.806 38 Pa (= 0.999972 kgf/m²)
pound per square foot psf ≡ 1 lb/sq ft × g ≈ 47.880 259 Pa
centimetre of water (3.98 °C) cmH2O ≈ 999.972 kg/m³ × 1 cm × g = 98.0638 Pa
torr torr ≡ 101 325/760 Pa ≈ 133.322 368 4 Pa
millimetre of mercury mmHg ≡ 13 595.1 kg/m³ × 1 mm × g ≈ 1 torr = 133.322 387 415 Pa
inch of water (3.98 °C) inH2O ≈ 999.972 kg/m³ × 1 in × g = 249.082 Pa
pièze (mts unit) pz ≡ 1000 kg/m·s² = 1 kPa
centimetre of mercury cmHg ≡ 13 595.1 kg/m³ × 1 cm × g = 1.333 223 874 15 kPa
foot of water (3.98 °C) ftH2O ≈ 999.972 kg/m³ × 1 ft × g = 2.988 98 kPa
inch of mercury inHg ≡ 13 595.1 kg/m³ × 1 in × g = 3.386 388 640 341 kPa
pound per square inch psi ≡ 1 lb × g / 1 sq in ≈ 6.894 757 kPa
foot of mercury ftHg ≡ 13 595.1 kg/m³ × 1 ft × g = 40.636 663 684 091 9 kPa
short ton per square foot   ≡ 1 sh tn × g / 1 sq ft ≈ 95.760 518 kPa
atmosphere (technical) atm ≡ 1 kgf/cm² = 98.0665 kPa
bar bar ≡ 105 Pa
atmosphere (standard) atm ≡ 101 325 Pa
kip per square inch ksi ≡ 1 kipf/sq in ≈ 6.894757 MPa
kilogram-force per square millimetre kgf/mm² ≡ 1 kgf/mm² = 9.806 65 MPa

Energy, work, or heat

Energy, E
Name of unit Symbol Definition Relation to SI units
joule (SI unit) J ≡ N·m = W·s = V·A·s = kg·m²/s²
electronvolt eV ≡ e × 1 V ≈ 1.602 176 x 10-19 J
rydberg Ry ≡ R∞·ℎ·c ≈ 2.179 872 x 10-18 J
hartree Eh ≡ me·α²·c² (= 2 Ry) ≈ 4.359 744 x 10-18 J
atomic unit of energy au ≡ Eh ≈ 4.359 744 x 10-18 J
erg (cgs unit) erg ≡ 1 g·cm²/s² = 10−7 J
foot-poundal ft pdl ≡ 1 lb·ft²/s² = 4.214 011 009 380 48 x 10-2 J
cubic centimetre of atmosphere; standard cubic centimetre cc atm; scc ≡ 1 atm × 1 cm³ = 0.101 325 J
inch-pound force in lbf ≡ g × 1 lb × 1 in = 0.112 984 829 027 616 7 J
foot-pound force ft lbf ≡ g × 1 lb × 1 ft = 1.355 817 948 331 400 4 J
calorie (20 °C) cal20 °C ≈ 4.1819 J
calorie (thermochemical) calth ≡ 4.184 J
calorie (15 °C) cal15 °C ≡ 4.1855 J
calorie (International Table) calIT ≡ 4.1868 J
calorie (mean) calmean ≈ 4.190 02 J
calorie (3.98 °C) cal3.98 °C ≈ 4.2045 J
litre-atmosphere l atm; sl ≡ 1 atm × 1 L = 101.325 J
gallon-atmosphere (U.S.) US gal atm ≡ 1 atm × 1 gal (US) = 383.556 849 013 8 J
gallon-atmosphere (Imperial) US gal atm ≡ 1 atm × 1 gal (Imp) = 460.632 569 25 J
British thermal unit (thermochemical) BTUth ≡ 1 lb/g × 1 calth × 1 °F/°C = 9.489 152 380 4 ÷ 9 kJ ≈ 1.054 350 kJ
British thermal unit (ISO) BTUISO ≡ 1.0545 kJ
British thermal unit (63 °F) BTU63 °F ≈ 1.0546 kJ
British thermal unit (60 °F) BTU60 °F ≈ 1.054 68 kJ
British thermal unit (59 °F) BTU59 °F ≡ 1.054 804 kJ
British thermal unit (International Table) BTUIT ≡ 1 lb/g × 1 calIT × 1 °F/°C = 1.055 055 852 62 kJ
British thermal unit (mean) BTUmean ≈ 1.055 87 kJ
British thermal unit (39 °F) BTU39 °F ≈ 1.059 67 kJ
Celsius heat unit (International Table) CHUIT ≡ 1 BTUIT × 1 °C/°F = 1.899 100 534 716 kJ
cubic foot of atmosphere; standard cubic foot cu ft atm; scf ≡ 1 atm × 1 ft³ = 2.869 204 480 934 4 kJ
kilocalorie; large calorie kcal; Cal ≡ 1000 calIT = 4.1868 kJ
cubic yard of atmosphere; standard cubic yard cu yd atm; scy ≡ 1 atm × 1 yd³ = 77.468 520 985 228 8 kJ
cubic foot of natural gas   ≡ 1000 BTUIT = 1.055 055 852 62 MJ
horsepower-hour hp·h ≡ 1 hp × 1 h = 2.6845 MJ
kilowatt-hour; Board of Trade Unit kW·h; B.O.T.U. ≡ 1 kW × 1 h = 3.6 MJ
thermie th ≡ 1 McalIT = 4.1868 MJ
therm (U.S.)   ≡ 100 000 BTU59 °F = 105.4804 MJ
therm (E.C.)   ≡ 100 000 BTUIT = 105.505 585 262 MJ
ton of TNT tTNT ≡ 1 Gcalth = 4.184 GJ
barrel of oil equivalent bboe ≈ 5.8 MBTU59 °F ≈ 6.12 GJ
ton of coal equivalent TCE ≡ 7 Gcalth = 29.3076 GJ
ton of oil equivalent TOE ≡ 10 Gcalth = 41.868 GJ
quad   ≡ 1015 BTUIT = 1.055 055 852 62 EJ

