This article gives a list of conversion factors for several physical quantities . 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.
The following quantities are considered: length , area , volume , plane angle , solid angle , mass , density , time , frequency , velocity , volumetric flow rate , acceleration , force , pressure (or mechanical stress ), torque (or moment of force ), energy , power (or heat flow rate ), action , dynamic viscosity , kinematic viscosity , electric current , electric charge , electric dipole , electromotive force (or electric potential difference ), electrical resistance , capacitance , magnetic flux , magnetic flux density , inductance , temperature , information entropy , luminous intensity , luminance , luminous flux , illuminance , radiation .
Legend
Symbol
Definition
≡
exactly equal
≈
approximately equal to
≘
(exactly) corresponds to (different types of quantity describing the same phenomenon)
digits
indicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369 369 369 369 ... )
(H)
of chiefly historical interest
Length
Length
Name of unit
Symbol
Definition
Relation to SI units
ångström
Å
≡ 1× 10−10 m
≡ 0.1 nm
astronomical unit
au
≡ 149597 870 700 m ≈ Distance from Earth to Sun
≡ 149597 870 700 m [ 1]
attometre
am
≡ 1× 10−18 m
≡ 1× 10−18 m
barleycorn (H)
= 1 ⁄3 in (see note above about rounding)
= 8.46 × 10 −3 m
bohr, atomic unit of length
a 0
= Bohr radius of hydrogen
≈ 5.291772 1092 (17)× 10−11 m[ 2]
cable length (imperial)
≡ 608 ft
≈ 185.3184 m
cable length (International)
≡ 1 ⁄10 nmi
≡ 185.2 m
cable length (US)
≡ 720 ft
= 219.456 m
chain (Gunter's ; Surveyor's)
ch
≡ 66 ft (US) ≡ 4 rods [ 3]
≈ 20.11684 m
cubit (H)
≡ Distance from fingers to elbow ≈ 18 in
≈ 0.5 m
ell (H)
ell
≡ 45 in [ 4] (In England usually)
= 1.143 m
fathom
ftm
≡ 6 ft [ 4]
= 1.8288 m
femtometre
fm
≡ 1× 10−15 m
≡ 1× 10−15 m
fermi
fm
≡ 1× 10−15 m[ 4]
≡ 1× 10−15 m
finger
≡ 7 ⁄8 in
= 0.022225 m
finger (cloth)
≡ 4+ 1 ⁄2 in
= 0.1143 m
foot (Benoît) (H)
ft (Ben)
≈ 0.304799 735 m
foot (Cape) (H)
Legally defined as 1.033 English feet in 1859
≈ 0.314858 m
foot (Clarke's) (H)
ft (Cla)
≈ 0.304797 2654 m
foot (Indian) (H)
ft Ind
≈ 0.304799 514 m
foot, metric
mf
≡ 300 mm
≡ 0.3 m
foot, metric (Mesures usuelles ) (H)
≡ 1 ⁄3 m
≡ 0.3 m
foot (International)
ft
≡ 0.3048 m ≡ 1 ⁄3 yd ≡ 12 inches
≡ 0.3048 m
foot (Sear's) (H)
ft (Sear)
≈ 0.304799 47 m
foot (US Survey)
ft (US)
≡ 1200 ⁄ 3937 m [ 5]
≈ 0.304800 610 m
french ; charriere
F
≡ 1 ⁄3 mm
= 0.3 × 10 −3 m
furlong
fur
≡ 10 chains = 660 ft = 220 yd [ 4]
= 201.168 m
hand
≡ 4 in [ 4]
≡ 0.1016 m
inch (International)
in
≡ 2.54 cm ≡ 1 ⁄36 yd ≡ 1 ⁄12 ft
≡ 0.0254 m
league (land)
lea
≈ 1 hour walk, Currently defined in US as 3 Statute miles,[ 3] but historically varied from 2 to 9 km
≈ 4828 m
light-day
≡ 24 light-hours
≡ 2.590206 837 12 × 1013 m
light-hour
≡ 60 light-minutes
≡ 1.079252 8488 × 1012 m
light-minute
≡ 60 light-seconds
≡ 1.798754 748 × 1010 m
light-second
≡ Distance light travels in one second in vacuum
≡ 299792 458 m
light-year
ly
≡ Distance light travels in vacuum in 365.25 days [ 6]
≡ 9.460730 472 5808 × 1015 m
line
ln
≡ 1 ⁄12 in [ 7]
= 0.002116 m
link (Gunter's; Surveyor's)
lnk
≡ 1 ⁄100 ch [ 4] ≡ 0.66 ft (US) ≡ 7.92 in
≈ 0.2011684 m
link (Ramsden's; Engineer's)
lnk
≡ 1 ft [ 4]
= 0.3048 m
metre (SI base unit )(meter)
m
≡ Distance light travels in 1 ⁄ 299792 458 of a second in vacuum.[ 8]
(SI base unit )
mickey
≡ 1 ⁄200 in
= 1.27× 10−4 m
micrometre (old: micron)
μ; μm
≡ 1× 10−6 m
≡ 1× 10−6 m
mil; thou
mil
≡ 1× 10−3 in
= 2.54× 10−5 m
mil (Sweden and Norway)
mil
≡ 10 km
= 10000 m
mile (geographical) (H)
≡ 6082 ft
= 1853 .7936 m
mile (international)
mi
≡ 80 chains ≡ 5280 ft ≡ 1760 yd
≡ 1609 .344 m
mile (tactical or data)
≡ 6000 ft
≡ 1828 .8 m
mile (telegraph) (H)
mi
≡ 6087 ft
= 1855 .3176 m
mile (US Survey)
mi
≡ 5280 US Survey feet ≡ ( 5280 × 1200 ⁄ 3937 ) m
≈ 1609 .347219 m
nail (cloth)
≡ 2+ 1 ⁄4 in [ 4]
= 0.05715 m
nanometre
nm
≡ 1× 10−9 m
≡ 1× 10−9 m
nautical league
NL; nl
≡ 3 nmi [ 4]
= 5556 m
nautical mile (Admiralty)
NM (Adm); nmi (Adm)
= 6080 ft
= 1853 .184 m
nautical mile (international)
NM; nmi
≡ 1852 m[ 9]
≡ 1852 m
nautical mile (US pre 1954)
≡ 1853.248 m
≡ 1853.248 m
pace
≡ 2.5 ft [ 4]
= 0.762 m
palm
≡ 3 in [ 4]
= 0.0762 m
parsec
pc
Distant point with a par allax shift of one arc sec ond from a base of one astronomical unit. ≡ 648000 / π au [ 10] [ 11]
≈ 30856 775 814 913 700 m[ 12]
pica
≡ 12 points
Dependent on point measures.
