List of conversion factors explained

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)
indicates that digits repeat infinitely (e.g. corresponds to)
(H)of chiefly historical interest

Length

Length!Name of unit!Symbol!Definition!Relation to SI units
Å≡ 0.1 nm
au
≈ Distance from Earth to Sun
[1]
am
barleycorn (H) = in (see note above about rounding)= 8.4 m
a0= Bohr radius of hydrogen[2]
cable length (imperial) ≡ 608 ft≈ 185.3184 m
cable length (International) nmi≡ 185.2 m
cable length (US) ≡ 720 ft= 219.456 m
chain (Gunter's; Surveyor's) ch≡ 66 ft (US) ≡ 4 rods[3]
cubit (H) ≡ Distance from fingers to elbow ≈ 18 in≈ 0.5 m
ell (H) ell≡ 45 in [4] (In England usually)= 1.143 m
ftm≡ 6 ft = 1.8288 m
fm
fm
finger ≡ in=
finger (cloth) ≡ in= 0.1143 m
foot (Benoît) (H) ft (Ben)
foot (Cape) (H) Legally defined as 1.033 English feet in 1859
foot (Clarke's) (H) ft (Cla)
foot (Indian) (H) ft Ind
mf≡ 300 mm≡ 0.3 m
foot, metric (Mesures usuelles) (H)≡ m≡ 0. m
foot (International) ft≡ 0.3048 m ≡ yd ≡ 12 inches≡ 0.3048 m
foot (Sear's) (H) ft (Sear)
foot (US Survey) ft (US)≡ m [5]
french
charriere
F≡ mm= 0. m
fur≡ 10 chains = 660 ft = 220 yd = 201.168 m
≡ 4 in ≡ 0.1016 m
inch (International) in≡ 2.54 cm ≡ yd ≡  ft≡ 0.0254 m
league (land) lea≈ 1 hour walk, Currently defined in US as 3 Statute miles, but historically varied from 2 to 9 km
≡ 24 light-hours
≡ 60 light-minutes
≡ 60 light-seconds
≡ Distance light travels in one second in vacuum
ly≡ Distance light travels in vacuum in 365.25 days [6]
ln≡ in [7] = m
link (Gunter's; Surveyor's) lnk≡ ch ≡ 0.66 ft (US) ≡ 7.92 in
link (Ramsden's; Engineer's) lnk≡ 1 ft = 0.3048 m
metre (SI base unit)
(meter)
m≡ Distance light travels in of a second in vacuum.(SI base unit)
mickey ≡ in=
micrometre (old: micron)μ; μm
mil=
mil (Sweden and Norway) mil≡ 10 km=
mile (geographical) (H) =
mile (international) mi≡ 80 chains ≡ ≡
mile (tactical or data)
mile (telegraph) (H) mi=
mile (US Survey) mi≡ US Survey feet ≡ (×) m
nail (cloth) ≡ in =
nm
nautical league NL; nl≡ 3 nmi =
nautical mile (Admiralty) NM (Adm);
nmi (Adm)
= =
nautical mile (international) NM; nmi[8]
nautical mile (US pre 1954) ≡ 1853.248 m≡ 1853.248 m
pace ≡ 2.5 ft = 0.762 m
≡ 3 in = 0.0762 m
pcDistant point with a parallax shift of one arc second from a base of one astronomical unit.
au[9] [10]
[11]
≡ 12 pointsDependent on point measures.
pm
point (American, English)[12] [13] ptin
point (Didot; European) [14] pt≡ × of pied du roi;
After 1878:
≡  cm
≈ ;
After 1878:
point (PostScript) ptin= m
point (TeX) ptin= 0.00 m
quarter ≡ yd= 0.2286 m
rod
pole; perch (H)
rd≡ ft= 5.0292 m
rope (H) rope≡ 20 ft = 6.096 m
shaku (Japan) ≡ 10/33 m≈ 0.303 0303 m
span (H) ≡ 9 in = 0.2286 m
stick (H) ≡ 2 in= 0.0508 m
toise (French, post 1667) (H) T≡ 27000/13853 m≈ 1.949 0363 m
twp≡ in= 1.763 m
x unit
siegbahn
xu≈ m
yard (International) yd≡ 0.9144 m ≡ 3 ft ≡ 36 in≡ 0.9144 m
ym
zm