Power

Power, P
Name of unit Symbol Definition Relation to SI units
watt (SI unit) W ≡ J/s = N·m/s = kg·m²/s³
lusec lusec ≡ 1 L·µmHg/s ≈ 1.333 x 10-4 W
foot-pound-force per hour ft lbf/h ≡ 1 ft lbf/h ≈ 3.766 161 x 10-4 W
atmosphere cubic centimetre per minute atm ccm ≡ 1 atm × 1 cm³/min = 1.688 75 x 10-3 W
foot-pound-force per minute ft lbf/min ≡ 1 ft lbf/min = 2.259 696 580 552 334x 10-2 W
atmosphere–cubic centimetre per second atm ccs ≡ 1 atm × 1 cm³/s = 0.101 325 W
BTU (International Table) per hour BTUIT/h ≡ 1 BTUIT/h ≈ 0.293 071 W
atmosphere–cubic foot per hour atm cfh ≡ 1 atm × 1 cu ft/h = 0.797 001 244 704 W
foot-pound-force per second ft lbf/s ≡ 1 ft lbf/s = 1.355 817 948 331 400 4 W
litre-atmosphere per minute L·atm/min ≡ 1 atm × 1 L/min = 1.688 75 W
calorie (International Table) per second calIT/s ≡ 1 calIT/s = 4.1868 W
BTU (International Table) per minute BTUIT/min ≡ 1 BTUIT/min ≈ 17.584 264 W
atmosphere-cubic foot per minute atm·cfm ≡ 1 atm × 1 cu ft/min = 47.820 074 682 24 W
square foot equivalent direct radiation sq ft EDR ≡ 240 BTUIT/h ≈ 70.337 057 W
litre-atmosphere per second L·atm/s ≡ 1 atm × 1 L/s = 101.325 W
horsepower (metric) hp ≡ 75 m kgf/s = 735.498 75 W
horsepower (European electrical) hp ≡ 75 kp·m/s = 736 W
horsepower (Imperial mechanical) hp ≡ 550 ft lbf/s = 745.699 871 582 270 22 W
horsepower (Imperial electrical) hp ≡ 746 W
ton of air conditioning   ≡ 1 t × 1005 J/kg × 1 °F/K ÷ 10 min = 844.2 W
poncelet p ≡ 100 m kgf/s = 980.665 W
BTU (International Table) per second BTUIT/s ≡ 1 BTUIT/s = 1.055 055 852 62 x 103 W
atmosphere-cubic foot per second atm cfs ≡ 1 atm × 1 cu ft/s = 2.869 204 480 934 4 x 103 W
ton of refrigeration (IT)   ≡ 1 BTUIT × 1 sh tn/lb ÷ 10 min/s ≈ 3.516 853 x 103 W
ton of refrigeration (Imperial)   ≡ 1 BTUIT × 1 lng tn/lb ÷ 10 min/s ≈ 3.938 875 x 103 W
boiler horsepower bhp ≈ 34.5 lb/h × 970.3 BTUIT/lb ≈ 9.810 657 x 103 W