picometre
pm
≡ 1× 10−12 m
≡ 1× 10−12 m
point (American, English)[ 13] [ 14]
pt
≡ 1 ⁄72.272 in
≈ 0.000351 450 m
point (Didot; European) [ 14] [ 15]
pt
≡ 1 ⁄12 × 1 ⁄72 of pied du roi ;After 1878: ≡ 5 ⁄133 cm
≈ 0.000375 97 m ;After 1878: ≈ 0.000375 939 85 m
point (PostScript ) [ 13]
pt
≡ 1 ⁄72 in
= 0.0003527 m
point (TeX ) [ 13]
pt
≡ 1 ⁄72.27 in
= 0.000351 4598 m
quarter
≡ 1 ⁄4 yd
= 0.2286 m
rod ; pole; perch (H)
rd
≡ 16+ 1 ⁄2 ft
= 5.0292 m
rope (H)
rope
≡ 20 ft [ 4]
= 6.096 m
shaku (Japan)
≡ 10/33 m
≈ 0.303 0303 m
span (H)
≡ 9 in [ 4]
= 0.2286 m
spat [ 16]
≡ 1× 1012 m
stick (H)
≡ 2 in
= 0.0508 m
toise (French, post 1667) (H)
T
≡ 27000/13853 m
≈ 1.949 0363 m
twip
twp
≡ 1 ⁄1440 in
= 1.7638 × 10−5 m
x unit ; siegbahn
xu
≈ 1.0021× 10−13 m [ 4]
yard (International)
yd
≡ 0.9144 m [ 5] ≡ 3 ft ≡ 36 in
≡ 0.9144 m
yoctometre
ym
≡ 1× 10−24 m
≡ 1× 10−24 m
zeptometre
zm
≡ 1× 10−21 m
≡ 1× 10−21 m
Area
Area
Name of unit
Symbol
Definition
Relation to SI units
acre (international)
ac
≡ 1 ch × 10 ch = 4840 sq yd
≡ 4046 .8564224 m2
acre (US survey)
ac
≡ 10 sq ch = 4840 sq yd , also 43560 sq ft
≈ 4046 .873 m2 [ 17]
are
a
≡ 100 m2
≡ 100 m2
barn
b
≡ 10−28 m2
≡ 10−28 m2
barony
≡ 4000 ac
≡ 1.618742 568 96 × 107 m2
board
bd
≡ 1 in × 1 ft
≡ 7.74192 × 10−3 m2
boiler horsepower equivalent direct radiation
bhp EDR
≡ 1 ft2 × 1 bhp / (240 BTUIT /h)
≈ 12.958174 m2
circular inch
circ in
≡ π ⁄4 sq in
≈ 5.067075 × 10−4 m2
circular mil; circular thou
circ mil
≡ π ⁄4 mil2
≈ 5.067075 × 10−10 m2
cord
≡ 192 bd
≡ 1.486448 64 m2
cuerda (PR Survey)
cda
≡ 1 cda x 1 cda = 0.971222 acre
≡ 3930 .395625 m2
dunam
≡ 1000 m2
≡ 1000 m2
guntha (India)
≡ 121 sq yd
≈ 101.17 m2
hectare
ha
≡ 10000 m2
≡ 10000 m2
hide
≈ 120 ac (variable)
≈ 5× 105 m2
rood
ro
≡ 1 ⁄4 ac
= 1011 .7141056 m2
ping
≡ 20 ⁄11 m × 20 ⁄11 m
≈ 3.306 m2
section
≡ 1 mi × 1 mi
= 2.589988 110 336 × 106 m2
shed
≡ 10−52 m2
= 10−52 m2
square (roofing)
≡ 10 ft × 10 ft
= 9.290304 m2
square chain (international)
sq ch
≡ 66 ft × 66 ft = 1 ⁄10 ac
≡ 404.685642 24 m2
square chain (US Survey)
sq ch
≡ 66 ft (US) × 66 ft (US) = 1 ⁄10 US survey acre
≈ 404.6873 m2
square foot
sq ft
≡ 1 ft × 1 ft
≡ 9.290304 × 10−2 m2
square foot (US Survey)
sq ft
≡ 1 ft (US) × 1 ft (US)
≈ 9.290341 161 3275 × 10−2 m2
square inch
sq in
≡ 1 in × 1 in
≡ 6.4516× 10−4 m2
square kilometre
km2
≡ 1 km × 1 km
= 106 m2
square link (Gunter's)(International)
sq lnk
≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft
= 4.046856 4224 × 10−2 m2
square link (Gunter's)(US Survey)
sq lnk
≡ 1 lnk × 1 lnk ≡ 0.66 ft (US) × 0.66 ft (US)
≈ 4.046872 × 10−2 m2
square link (Ramsden's)
sq lnk
≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft
= 0.092903 04 m2
square metre (SI unit)
m2
≡ 1 m × 1 m
= 1 m2
square mil; square thou
sq mil
≡ 1 mil × 1 mil
= 6.4516× 10−10 m2
square mile
sq mi
≡ 1 mi × 1 mi
≡ 2.589988 110 336 × 106 m2
square mile (US Survey)
sq mi
≡ 1 mi (US) × 1 mi (US)
≈ 2.589998 47 × 106 m2
square rod/pole/perch
sq rd
≡ 1 rd × 1 rd
= 25.292852 64 m2
square yard (International)
sq yd
≡ 1 yd × 1 yd
≡ 0.836127 36 m2
stremma
≡ 1000 m2
= 1000 m2
township
≡ 36 sq mi (US)
≈ 9.323994 × 107 m2
yardland
≈ 30 ac
≈ 1.2× 105 m2
Volume
Volume
Name of unit
Symbol
Definition
Relation to SI units
acre-foot
ac ft
≡ 1 ac x 1 ft = 43560 cu ft
= 1233 .481837 547 52 m3
acre-inch
≡ 1 ac × 1 in
= 102.790153 128 96 m3
barrel (imperial)
bl (imp)
≡ 36 gal (imp)
= 0.163659 24 m3
barrel (petroleum); archaic blue-barrel
bl; bbl
≡ 42 gal (US)
≡ 0.158987 294 928 m3
barrel (US dry)
bl (US)
≡ 105 qt (US) = 105/32 bu (US lvl)
= 0.115628 198 985 075 m3
barrel (US fluid)
fl bl (US)
≡ 31+ 1 ⁄2 gal (US)
= 0.119240 471 196 m3
board-foot
bdft
≡ 144 cu in
≡ 2.359737 216 × 10−3 m3
bucket (imperial)
bkt
≡ 4 gal (imp)
= 0.018184 36 m3
bushel (imperial)
bu (imp)
≡ 8 gal (imp)
= 0.036368 72 m3
bushel (US dry heaped)
bu (US)
≡ 1+ 1 ⁄4 bu (US lvl)
= 0.044048 837 7086 m3
bushel (US dry level)
bu (US lvl)
≡ 2150 .42 cu in
= 0.035239 070 166 88 m3
butt , pipe
≡ 126 gal (US) (wine)
= 0.476961 884 784 m3
coomb
≡ 4 bu (imp)
= 0.145474 88 m3
cord (firewood )
≡ 8 ft × 4 ft × 4 ft
= 3.624556 363 776 m3
cord-foot
≡ 16 cu ft
= 0.453069 545 472 m3
cubic fathom
cu fm
≡ 1 fm × 1 fm × 1 fm
= 6.116438 863 872 m3
cubic foot
ft3
≡ 1 ft × 1 ft × 1 ft
≡ 0.028316 846 592 m3
cubic inch
in3
≡ 1 in × 1 in × 1 in
≡ 16.387064 × 10−6 m3
cubic metre (SI unit)
m3
≡ 1 m × 1 m × 1 m
≡ 1 m3
cubic mile
cu mi
≡ 1 mi × 1 mi × 1 mi
≡ 4168 181 825 .440579 584 m3
cubic yard
yd3
≡ 27 cu ft
≡ 0.764554 857 984 m3
cup (breakfast)
≡ 10 fl oz (imp)
= 284.130625 × 10−6 m3
cup (Canadian)
c (CA)
≡ 8 fl oz (imp)
= 227.3045× 10−6 m3
cup (metric)
c
≡ 250.0× 10−6 m3
≡ 250.0× 10−6 m3
cup (US customary)
c (US)
≡ 8 US fl oz ≡ 1 ⁄16 gal (US)
= 236.5882365 × 10−6 m3
cup (US food nutrition labeling)
c (US)
≡ 240 mL[ 18]
= 2.4× 10−4 m3
dash (imperial)
≡ 1 ⁄192 gi (imp) = 1/8 tsp (imp)
= 739.923502 604 16 × 10−9 m3
dash (US)
≡ 1 ⁄48 US fl oz = 1/8 US tsp
= 616.115199 218 75 × 10−9 m3
dessertspoon (imperial)