Area

Area!Name of unit!Symbol!Definition!Relation to SI units
acre (international) ac≡ =
acre (US survey) ac≡ 10 sq ch =, also [15]
a≡ 100 m2≡ 100 m2
b≡ 10−28 m2≡ 10−28 m2
barony ≡  ac
board bd
boiler horsepower equivalent direct radiation bhp EDR≡ 1 ft2 × 1 bhp / (240 BTUIT/h)
circ in≡  sq in
circular mil; circular thou circ mil≡  mil2
cord ≡ 192 bd
cuerda (PR Survey) cda≡ 1 cda x 1 cda = acre
guntha (India) ≡ 121 sq yd≈ 101.17 m2
ha
≈ 120 ac (variable)
rood ro≡  ac=
≡  m ×  m
section =
≡ 10−52 m2= 10−52 m2
square (roofing) =
square chain (international) sq ch≡ = ac
square chain (US Survey) sq ch≡ = US survey acre
sq ft
square foot (US Survey) sq ft
sq in
km2≡ 1 km × 1 km= 106 m2
square link (Gunter's)(International) sq lnk≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft=
square link (Gunter's)(US Survey) sq lnk≡ ≡
square link (Ramsden's) sq lnk≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft=
square metre (SI unit) m2≡ 1 m × 1 m= 1 m2
square mil; square thou sq mil≡ 1 mil × 1 mil=
sq mi≡ 1 mi × 1 mi
square mile (US Survey) sq mi≡ 1 mi (US) × 1 mi (US)
square rod/pole/perch sq rd≡ 1 rd × 1 rd=
square yard (International) sq yd≡ 1 yd × 1 yd
=
≡ 36 sq mi (US)
≈ 30 ac