Angular momentum

Action, Angular momentum, L, J
Name of unit Symbol Definition Relation to SI units
SI unit J·s ≡ kg·m²/s
atomic unit of action au ≡ ℏ = ℎ/2π ≈ 1.054 571 596 x 10-34 J·s
cgs unit erg·s = 10−7 J·s

Electric current

Electric current, I
Name of unit Symbol Definition Relation to SI units
ampere A (SI base unit)
esu per second; statampere (cgs unit) esu/s ≡ (0.1 A·m/s) /c ≈ 3.335 641 x 10-10 A
electromagnetic unit; abampere (cgs unit) abamp ≡ 10 A

Electric charge

Electric charge, Q
Name of unit Symbol Definition Relation to SI units
coulomb (SI unit) C ≡ A·s
atomic unit of charge au ≡ e ≈ 1.602 176 462 x 10-19 C
statcoulomb; franklin; electrostatic unit (cgs unit) statC; Fr; esu ≡ (0.1 A·m) /c ≈ 3.335 641 x 10-10 C
abcoulomb; electromagnetic unit (cgs unit) abC; emu ≡ 10 C
faraday F ≡ 1 mol × NA·e ≈ 96,485.3383 C

Electromotive force

Voltage, Electromotive force, U
Name of unit Symbol Definition Relation to SI units
volt (SI unit) V ≡ kg·m²/(A·s³)
abvolt (cgs unit) abV ≡ 1 x 10-8 V
statvolt (cgs unit) statV ≡ c· (1 μJ/A·m) = 299.792 458 V

Electrical resistance

Electrical resistance, R
Name of unit Symbol Definition Relation to SI units
ohm (SI unit) Ω ≡ V/A = kg·m²/(A²·s³)

Dynamic viscosity

Dynamic viscosity, η
Name of unit Symbol Definition Relation to SI units
pascal second (SI unit) Pa·s ≡ N·s/m² = kg/m·s
poise (cgs unit) P ≡ 10−1 Pa·s

Kinematic viscosity

Kinematic viscosity, ν
Name of unit Symbol Definition Relation to SI units
SI unit m²/s ≡ m²/s
stokes (cgs unit) St ≡ 10−4 m²/s

Information entropy

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

Temperature

Temperature, T
Name of unit Symbol Relation to SI units Relation to °C
kelvin K SI base unit T[K] = T[°C] + 273.15
degree Celsius °C T[°C] = T[K] − 273.15
degree Rankine °R; °Ra T[°Ra] = 1.8 × T[K]
degree Fahrenheit °F T[°F] = T[K] × 1.8 − 459.67 T[°F] = 1.8 × T[°C] + 32


Software tools

Units and measurements can be easily converted using software tools, but only if the units are explicitly defined and the conversion is compatible (e.g., cmHg to kPa).

One popular command-line utility is units. Another utility and programming library is UDUNITS.

References

  • Klein, Herbert. 1988. The science of measurement: A historical survey. New York: Dover Publications.

See also

External links

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