≡ 1 ⁄12 gi (imp)
= 11.838776 0416 × 10−6 m3
drop (imperial)
gtt
≡ 1 ⁄288 fl oz (imp)
= 98.656467 0138 × 10−9 m3
drop (imperial) (alt)
gtt
≡ 1 ⁄ 1824 gi (imp)
≈ 77.886684 × 10−9 m3
drop (medical)
≡ 1 ⁄12 mL
= 83.3 × 10−9 m3
drop (metric)
≡ 1 ⁄20 mL
= 50.0× 10−9 m3
drop (US)
gtt
≡ 1 ⁄360 US fl oz
= 82.148693 229 16 × 10−9 m3
drop (US) (alt)
gtt
≡ 1 ⁄456 US fl oz
≈ 64.854231 496 71 × 10−9 m3
drop (US) (alt)
gtt
≡ 1 ⁄576 US fl oz
≈ 51.342933 268 23 × 10−9 m3
fifth
≡ 1 ⁄5 US gal
= 757.0823568 × 10−6 m3
firkin
≡ 9 gal (imp)
= 0.040914 81 m3
fluid drachm (imperial)
fl dr
≡ 1 ⁄8 fl oz (imp)
= 3.551632 8125 × 10−6 m3
fluid dram (US); US fluidram
fl dr
≡ 1 ⁄8 US fl oz
= 3.696691 195 3125 × 10−6 m3
fluid scruple (imperial)
fl s
≡ 1 ⁄24 fl oz (imp)
= 1.183877 604 16 × 10−6 m3
gallon (beer)
beer gal
≡ 282 cu in
= 4.621152 048 × 10−3 m3
gallon (imperial)
gal (imp)
≡ 4.54609 L
≡ 4.54609 × 10−3 m3
gallon (US dry)
gal (US)
≡ 1 ⁄8 bu (US lvl)
= 4.404883 770 86 × 10−3 m3
gallon (US fluid; Wine)
gal (US)
≡ 231 cu in
≡ 3.785411 784 × 10−3 m3
gill (imperial); Noggin
gi (imp); nog
≡ 5 fl oz (imp)
= 142.0653125 × 10−6 m3
gill (US)
gi (US)
≡ 4 US fl oz
= 118.294118 25 × 10−6 m3
hogshead (imperial)
hhd (imp)
≡ 2 bl (imp)
= 0.327318 48 m3
hogshead (US)
hhd (US)
≡ 2 fl bl (US)
= 0.238480 942 392 m3
jigger (bartending)
≡ 1+ 1 ⁄2 US fl oz
≈ 44.36× 10−6 m3
kilderkin
≡ 18 gal (imp)
= 0.081829 62 m3
lambda
λ
≡ 1 mm3
= 1× 10−9 m3
last
≡ 80 bu (imp)
= 2.9094976 m3
litre (liter)
L or l
≡ 1 dm3 [ 19]
≡ 0.001 m3
load
≡ 50 cu ft
= 1.415842 3296 m3
minim (imperial)
min
≡ 1 ⁄480 fl oz (imp) = 1/60 fl dr (imp)
= 59.193880 2083 × 10−9 m3
minim (US)
min
≡ 1 ⁄480 US fl oz = 1 ⁄60 US fl dr
= 61.611519 921 875 × 10−9 m3
ounce (fluid imperial)
fl oz (imp)
≡ 1 ⁄160 gal (imp)
≡ 28.4130625 × 10−6 m3
ounce (fluid US customary)
US fl oz
≡ 1 ⁄128 gal (US)
≡ 29.573529 5625 × 10−6 m3
ounce (fluid US food nutrition labeling)
US fl oz
≡ 30 mL[ 18]
≡ 3× 10−5 m3
peck (imperial)
pk
≡ 2 gal (imp)
= 9.09218 × 10−3 m3
peck (US dry)
pk
≡ 1 ⁄4 US lvl bu
= 8.809767 541 72 × 10−3 m3
perch
per
≡ 16+ 1 ⁄2 ft × 1+ 1 ⁄2 ft × 1 ft
= 0.700841 953 152 m3
pinch (imperial)
≡ 1 ⁄384 gi (imp) = 1 ⁄2 dash (imp)
= 369.961751 302 083 × 10−9 m3
pinch (US)
≡ 1 ⁄96 US fl oz = 1 ⁄2 US dash
= 308.057599 609 375 × 10−9 m3
pint (imperial)
pt (imp)
≡ 1 ⁄8 gal (imp)
= 568.26125 × 10−6 m3
pint (US dry)
pt (US dry)
≡ 1 ⁄64 bu (US lvl) ≡ 1 ⁄8 gal (US dry)
= 550.610471 3575 × 10−6 m3
pint (US fluid)
pt (US fl)
≡ 1 ⁄8 gal (US)
= 473.176473 × 10−6 m3
pony
≡ 3 ⁄4 US fl oz
= 22.180147 171 875 × 10−6 m3
pottle; quartern
≡ 1 ⁄2 gal (imp) = 80 fl oz (imp)
= 2.273045 × 10−3 m3
quart (imperial)
qt (imp)
≡ 1 ⁄4 gal (imp)
= 1.1365225 × 10−3 m3
quart (US dry)
qt (US)
≡ 1 ⁄32 bu (US lvl) = 1 ⁄4 gal (US dry)
= 1.101220 942 715 × 10−3 m3
quart (US fluid)
qt (US)
≡ 1 ⁄4 gal (US fl)
= 946.352946 × 10−6 m3
quarter; pail
≡ 8 bu (imp)
= 0.290949 76 m3
register ton
≡ 100 cu ft
= 2.831684 6592 m3
sack (US)
≡ 3 bu (US lvl)
= 0.105717 210 500 64 m3
seam
≡ 8 bu [ 16]
= 0.29095 m3
shot (US)
usually 1.5 US fl oz[ 16]
≈ 44.4× 10−6 m3
strike (imperial)
≡ 2 bu (imp)
= 0.072737 44 m3
strike (US)
≡ 2 bu (US lvl)
= 0.070478 140 333 76 m3
tablespoon (Australian metric)
≡ 20.0× 10−6 m3
tablespoon (Canadian)
tbsp
≡ 1 ⁄2 fl oz (imp)
= 14.206531 25 × 10−6 m3
tablespoon (imperial)
tbsp
≡ 5 ⁄8 fl oz (imp)
= 17.758164 0625 × 10−6 m3
tablespoon (metric)
≡ 15× 10−6 m3
tablespoon (US customary)
tbsp
≡ 1 ⁄2 US fl oz
= 14.786764 781 25 × 10−6 m3
tablespoon (US food nutrition labeling)
tbsp
≡ 15 mL[ 18]
= 15× 10−6 m3
teaspoon (Canadian)
tsp
≡ 1 ⁄6 fl oz (imp)
= 4.735510 416 × 10−6 m3
teaspoon (imperial)
tsp
≡ 1 ⁄24 gi (imp)
= 5.919388 020 83 × 10−6 m3
teaspoon (metric)
≡ 5.0× 10−6 m3
≡ 5.0× 10−6 m3
teaspoon (US customary)
tsp
≡ 1 ⁄6 US fl oz
= 4.928921 593 75 × 10−6 m3
teaspoon (US food nutrition labeling)
tsp
≡ 5 mL[ 18]
= 5× 10−6 m3
timber foot
≡ 1 cu ft
= 0.028316 846 592 m3
ton (displacement)
≡ 35 cu ft
= 0.991089 630 72 m3
ton (freight)
≡ 40 cu ft
= 1.132673 863 68 m3
ton (water)
≡ 28 bu (imp)
= 1.018324 16 m3
tun
≡ 252 gal (wine)
= 0.953923 769 568 m3
wey (US)
≡ 40 bu (US lvl)
= 1.409562 806 6752 m3
Plane angle
Plane angle
Name of unit
Symbol
Definition
Relation to SI units
NATO mil
(various )
≡ 2π ⁄ 6400 rad
≈ 0.981748 × 10−3 rad
Swedish streck
≡ 2π ⁄ 6300 rad
≈ 0.997302 × 10−3 rad
milliradian
mrad
≡ 1 ⁄1000 rad
≈ 1× 10−3 rad
Warsaw Pact mil
≡ 2π ⁄ 6000 rad
≈ 1.047167 × 10−3 rad
arcminute ; MOA
'
≡ 1° ⁄60
≈ 0.290888 × 10−3 rad
arcsecond
"
≡ 1° ⁄ 3600
≈ 4.848137 × 10−6 rad
centesimal minute of arc
'
≡ 1 ⁄100 grad
≈ 0.157080 × 10−3 rad
centesimal second of arc
"
≡ 1 ⁄ 10000 grad
≈ 1.570796 × 10−6 rad
degree (of arc)
°
≡ 1 ⁄360 of a revolution ≡ π ⁄180 rad
≈ 17.453293 × 10−3 rad
grad ; gradian; gon
grad
≡ 1 ⁄400 of a revolution ≡ π ⁄200 rad ≡ 0.9°
≈ 15.707963 × 10−3 rad
octant
≡ 45°
≈ 0.785398 rad
quadrant
≡ 90°
≈ 1.570796 rad
radian (SI unit)
rad
The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians.