Volume

Volume!Name of unit!Symbol!Definition!Relation to SI units
ac ft≡ 1 ac x 1 ft = =
acre-inch ≡ 1 ac × 1 in=
barrel (imperial) bl (imp)≡ 36 gal (imp)=
barrel (petroleum); archaic blue-barrel bl; bbl≡ 42 gal (US)
barrel (US dry) bl (US)≡ 105 qt (US) = 105/32 bu (US lvl)=
barrel (US fluid) fl bl (US)≡ gal (US)=
bdft≡ 144 cu in
bucket (imperial) bkt≡ 4 gal (imp)=
bushel (imperial) bu (imp)≡ 8 gal (imp)=
bushel (US dry heaped) bu (US)≡ bu (US lvl)=
bushel (US dry level) bu (US lvl)=
butt, pipe ≡ 126 gal (US) (wine)=
≡ 4 bu (imp)=
cord (firewood) =
cord-foot ≡ 16 cu ft=
cu fm≡ 1 fm × 1 fm × 1 fm=
ft3≡ 1 ft × 1 ft × 1 ft
in3≡ 1 in × 1 in × 1 in
cubic metre (SI unit) m3≡ 1 m × 1 m × 1 m≡ 1 m3
cu mi≡ 1 mi × 1 mi × 1 mi
yd3≡ 27 cu ft
cup (breakfast) ≡ 10 fl oz (imp)=
cup (Canadian) c (CA)≡ 8 fl oz (imp)=
cup (metric) c
cup (US customary) c (US)≡ 8 US fl oz ≡ gal (US)=
cup (US food nutrition labeling) c (US)≡ 240 mL=
dash (imperial) ≡ gi (imp) = 1/8 tsp (imp)= m3
dash (US) ≡ US fl oz = 1/8 US tsp=
dessertspoon (imperial) ≡ gi (imp)= m3
drop (imperial) gtt≡ fl oz (imp)= m3
drop (imperial) (alt) gtt≡ gi (imp)
drop (medical) ≡ mL= 83. m3
drop (metric) ≡ mL=
drop (US) gtt≡ US fl oz= m3
drop (US) (alt) gtt≡ US fl oz
drop (US) (alt) gtt≡ US fl oz
fifth ≡ US gal=
≡ 9 gal (imp)=
fluid drachm (imperial) fl dr≡ fl oz (imp)=
fluid dram (US); US fluidram fl dr≡ US fl oz=
fluid scruple (imperial) fl s≡ fl oz (imp)= m3
gallon (beer) beer gal≡ 282 cu in=
gallon (imperial) gal (imp)
gallon (US dry) gal (US)≡ bu (US lvl)=
gallon (US fluid; Wine) gal (US)≡ 231 cu in
gill (imperial); Noggin gi (imp); nog≡ 5 fl oz (imp)=
gill (US) gi (US)≡ 4 US fl oz=
hogshead (imperial) hhd (imp)≡ 2 bl (imp)=
hogshead (US) hhd (US)≡ 2 fl bl (US)=
≡ US fl oz
≡ 18 gal (imp)=
λ≡ 1 mm3=
≡ 80 bu (imp)=
litre
(liter)
L or l≡ 1 dm3 [16] ≡ 0.001 m3
load ≡ 50 cu ft=
minim (imperial) min≡ fl oz (imp) = 1/60 fl dr (imp)= m3
minim (US) min≡ US fl oz = US fl dr=
ounce (fluid imperial) fl oz (imp)≡ gal (imp)
ounce (fluid US customary) US fl oz≡ gal (US)
ounce (fluid US food nutrition labeling) US fl oz≡ 30 mL
peck (imperial) pk≡ 2 gal (imp)=
peck (US dry) pk≡ US lvl bu=
per=
pinch (imperial) ≡ gi (imp) = dash (imp)= m3
pinch (US) ≡ US fl oz = US dash=
pint (imperial) pt (imp)≡ gal (imp)=
pint (US dry) pt (US dry)≡ bu (US lvl) ≡ gal (US dry)=
pint (US fluid) pt (US fl)≡ gal (US)=
pony ≡ US fl oz=
pottle; quartern ≡ gal (imp) = 80 fl oz (imp)=
quart (imperial) qt (imp)≡ gal (imp)=
quart (US dry) qt (US)≡ bu (US lvl) = gal (US dry)=
quart (US fluid) qt (US)≡ gal (US fl)=
quarter; pail ≡ 8 bu (imp)=
register ton ≡ 100 cu ft=
sack (US) ≡ 3 bu (US lvl)=
seam ≡ 8 bu =
shot (US) usually 1.5 US fl oz
strike (imperial) ≡ 2 bu (imp)=
strike (US) ≡ 2 bu (US lvl)=
tablespoon (Australian metric)
tablespoon (Canadian) tbsp≡ fl oz (imp)=
tablespoon (imperial) tbsp≡ fl oz (imp)=
tablespoon (metric)
tablespoon (US customary) tbsp≡ US fl oz=
tablespoon (US food nutrition labeling) tbsp≡ 15 mL=
teaspoon (Canadian) tsp≡ fl oz (imp)= m3
teaspoon (imperial) tsp≡ gi (imp)= m3
teaspoon (metric)
teaspoon (US customary) tsp≡ US fl oz=
teaspoon (US food nutrition labeling) tsp≡ 5 mL=
≡ 1 cu ft=
ton (displacement) ≡ 35 cu ft=
ton (freight) ≡ 40 cu ft=
ton (water) ≡ 28 bu (imp)=
≡ 252 gal (wine)=
wey (US) ≡ 40 bu (US lvl)=

Plane angle

Plane angle!Name of unit!Symbol!Definition!Relation to SI units
(various)≡ rad
≡ rad
mrad≡  rad
≡ rad
arcminute
MOA
'
"
'≡ grad
"≡ grad
°≡ of a revolution ≡ rad
grad
gradian; gon
grad≡ of a revolution ≡ rad ≡ 0.9°
≡ 45°
≡ 90°
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°
sign ≡ 30°

Solid angle

Solid angle!Name of unit!Symbol!Definition!Relation to SI units
– The solid angle subtended by a sphere at its centre.
deg2; sq.deg.; (°)2
steradian (SI unit) srThe solid angle subtended at the center of a sphere of radius r by a portion of the sphere having an area r2.
A sphere subtends 4π sr.
= 1 sr

Mass

Notes:

Mass!Name of unit!Symbol!Definition!Relation to SI units
u; AMUSame as dalton (see below)
atomic unit of mass, electron rest mass me[17]
bag (coffee) ≡ 60 kg= 60 kg
bag (Portland cement)≡ 94 lb av=
barge ≡ short ton=
kt≡ gr=  mg
carat (metric) ct≡ 200 mg= 200 mg
≡ 8 lb av=
crith ≡ mass of 1 L of hydrogen gas at STP≈ 89.9349 mg
Da1/12 the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest
dram (apothecary; troy) dr t≡ 60 gr=
dram (avoirdupois) dr av≡ gr=
eV/c2≡ 1 eV / c2=
gamma γ≡ 1 μg= 1 μg
gr≡  lb av
gvgrave was the original name of the kilogram≡ 1 kg
hundredweight (long) long cwt or cwt≡ 112 lb av=
hundredweight (short); cental sh cwt≡ 100 lb av=
hyl
metric slug
≡ 1 kgf / 1 m/s2=
kilogram
(kilogramme)
kg≈ mass of the prototype near Paris
≈ mass of 1 litre of water
(SI base unit)
kip≡ av=
≡ 8 oz t=
mite ≡ gr=
mite (metric) ≡ g= 50 mg
oz t≡  lb t=
ounce (avoirdupois) oz av≡  lb=
ounce (US food nutrition labelling) oz≡ 28 g= 28 g
dwt; pwt≡ oz t=
≡ ct= 2 mg
lb av≡ = grains
≡ 500 g= 500 g
lb t≡ grains=
quarter (imperial) ≡ long cwt = 2 st = 28 lb av=
quarter (informal)≡ short ton=
quarter, long (informal)≡ long ton=
quintal (metric) q≡ 100 kg= 100 kg
scruple (apothecary) s ap≡ 20 gr=
sheet ≡  lb av= 647.9891 mg
slug
geepound
slug≡ × 1 lb av × 1 s2/ft
st≡ 14 lb av=
ton, assay (long) AT≡ 1 mg × 1 long ton ÷ 1 oz t= 32. g
ton, assay (short) AT≡ 1 mg × 1 short ton ÷ 1 oz t= 29.1 g
ton, longlong tn or ton=
sh tn=
tonne (mts unit) t=
≡ 252 lb = 18 st= (variants exist)
zentner Ztr.Definitions vary.[18]

Density

Density!Name of unit!Symbol!Definition!Relation to SI units
gram per millilitreg/mL≡ g/mL=
kilogram per cubic metre (SI unit)kg/m3≡ kg/m3= 1 kg/m3
kilogram per litrekg/L≡ kg/L=
ounce (avoirdupois) per cubic footoz/ft3≡ oz/ft3
ounce (avoirdupois) per cubic inchoz/in3≡ oz/in3
ounce (avoirdupois) per gallon (imperial)oz/gal≡ oz/gal
ounce (avoirdupois) per gallon (US fluid)oz/gal≡ oz/gal
pound (avoirdupois) per cubic footlb/ft3≡ lb/ft3
pound (avoirdupois) per cubic inchlb/in3≡ lb/in3
pound (avoirdupois) per gallon (imperial)lb/gal≡ lb/gal
pound (avoirdupois) per gallon (US fluid)lb/gal≡ lb/gal
slug per cubic footslug/ft3≡ slug/ft3

Time

Time!Name of unit!Symbol!Definition!Relation to SI units
a.u.a0/(αc)
≡ 441 mo (hollow) + 499 mo (full) = 76 a of 365.25 d= or [19]
c≡ 100 years (100 a)[20] [21]
d= 24 h = min=
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)
dec≡ 10 years (10 a)=
fn≡ 2 wk=
≡ h= 3. s
≡ 4 Callippic cycles - 1 d=
h≡ 60 min=
j≡ s= 16. ms
jiffy (alternative) ja≡ s= 10 ms
(quarter of an hour) ≡ h = d = 15 min= 900 s
kè (traditional) ≡ d = 14.4 min= 864 s
lustre; lūstrum ≡ 5 a of 365 d[22] =
Metonic cycle
enneadecaeteris
≡ 110 mo (hollow) + 125 mo (full) = 6940 d ≈ 19 a=
≡ years
md≡ d= 86.4 s
min≡ 60 s, due to leap seconds sometimes 59 s or 61 s,= 60 s
≡ 90 s= 90 s
month (full) mo≡ 30 d[23] =
month (Greg. av.) mo=
month (hollow) mo≡ 29 d=
Month (synodic) moCycle time of moon phases ≈ (average)
= 48 mo (full) + 48 mo (hollow) + 3 mo (full) = 8 a of 365.25 d = 2922 d=
[24]
second (SI base unit) s≡ Time of 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 (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of metres.(SI base unit)
≡ 10−8 s= 10 ns
sigma ≡ 10−6 s= 1 μs
≡ a of 365 d=
S≡ 10−13 s= 100 fs
wk≡ 7 d = 168 h = =
year (common) 365 d = [25]
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.=
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=
year (leap)a, y, or yr 366 d =
a, y, or yrConceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, [26] approximately d, each day being SI seconds[27]
a, y, or yr≡ Time taken for Sun to return to the same position with respect to the stars of the celestial sphere, approximately
Notes:

Frequency

Frequency!Name of unit!Symbol!Definition!Relation to SI units
actions per minute APM≡ 1/60 Hz
cps≡ 1 Hz= 1 cps = 1 Hz
degree per second deg/s≡ 1 °/s ≡ 1/360 Hz= Hz
hertz (SI unit) Hz≡ One cycle per second= 1 Hz = 1/s
rad/s≡ 1/(2π) Hz
rpm≡ One rpm equals one rotation completed around a fixed axis in one minute of time.