= 1 rad
sextant
≡ 60°
≈ 1.047198 rad
sign
≡ 30°
≈ 0.523599 rad
Solid angle
Solid angle
Name of unit
Symbol
Definition
Relation to SI units
spat
≡ 4π sr [ 16] – The solid angle subtended by a sphere at its centre.
≈ 12.56637 sr
square degree
deg2 ; sq.deg.; (°)2
≡ (π ⁄180 )2 sr
≈ 0.30462 × 10−3 sr
steradian (SI unit)
sr
The solid angle subtended at the center of a sphere of radius r by a portion of the sphere having an area r 2 . A sphere subtends 4π sr.[ 16]
= 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.
The symbol g 0 is used to denote standard gravity in order to avoid confusion with the (upright) g symbol for gram.
Mass
Name of unit
Symbol
Definition
Relation to SI units
atomic mass unit, unified
u; AMU
Same as dalton (see below)
≈ 1.660539 040 (20)× 10−27 kg[ 3]
atomic unit of mass , electron rest mass
m e
≈ 9.109382 91 (40)× 10−31 kg[ 20]
bag (coffee )
≡ 60 kg
= 60 kg
bag (Portland cement )
≡ 94 lb av
= 42.637682 78 kg
barge
≡ 22+ 1 ⁄2 short ton
= 20411 .65665 kg
carat
kt
≡ 3+ 1 ⁄6 gr
= 205.196548 3 mg
carat (metric)
ct
≡ 200 mg
= 200 mg
clove
≡ 8 lb av
= 3.628738 96 kg
crith
≡ mass of 1 L of hydrogen gas at STP
≈ 89.9349 mg
dalton
Da
1/12 the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest
≈ 1.660538 921 (73)× 10−27 kg[ 3]
dram (apothecary; troy )
dr t
≡ 60 gr
= 3.8879346 g
dram (avoirdupois)
dr av
≡ 27+ 11 ⁄32 gr
= 1.771845 195 3125 g
electronvolt mass-equivalent
eV/c 2
≡ 1 eV / c 2
= 1.782661 84 (45)× 10−36 kg[ 3]
gamma
γ
≡ 1 μg
= 1 μg
grain
gr
≡ 1 ⁄ 7000 lb av
≡ 64.79891 mg
grave
gv
grave was the original name of the kilogram
≡ 1 kg
hundredweight (long)
long cwt or cwt
≡ 112 lb av
= 50.802345 44 kg
hundredweight (short); cental
sh cwt
≡ 100 lb av
= 45.359237 kg
hyl ; metric slug
≡ 1 kgf / 1 m/s2
= 9.80665 kg
kilogram (kilogramme)
kg
≈ mass of the prototype near Paris ≈ mass of 1 litre of water
(SI base unit )[ 8]
kip
kip
≡ 1000 lb av
= 453.59237 kg
mark
≡ 8 oz t
= 248.8278144 g
mite
≡ 1 ⁄20 gr
= 3.2399455 mg
mite (metric)
≡ 1 ⁄20 g
= 50 mg
ounce (apothecary; troy)
oz t
≡ 1 ⁄12 lb t
= 31.1034768 g
ounce (avoirdupois )
oz av
≡ 1 ⁄16 lb
= 28.349523 125 g
ounce (US food nutrition labelling)
oz
≡ 28 g[ 18]
= 28 g
pennyweight
dwt; pwt
≡ 1 ⁄20 oz t
= 1.555173 84 g
point
≡ 1 ⁄100 ct
= 2 mg
pound (avoirdupois)
lb av
≡ 0.453592 37 kg = 7000 grains
≡ 0.453592 37 kg
pound (metric)
≡ 500 g
= 500 g
pound (troy)
lb t
≡ 5760 grains
= 0.373241 7216 kg
quarter (imperial)
≡ 1 ⁄4 long cwt = 2 st = 28 lb av
= 12.700586 36 kg
quarter (informal)
≡ 1 ⁄4 short ton
= 226.796185 kg
quarter, long (informal)
≡ 1 ⁄4 long ton
= 254.0117272 kg
quintal (metric)
q
≡ 100 kg
= 100 kg
scruple (apothecary )
s ap
≡ 20 gr
= 1.2959782 g
sheet
≡ 1 ⁄700 lb av
= 647.9891 mg
slug ; geepound
slug
≡ g 0 × 1 lb av × 1 s2 /ft
≈ 14.593903 kg
stone
st
≡ 14 lb av
= 6.350293 18 kg
ton, assay (long)
AT
≡ 1 mg × 1 long ton ÷ 1 oz t
= 32.6 g
ton, assay (short)
AT
≡ 1 mg × 1 short ton ÷ 1 oz t
= 29.16 g
ton, long
long tn or ton
≡ 2240 lb
= 1016 .0469088 kg
ton, short
sh tn
≡ 2000 lb
= 907.18474 kg
tonne (mts unit)
t
≡ 1000 kg
= 1000 kg
wey
≡ 252 lb = 18 st
= 114.305277 24 kg (variants exist)
zentner
Ztr.
Definitions vary.[ 16] [ 21]
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
≈ 1.001153 961 kg/m3
ounce (avoirdupois) per cubic inch
oz/in3
≡ oz/in3
≈ 1.729994 044 × 103 kg/m3
ounce (avoirdupois) per gallon (imperial)
oz/gal
≡ oz/gal
≈ 6.236023 291 kg/m3
ounce (avoirdupois) per gallon (US fluid)
oz/gal
≡ oz/gal
≈ 7.489151 707 kg/m3
pound (avoirdupois) per cubic foot
lb/ft3
≡ lb/ft3
≈ 16.018463 37 kg/m3
pound (avoirdupois) per cubic inch
lb/in3
≡ lb/in3
≈ 2.767990 471 × 104 kg/m3
pound (avoirdupois) per gallon (imperial)
lb/gal
≡ lb/gal
≈ 99.776372 66 kg/m3
pound (avoirdupois) per gallon (US fluid)
lb/gal
≡ lb/gal
≈ 119.8264273 kg/m3
slug per cubic foot
slug/ft3
≡ slug/ft3
≈ 515.3788184 kg/m3
Time
Time
Name of unit
Symbol
Definition
Relation to SI units
atomic unit of time
a.u.
≡ a 0 /(α ⋅c )
≈ 2.418884 254 × 10−17 s
Callippic cycle
≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d
= 2.396736 Gs or 2.3983776 Gs[ note 1]
century
c
≡ 100 years (100 a)
= 3.1556952 Gs[ note 2] [ note 3]
day
d
= 24 h = 1440 min
= 86.4 ks[ note 3]
day (sidereal)
d
≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame )
≈ 86.1641 ks
decade
dec
≡ 10 years (10 a)
= 315.569520 Ms[ note 2] [ note 3]
fortnight
fn
≡ 2 wk
= 1.2096 Ms[ note 3]
helek
≡ 1 ⁄ 1080 h
= 3.3 s
Hipparchic cycle
≡ 4 Callippic cycles - 1 d
= 9.593424 Gs
hour
h
≡ 60 min
= 3.6 ks[ note 3]
jiffy
j
≡ 1 ⁄60 s
= 16.6 ms
jiffy (alternative)
ja
≡ 1 ⁄100 s
= 10 ms
kè (quarter of an hour)
≡ 1 ⁄4 h = 1 ⁄96 d = 15 min
= 900 s
kè (traditional)
≡ 1 ⁄100 d = 14.4 min
= 864 s
lustre; lūstrum
≡ 5 a of 365 d[ note 4]
= 157.68 Ms
Metonic cycle ; enneadecaeteris
≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a
= 599.616 Ms
millennium
≡ 1000 years ( 1000 a )
= 31.556952 Gs[ note 2] [ note 3]
milliday
md
≡ 1 ⁄ 1000 d
= 86.4 s
minute
min
≡ 60 s, due to leap seconds sometimes 59 s or 61 s,
= 60 s[ note 3]
moment
≡ 90 s
= 90 s
month (full)
mo
≡ 30 d[ 22]
= 2.592× 106 s[ note 3]
month (Greg. av.)
mo
= 30.436875 d
≈ 2.6297 Ms[ note 3]
month (hollow)
mo
≡ 29 d[ 22]
= 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)[ 23] [ 24] = 8 a of 365.25 d = 2922 d
= 252.4608 Ms[ note 3]
Planck time
≡ (G ℏ ⁄c 5 )1 ⁄2
≈ 5.39116 × 10−44 s[ 25]
second (SI base unit)
s
≡ Time of 9192 631 770 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[ 8] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of 299792 458 metres.
(SI base unit )
shake
≡ 10−8 s
= 10 ns
sigma
≡ 10−6 s
= 1 μs
Sothic cycle
≡ 1461 a of 365 d
= 46.074096 Gs
svedberg
S
≡ 10−13 s
= 100 fs
week
wk
≡ 7 d = 168 h = 10080 min
= 604.8 ks[ note 3]
year (common)
a, y, or yr
365 d
= 31.536 Ms[ note 3] [ 26]
year (Gregorian)
a, y, or yr
= 365.2425 d average, calculated from common years (365 d) plus leap years (366 d) on most years divisible by 4. See leap year for details.
= 31.556952 Ms[ note 3]
year (Julian)
a, y, or yr
= 365.25 d average, calculated from common years (365 d) plus one leap year (366 d) every four years
= 31.5576 Ms
year (leap)
a, y, or yr
366 d
= 31.6224 Ms[ note 3] [ 26]
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[ 27]
≈ 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
≈ 31.558149 7632 Ms
Notes:
^ see Callippic cycle for explanation of the differences
^ a b c This is based on the average Gregorian year. See above for definition of year lengths.
^ a b c d e f g h i j k l m n o 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.
^ The length of ancient lustral cycles was not constant; see Lustrum for more details
Frequency
Frequency
Name of unit
Symbol
Definition
Relation to SI units
actions per minute
APM
≡ 1/60 Hz
≈ 0.0167 Hz
cycle per second
cps
≡ 1 Hz
= 1 cps = 1 Hz
degree per second
deg/s
≡ 1 °/s ≡ 1/360 Hz
= 0.0027 Hz
hertz (SI unit)
Hz
≡ One cycle per second
= 1 Hz = 1/s
radian per second
rad/s
≡ 1/(2π) Hz
≈ 0.159155 Hz
revolution per minute
rpm
≡ One rpm equals one rotation completed around a fixed axis in one minute of time.
≈ 0.104719 755 rad/s
Speed or velocity
Speed
Name of unit
Symbol
Definition
Relation to SI units
foot per hour
fph
≡ 1 ft/h
= 8.46 × 10−5 m/s
foot per minute
fpm
≡ 1 ft/min
= 5.08× 10−3 m/s
foot per second
fps
≡ 1 ft/s
= 3.048× 10−1 m/s
furlong per fortnight
≡ furlong/fortnight
≈ 1.663095 × 10−4 m/s
inch per hour
iph
≡ 1 in/h
= 7.05 × 10−6 m/s
inch per minute
ipm
≡ 1 in/min
= 4.23 × 10−4 m/s
inch per second
ips
≡ 1 in/s
= 2.54× 10−2 m/s
kilometre per hour
km/h
≡ 1 km/h
= 2.7 × 10−1 m/s
knot
kn
≡ 1 nmi /h = 1.852 km/h
= 0.514 m/s
knot (Admiralty)
kn
≡ 1 NM (Adm)/h = 1.853184 km/h[ 28]
= 0.51477 3 m/s
mach number
M
Ratio of the speed to the speed of sound[ note 1] in the medium (unitless).
≈ 340 m/s in air at sea level ≈ 295 m/s in air at jet altitudes
metre per second (SI unit)
m/s
≡ 1 m/s
= 1 m/s
mile per hour
mph
≡ 1 mi/h
= 0.44704 m/s
mile per minute
mpm
≡ 1 mi/min
= 26.8224 m/s
mile per second
mps
≡ 1 mi/s
= 1609 .344 m/s
speed of light in vacuum
c
≡ 299792 458 m/s
= 299792 458 m/s
speed of sound in air
s
1225 to 1062 km/h (761–660 mph or 661–574 kn)[ note 1]
≈ 340 to 295 m/s
Note
^ a b The speed of sound varies especially with temperature and pressure from about 340 m/s (1,225 km/h or 761 mph or 661 kn) in air at sea level to about 300 m/s (1,062 km/h or 660 mph or 573 kn) at jet altitudes (12200 m or 40000 ft).[ 29]
A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.