Speed or velocity

Definition!Relation to SI units
fph≡ 1 ft/h= 8.4 m/s
fpm≡ 1 ft/min=
fps≡ 1 ft/s=
≡ furlong/fortnight
iph≡ 1 in/h= 7.0 m/s
ipm≡ 1 in/min= 4.2 m/s
ips≡ 1 in/s=
km/h≡ 1 km/h= 2. m/s
kn≡ 1 nmi/h = 1.852 km/h= 0.51 m/s
knot (Admiralty) kn≡ 1 NM (Adm)/h = [28] =  m/s
MRatio of the speed to the speed of sound 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
mph≡ 1 mi/h=
mpm≡ 1 mi/min=
mps≡ 1 mi/s=
speed of light in vacuum c=
speed of sound in air s to (761-)
Note
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 minuteCFM≡ 1 ft3/min=
cubic foot per secondft3/s≡ 1 ft3/s=
cubic inch per minutein3/min≡ 1 in3/min=  m3/s
cubic inch per secondin3/s≡ 1 in3/s=
cubic metre per second (SI unit)m3/s≡ 1 m3/s= 1 m3/s
gallon (US fluid) per dayGPD≡ 1 gal/d=  m3/s
gallon (US fluid) per hourGPH≡ 1 gal/h=  m3/s
gallon (US fluid) per minuteGPM≡ 1 gal/min=
litre per minutel/min or L/min≡ 1 L/min= 1. m3/s

Acceleration

Acceleration!Name of unit!Symbol!Definition!Relation to SI units
fph/s≡ 1 ft/(h⋅s)= 8.4 m/s2
fpm/s≡ 1 ft/(min⋅s)=
foot per second squared fps2≡ 1 ft/s2=
gal
galileo
Gal≡ 1 cm/s2= 10−2 m/s2
ipm/s≡ 1 in/(min⋅s)= 4.2 m/s2
inch per second squared ips2≡ 1 in/s2=
kn/s≡ 1 kn/s≈ 5.1 m/s2
metre per second squared (SI unit)m/s2≡ 1 m/s2= 1 m/s2
mph/s≡ 1 mi/(h⋅s)=
mpm/s≡ 1 mi/(min⋅s)= 26.8224 m/s2
mile per second squared mps2≡ 1 mi/s2=
=

Force

See also: Mass versus weight.

Definition!Relation to SI units
[29]
dyne (CGS unit) dyn≡ g⋅cm/s2= 10−5 N
kilogram-force
kilopond; grave-force
kgf; kp; gvf≡ × 1 kg=
kip
kip-force
kip; kipf; klbf≡ × =
milligrave-force, gravet-force mgvf; gvtf≡ × 1 g=
long ton-force tnf≡ × 1 long ton=
newton (SI unit) NA force capable of giving a mass of one kilogram an acceleration of one metre per second per second.= 1 N = 1 kg⋅m/s2
ozf≡ × 1 oz=
lbf≡ × 1 lb=
pdl≡ 1 lb⋅ft/s2=
short ton-force tnf≡ × 1 short ton=
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[30]
atmosphere (technical) at≡ 1 kgf/cm2=
bar≡  Pa≡ 105 Pa
barye (CGS unit) ≡ 1 dyn/cm2= 0.1 Pa
centimetre of mercury cmHg≡ × 1 cm ×
centimetre of water (4 °C) cmH2O≈ 999.972 kg/m3 × 1 cm ×
foot of mercury (conventional)ftHg≡ × 1 ft ×
foot of water (39.2 °F) ftH2O≈ 999.972 kg/m3 × 1 ft ×
inch of mercury (conventional) inHg≡ × 1 in ×
inch of water (39.2 °F) inH2O≈ 999.972 kg/m3 × 1 in ×
kilogram-force per square millimetre kgf/mm2≡ 1 kgf/mm2=
ksi≡ 1 kipf/sq in
≡ 1 long ton × / 1 sq ft
micrometre of mercury μmHg≡ × 1 μm × ≈ 0.001 torr
mmHg≡ × 1 mm × ≈ 1 torr
millimetre of water (3.98 °C) mmH2O≈ 999.972 kg/m3 × 1 mm × = =
pascal (SI unit) Pa≡ N/m2 = kg/(m⋅s2)= 1 Pa[31]
pièze (mts unit) pz= = 1 kPa
psf≡ 1 lbf/ft2
psi≡ 1 lbf/in2
pdl/sq ft≡ 1 pdl/sq ft
≡ 1 short ton × / 1 sq ft
torr≡ Pa