Flow (volume)
Volumetric flow rate
Name of unit
Symbol
Definition
Relation to SI units
cubic foot per minute
CFM[citation needed ]
≡ 1 ft3 /min
= 4.719474 432 × 10−4 m3 /s
cubic foot per second
ft3 /s
≡ 1 ft3 /s
= 0.028316 846 592 m3 /s
cubic inch per minute
in3 /min
≡ 1 in3 /min
= 2.731177 3 × 10 −7 m3 /s
cubic inch per second
in3 /s
≡ 1 in3 /s
= 1.6387064 × 10−5 m3 /s
cubic metre per second (SI unit)
m3 /s
≡ 1 m3 /s
= 1 m3 /s
gallon (US fluid) per day
GPD[citation needed ]
≡ 1 gal/d
= 4.381263 63 8 × 10 −8 m3 /s
gallon (US fluid) per hour
GPH[citation needed ]
≡ 1 gal/h
= 1.051503 27 3 × 10 −6 m3 /s
gallon (US fluid) per minute
GPM[citation needed ]
≡ 1 gal/min
= 6.309019 64 × 10−5 m3 /s
litre per minute
l/min or L/min
≡ 1 L/min
= 1.6 × 10 −5 m3 /s
Acceleration
Force
Force
Name of unit
Symbol
Definition
Relation to SI units
atomic unit of force
≡ me ⋅α 2 ⋅c 2 ⁄a0
≈ 8.238722 06 × 10−8 N[ 30]
dyne (CGS unit )
dyn
≡ g⋅cm/s2
= 10−5 N
kilogram-force ; kilopond; grave -force
kgf; kp; gvf
≡ g 0 × 1 kg
= 9.80665 N
kip ; kip-force
kip; kipf; klbf
≡ g 0 × 1000 lb
= 4.448221 615 2605 × 103 N
milligrave -force, gravet-force
mgvf; gvtf
≡ g 0 × 1 g
= 9.80665 mN
long ton -force
tnf[citation needed ]
≡ g 0 × 1 long ton
= 9.964016 418 183 52 × 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.[ 31]
= 1 N = 1 kg⋅m/s2
ounce-force
ozf
≡ g 0 × 1 oz
= 0.278013 850 953 781 25 N
pound-force
lbf
≡ g 0 × 1 lb
= 4.448221 615 2605 N
poundal
pdl
≡ 1 lb⋅ft/s2
= 0.138254 954 376 N
short ton-force
tnf[citation needed ]
≡ g 0 × 1 short ton
= 8.896443 230 521 × 103 N
sthene (mts unit)
sn
≡ 1 t⋅m/s2
= 103 N
Pressure or mechanical stress
Pressure
Name of unit
Symbol
Definition
Relation to SI units
atmosphere (standard)
atm
≡ 101325 Pa[ 32]
atmosphere (technical)
at
≡ 1 kgf/cm2
= 9.80665 × 104 Pa[ 32]
bar
bar
≡ 100000 Pa
≡ 105 Pa
barye (CGS unit )
≡ 1 dyn/cm2
= 0.1 Pa
centimetre of mercury
cmHg
≡ 13595 .1 kg/m3 × 1 cm × g 0
≈ 1.33322 × 103 Pa[ 32]
centimetre of water (4 °C)
cmH2 O
≈ 999.972 kg/m3 × 1 cm × g 0
≈ 98.0638 Pa[ 32]
foot of mercury (conventional)
ftHg
≡ 13595 .1 kg/m3 × 1 ft × g 0
≈ 4.063666 × 104 Pa[ 32]
foot of water (39.2 °F)
ftH2 O
≈ 999.972 kg/m3 × 1 ft × g 0
≈ 2.98898 × 103 Pa[ 32]
inch of mercury (conventional)
inHg
≡ 13595 .1 kg/m3 × 1 in × g 0
≈ 3.386389 × 103 Pa[ 32]
inch of water (39.2 °F)
inH2 O
≈ 999.972 kg/m3 × 1 in × g 0
≈ 249.082 Pa[ 32]
kilogram-force per square millimetre
kgf/mm2
≡ 1 kgf/mm2
= 9.80665 × 106 Pa[ 32]
kip per square inch
ksi
≡ 1 kipf/sq in
≈ 6.894757 × 106 Pa[ 32]
long ton per square foot
≡ 1 long ton × g 0 / 1 sq ft
≈ 1.072517 801 1595 × 105 Pa
micrometre of mercury
μmHg
≡ 13595 .1 kg/m3 × 1 μm × g 0 ≈ 0.001 torr
≈ 0.1333224 Pa[ 32]
millimetre of mercury
mmHg
≡ 13595 .1 kg/m3 × 1 mm × g 0 ≈ 1 torr
≈ 133.3224 Pa[ 32]
millimetre of water (3.98 °C)
mmH2 O
≈ 999.972 kg/m3 × 1 mm × g 0 = 0.999972 kgf/m2
= 9.80638 Pa
pascal (SI unit)
Pa
≡ N/m2 = kg/(m⋅s2 )
= 1 Pa[ 33]
pièze (mts unit)
pz
≡ 1000 kg/m⋅s2
= 103 Pa = 1 kPa
pound per square foot
psf
≡ 1 lbf/ft2
≈ 47.88026 Pa[ 32]
pound per square inch
psi
≡ 1 lbf/in2
≈ 6.894757 × 103 Pa[ 32]
poundal per square foot
pdl/sq ft
≡ 1 pdl/sq ft
≈ 1.488164 Pa[ 32]
short ton per square foot
≡ 1 short ton × g 0 / 1 sq ft
≈ 9.5760518 × 104 Pa
torr
torr
≡ 101325 ⁄760 Pa
≈ 133.3224 Pa[ 32]
Torque or moment of force
Torque
Name of unit
Symbol
Definition
Relation to SI units
pound-force-foot
lbf⋅ft
≡ g 0 × 1 lb × 1 ft
= 1.355817 948 331 4004 N⋅m
poundal-ft
pdl⋅ft
≡ 1 lb⋅ft2 /s2
= 4.214011 009 380 48 × 10−2 N⋅m
pound force-inch
lbf⋅in
≡ g 0 × 1 lb × 1 in
= 0.112984 829 027 6167 N⋅m
kilogram force-meter
kgf⋅m
≡ g 0 × N × m
= 9.80665 N⋅m
newton-metre (SI unit)
N⋅m
≡ N × m = kg⋅m2 /s2
= 1 N⋅m
Energy
Energy
Name of unit
Symbol
Definition
Relation to SI units
barrel of oil equivalent
boe
≈ 5.8× 106 BTU59 °F
≈ 6.12× 109 J
British thermal unit (ISO)
BTUISO
≡ 1.0545× 103 J
= 1.0545× 103 J
British thermal unit (International Table)
BTUIT
= 1.055055 852 62 × 103 J
British thermal unit (mean)
BTUmean
≈ 1.05587 × 103 J
British thermal unit (thermochemical)
BTUth
≈ 1.054350 × 103 J
British thermal unit (39 °F)
BTU39 °F
≈ 1.05967 × 103 J
British thermal unit (59 °F)
BTU59 °F
≡ 1.054804 × 103 J
= 1.054804 × 103 J
British thermal unit (60 °F)
BTU60 °F
≈ 1.05468 × 103 J
British thermal unit (63 °F)
BTU63 °F
≈ 1.0546× 103 J
calorie (International Table)
calIT
≡ 4.1868 J
= 4.1868 J
calorie (mean)
calmean
1 ⁄100 of the energy required to warm one gram of air-free water from 0 °C to 100 °C 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
= 1.899100 534 716 × 103 J
cubic centimetre of atmosphere ; standard cubic centimetre
cc atm; scc
≡ 1 atm × 1 cm3
= 0.101325 J
cubic foot of atmosphere; standard cubic foot
cu ft atm; scf
≡ 1 atm × 1 ft3
= 2.869204 480 9344 × 103 J
cubic foot of natural gas
≡ 1000 BTUIT
= 1.055055 852 62 × 106 J
cubic yard of atmosphere; standard cubic yard
cu yd atm; scy
≡ 1 atm × 1 yd3
= 77.468520 985 2288 × 103 J
electronvolt
eV
≡ e × 1 V
≡ 1.602176 634 × 10−19 J
erg (CGS unit )
erg
≡ 1 g⋅cm2 /s2
= 10−7 J
foot-pound force
ft lbf
≡ g 0 × 1 lb × 1 ft
= 1.355817 948 331 4004 J
foot-poundal
ft pdl
≡ 1 lb⋅ft2 /s2
= 4.214011 009 380 48 × 10−2 J
gallon -atmosphere (imperial)
imp gal atm
≡ 1 atm × 1 gal (imp)
= 460.632569 25 J
gallon-atmosphere (US)
US gal atm
≡ 1 atm × 1 gal (US)
= 383.556849 0138 J
hartree , atomic unit of energy
E h
≡ me ⋅α 2 ⋅c 2 (= 2 Ry)
≈ 4.359744 × 10−18 J
horsepower-hour
hp⋅h
≡ 1 hp × 1 h
= 2.684519 537 696 172 792 × 106 J
inch-pound force
in lbf
≡ g 0 × 1 lb × 1 in
= 0.112984 829 027 6167 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.[ 31]
= 1 J = 1 m⋅N = 1 kg⋅m2 /s2 = 1 C⋅V = 1 W⋅s
kilocalorie; large calorie
kcal; Cal
≡ 1000 calIT
= 4.1868× 103 J
kilowatt-hour ; Board of Trade Unit
kW⋅h; B.O.T.U.
≡ 1 kW × 1 h
= 3.6× 106 J
litre -atmosphere
l atm; sl
≡ 1 atm × 1 L
= 101.325 J
quad
≡ 1015 BTUIT
= 1.055055 852 62 × 1018 J
rydberg
Ry
≡ R ∞ ⋅ℎ ⋅c
≈ 2.179872 × 10−18 J
therm (E.C.)
≡ 100000 BTUIT
= 105.505585 262 × 106 J
therm (US)
≡ 100000 BTU59 °F
= 105.4804× 106 J
thermie
th
≡ 1 McalIT
= 4.1868× 106 J
tonne of coal equivalent
TCE
≡ 7 Gcalth
= 29.288× 109 J
tonne of oil equivalent
toe
≡ 10 GcalIT
= 41.868× 109 J
ton of TNT
tTNT
≡ 1 Gcalth
= 4.184× 109 J
watt-hour
W⋅h
≡ 1 W × 1 h
= 3.6× 103 J
watt-second
W⋅s
≡ 1 J
= 1× 100 J
Power or heat flow rate
Power
Name of unit
Symbol
Definition
Relation to SI units
atmosphere -cubic centimetre per minute
atm ccm[citation needed ]
≡ 1 atm × 1 cm3 /min
= 1.68875 × 10−3 W
atmosphere-cubic centimetre per second
atm ccs[citation needed ]
≡ 1 atm × 1 cm3 /s
= 0.101325 W
atmosphere-cubic foot per hour
atm cfh[citation needed ]
≡ 1 atm × 1 cu ft/h
= 0.797001 247 04 W
atmosphere-cubic foot per minute
atm cfm[citation needed ]
≡ 1 atm × 1 cu ft/min
= 47.820074 682 24 W
atmosphere-cubic foot per second
atm cfs[citation needed ]
≡ 1 atm × 1 cu ft/s
= 2.869204 480 9344 × 103 W
BTU (International Table) per hour
BTUIT /h
≡ 1 BTUIT /h
≈ 0.293071 W
BTU (International Table) per minute
BTUIT /min
≡ 1 BTUIT /min
≈ 17.584264 W
BTU (International Table) per second
BTUIT /s
≡ 1 BTUIT /s
= 1.055055 852 62 × 103 W
calorie (International Table) per second
calIT /s
≡ 1 calIT /s
= 4.1868 W
erg per second
erg/s
≡ 1 erg/s
= 10−7 W
foot-pound-force per hour
ft⋅lbf/h
≡ 1 ft lbf/h
≈ 3.766161 × 10−4 W
foot-pound-force per minute
ft⋅lbf/min
≡ 1 ft lbf/min
= 2.259696 580 552 334 × 10−2 W
foot-pound-force per second
ft⋅lbf/s
≡ 1 ft lbf/s
= 1.355817 948 331 4004 W
horsepower (boiler)
hp
≈ 34.5 lb/h × 970.3 BTUIT /lb
≈ 9809 .5 W[ 34]
horsepower (European electrical)
hp
≡ 75 kp⋅m/s
= 736 W[citation needed ]
horsepower (electrical)
hp
≡ 746 W
= 746 W[ 34]
horsepower (mechanical)
hp
≡ 550 ft⋅lbf/s[ 34]
= 745.699871 582 270 22 W
horsepower (metric)
hp or PS
≡ 75 m⋅kgf/s
= 735.49875 W[ 34]
litre -atmosphere per minute
L·atm/min
≡ 1 atm × 1 L/min
= 1.68875 W
litre-atmosphere per second
L·atm/s
≡ 1 atm × 1 L/s
= 101.325 W
lusec
lusec
≡ 1 L·μmHg/s [ 16]
≈ 1.333× 10−4 W
poncelet
p
≡ 100 m⋅kgf/s
= 980.665 W
square foot equivalent direct radiation
sq ft EDR
≡ 240 BTUIT /h
≈ 70.337057 W
ton of air conditioning
≡ 2000 lb of ice melted / 24 h
≈ 3504 W
ton of refrigeration (imperial)
≡ 2240 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F
≈ 3.938875 × 103 W
ton of refrigeration (IT)
≡ 2000 lb × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F
≈ 3.516853 × 103 W
watt (SI unit)
W
The power which in one second of time gives rise to one joule of energy.[ 31]
= 1 W = 1 J/s = 1 N⋅m/s = 1 kg⋅m2 /s3
Action
Dynamic viscosity
Dynamic viscosity
Name of unit
Symbol
Definition
Relation to SI units
pascal second (SI unit)
Pa⋅s
≡ N⋅s/m2 , kg/(m⋅s)
= 1 Pa⋅s
poise (CGS unit )
P
≡ 1 barye⋅s
= 0.1 Pa⋅s
pound per foot hour
lb/(ft⋅h)
≡ 1 lb/(ft⋅h)
≈ 4.133789 × 10−4 Pa⋅s
pound per foot second
lb/(ft⋅s)
≡ 1 lb/(ft⋅s)
≈ 1.488164 Pa⋅s
pound-force second per square foot
lbf⋅s/ft2
≡ 1 lbf⋅s/ft2
≈ 47.88026 Pa⋅s
pound-force second per square inch
lbf⋅s/in2
≡ 1 lbf⋅s/in2
≈ 6894 .757 Pa⋅s
Kinematic viscosity
Kinematic viscosity
Name of unit
Symbol
Definition
Relation to SI units
square foot per second
ft2 /s
≡ 1 ft2 /s
= 0.092903 04 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 charge
Electric dipole
Electric dipole
Name of unit
Symbol
Definition
Relation to SI units
atomic unit of electric dipole moment
e a 0
≈ 8.478352 81 × 10−30 C⋅m[ 37]
coulomb-meter
C⋅m
= 1 C⋅m
debye
D
≡ 10−10 esu⋅Å
≘ 3.335640 95 × 10−30 C⋅m[ 38]
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.[ 31]
= 1 V = 1 W/A = 1 kg⋅m2 /(A⋅s3 ) = 1 J/C
Electrical resistance
Electrical resistance
Name of unit
Symbol
Definition
Relation to SI units
ohm (SI unit)
Ω
The resistance between two points in a conductor when one volt of electric potential difference, applied to these points, produces one ampere of current in the conductor.[ 31]
= 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.[ 31]
= 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[ 34]
= 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.[ 31]
= 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 [ 39]
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.[ 31]
= 1 H = 1 Wb/A = 1 kg⋅m2 /(A⋅s)2
Temperature
Temperature
Name of unit
Symbol
Definition
Relation to SI units
degree Celsius
°C
[°C] ≡ [K] − 273.15
[K] ≡ [°C] + 273.15
degree Delisle
°De
[K] = 373.15 − [°De] × 2 ⁄3
degree Fahrenheit
°F
[°F] ≡ [°C] × 9 ⁄5 + 32
[K] ≡ ([°F] + 459.67) × 5 ⁄9
degree Newton
°N
[K] = [°N] × 100 ⁄33 + 273.15
degree Rankine
°R;
[°R] ≡ [K] × 9 ⁄5
[K] ≡ [°R] × 5/9
degree Réaumur
°Ré
[K] = [°Ré] × 5 ⁄4 + 273.15
degree Rømer
°Rø
[K] = ([°Rø] − 7.5) × 40 ⁄21 + 273.15
Regulo Gas Mark
GM
[°F] ≡ [GM] × 25 + 250
[K] ≡ [GM] × 125 ⁄9 + 394.26
kelvin (SI base unit)
K
≡ change in the thermodynamic temperature T that results in a change of thermal energy kT by 1.380 649 × 10−23 J.[ 40]
(SI base unit )
Modern standards (such as ISO 80000 ) prefer the shannon to the bit as a unit for a quantity of information entropy, whereas the (discrete) storage space of digital devices is measured in bits. Thus, uncompressed redundant data occupy more than one bit of storage per shannon of information entropy. The multiples of a bit listed above are usually used with this meaning.
Luminous intensity
The candela is the preferred nomenclature for the SI unit.
Luminous intensity
Name of unit
Symbol
Definition
Relation to SI units
candela (SI base unit)
cd
The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540× 10 12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.[ 36]
(SI base unit )
candlepower (new)
cp
≡ cd The use of candlepower as a unit is discouraged due to its ambiguity.
= 1 cd
candlepower (old, pre-1948)
cp
Varies and is poorly reproducible.[ 41] Approximately 0.981 cd.[ 16]
≈ 0.981 cd
Luminance
Luminance
Name of unit
Symbol
Definition
Relation to SI units
candela per square foot
cd/ft2
≡ cd/ft2
≈ 10.763910 417 cd/m2
candela per square inch
cd/in2
≡ cd/in2
≈ 1550 .0031 cd/m2
candela per square metre (SI unit); nit (deprecated[ 16] )
cd/m2
≡ cd/m2
= 1 cd/m2
footlambert
fL
≡ (1/π) cd/ft2
≈ 3.426259 0996 cd/m2
lambert
L
≡ (104 /π) cd/m2
≈ 3183 .0988618 cd/m2
stilb (CGS unit)
sb
≡ 104 cd/m2
= 104 cd/m2
Luminous flux
Luminous flux
Name of unit
Symbol
Definition
Relation to SI units
lumen (SI unit)
lm
The luminous flux of a source that emits monochromatic radiation of frequency 540× 10 12 hertz and that has a radiant flux of 1/683 watt.[ 36]
= 1 lm = 1 cd⋅sr
Illuminance
Illuminance
Name of unit
Symbol
Definition
Relation to SI units
footcandle ; lumen per square foot
fc
≡ lm/ft2
= 10.763910 417 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
Radiation – source activity
Radioactivity
Name of unit
Symbol
Definition
Relation to SI units
becquerel (SI unit)
Bq
≡ Number of disintegrations per second
= 1 Bq = 1/s
curie
Ci
≡ 3.7× 1010 Bq[ 42]
= 3.7× 1010 Bq
rutherford (H)
Rd
≡ 1 MBq
= 106 Bq
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
roentgen
R
1 R ≡ 2.58× 10−4 C/kg[ 34]
= 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[ 45]
= 1 Gy = 1 J/kg = 1 m2 ⋅s2
rad
rad
≡ 0.01 Gy[ 34]
= 0.01 Gy
Radiation – equivalent dose
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]
Notes
^ 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)
References
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^ a b c d e "NIST - National Institute of Standards and Technology" . NIST .
^ a b c d e f g h i j k l m n Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
^ a b National Bureau of Standards. (June 30, 1959). Refinement of values for the yard and the pound . Federal Register, viewed September 20, 2006 at National Geodetic Survey web site .
^ "International Astronomical Union - IAU" . www.iau.org .
^
Klein, Herbert Arthur.
(1988). The Science of Measurement: a Historical Survey . Mineola, NY: Dover Publications 0-4862-5839-4.
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^ 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.
^ Cox, Arthur N., ed. (2000). Allen's Astrophysical Quantities (4th ed.). New York: AIP Press / Springer. Bibcode :2000asqu.book.....C . ISBN 0387987460 .
^ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (2nd ed.). Princeton, NJ: Princeton University Press. Bibcode :2008gady.book.....B . ISBN 978-0-691-13026-2 .
^ P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
^ a b c Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement . New York: Macmillan 0-312-37026-1. p. 152.
^ a b De Vinne, Theodore Low (1900). The practice of typography: a treatise on the processes of type-making, the point system, the names, sizes, styles and prices of plain printing types 2nd ed. New York: The Century Co. p. 142–150.
^ Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking . (1894). New York: Howard Lockwood. p. 521.
^ a b c d e f g h i Rowlett, Russ (2005), How Many? A Dictionary of Units of Measurement
^ 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.
^ a b c d e 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
^ 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".
^ CODATA Value: atomic unit of mass. (2010). National Institute of Standards and Technology . Retrieved 29 May 2015.
^ The Swiss Federal Office for Metrology gives Zentner on a German language web page "Metas: Masseinheiten - SI-Einheiten" . Archived from the original on 2006-09-28. Retrieved 2006-10-09 . and quintal on the English translation of that page "OFMET: Units of measure - SI units" . Archived from the original on 2001-03-09. Retrieved 2006-10-09 . ; the unit is marked "spécifiquement suisse !"
^ a b Pedersen O. (1983). "Glossary" in Coyne, G. , Hoskin, M., and Pedersen, O. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary . Vatican Observatory. Available from Astrophysics Data System .
^ Richards, E.G. (1998), Mapping Time , Oxford University Press, pp. 94–95 , ISBN 0-19-850413-6
^ Steel, Duncan (2000), Marking Time , John Wiley & Sons, p. 46 , ISBN 0-471-29827-1
^ "CODATA Value: Planck time" . physics.nist.gov . Retrieved 2018-06-20 .
^ a b Richards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac . Mill Valley, CA: University Science Books.
^ 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.
^ Until 1970 the UK Admiralty (and until 1954 the US) used other definitions of the nautical mile and hence the knot. See also #Length
^ Tom Benson. (2010.) "Mach Number" Archived 2006-04-10 at the Wayback Machine in Beginner's Guide to Aeronautics . NASA .
^ CODATA Value: atomic unit of force . (2006). National Institute of Standards and Technology . Retrieved September 14, 2008.
^ a b c d e f g h Comité International des Poids et Mesures, Resolution 2 , 1946, retrieved August 26, 2009
^ a b c d e f g h i j k l m n o p Barry N. Taylor, (April 1995), Guide for the Use of the International System of Units (SI) (NIST Special Publication 811), Washington, DC: US Government Printing Office, pp. 57–68.
^ 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.
^ a b c d e f g "NIST Guide to SI Units, Appendix B.9" , NIST , 2 July 2009, retrieved August 27, 2009
^ 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.
^ a b c d "SI brochure (2019)" (PDF) . SI Brochure . BIPM . p. 132. Retrieved May 23, 2019 .
^ The NIST Reference on Constants, Units, and Uncertainty , 2006, retrieved August 26, 2009
^ Robert G. Mortimer Physical chemistry , Academic Press, 2000 ISBN 0-12-508345-9 , page 677
^ 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.
^ "Mise en pratique" (PDF) . BIPM .
^ The NIST Reference on Constants, Units, and Uncertainty , retrieved August 28, 2009
^ 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.
^ a b The International System of Units, Section 2.2.2., Table 3 (8 ed.), Bureau International des Poids et Mesures , 2006, archived from the original on June 18, 2007, retrieved August 27, 2009
^ "The NIST Guide to the SI (Special Publication 811), section 5.2" , NIST , 2008, retrieved August 27, 2009
^ 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.
^ Comité international des poids et mesures, 2002, Recommendation 2 , retrieved August 27, 2009