Torque or moment of force

Torque!Name of unit!Symbol!Definition!Relation to SI units
pound-force-foot lbf⋅ft≡ × 1 lb × 1 ft=
poundal-ft pdl⋅ft≡ 1 lb⋅ft2/s2=
lbf⋅in≡ × 1 lb × 1 in=
kgf⋅m≡ × N × m=
newton-metre (SI unit) N⋅m≡ N × m = kg⋅m2/s2=

Energy

See also: Units of energy.

Definition!Relation to SI units
boe
British thermal unit (ISO) BTUISO=
British thermal unit (International Table) BTUIT=
British thermal unit (mean) BTUmean
British thermal unit (thermochemical) BTUth
British thermal unit (39 °F) BTU39 °F
British thermal unit (59 °F) BTU59 °F=
British thermal unit (60 °F) BTU60 °F
British thermal unit (63 °F) BTU63 °F
calorie (International Table) calIT=
calorie (mean) calmean of the energy required to warm one gram of air-free water from 0 °C to 100 °C at a pressure of 1 atm
calorie (thermochemical) calth≡ 4.184 J=
Calorie (US; FDA)Cal≡ 1 kcal = =
calorie (3.98 °C) cal3.98 °C
calorie (15 °C) cal15 °C≡ 4.1855 J=
calorie (20 °C) cal20 °C
Celsius heat unit (International Table) CHUIT≡ 1 BTUIT × 1 K/°R=
cubic centimetre of atmosphere; standard cubic centimetre cc atm; scc≡ 1 atm × 1 cm3=
cubic foot of atmosphere; standard cubic foot cu ft atm; scf≡ 1 atm × 1 ft3=
cubic foot of natural gas =
cubic yard of atmosphere; standard cubic yard cu yd atm; scy≡ 1 atm × 1 yd3=
eVe × 1 V
erg (CGS unit) erg≡ 1 g⋅cm2/s2= 10−7 J
ft lbf≡ × 1 lb × 1 ft=
foot-poundal ft pdl≡ 1 lb⋅ft2/s2=
gallon-atmosphere (imperial) imp gal atm≡ 1 atm × 1 gal (imp)=
gallon-atmosphere (US) US gal atm≡ 1 atm × 1 gal (US)=
Eh≡ meα2c2 (= 2 Ry)
hp⋅h≡ 1 hp × 1 h=
in lbf≡ × 1 lb × 1 in=
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.= 1 J = 1 m⋅N = 1 kg⋅m2/s2 = 1 C⋅V = 1 W⋅s
kcal; Cal=
kilowatt-hour
Board of Trade Unit
kW⋅h; B.O.T.U.≡ 1 kW × 1 h=
l atm; sl≡ 1 atm × 1 L=
≡ 1015 BTUIT=
RyRc
therm (E.C.) =
therm (US) =
thermie th≡ 1 McalIT=
TCE≡ 7 Gcalth=
toe≡ 10 GcalIT=
tTNT≡ 1 Gcalth=
W⋅h≡ 1 W × 1 h=
W⋅s≡ 1 J =

Power or heat flow rate

Definition!Relation to SI units
atm ccm≡ 1 atm × 1 cm3/min=
atm ccs≡ 1 atm × 1 cm3/s=
atm cfh≡ 1 atm × 1 cu ft/h=
atmosphere-cubic foot per minute atm cfm≡ 1 atm × 1 cu ft/min=
atmosphere-cubic foot per second atm cfs≡ 1 atm × 1 cu ft/s=
BTU (International Table) per hour BTUIT/h≡ 1 BTUIT/h
BTU (International Table) per minute BTUIT/min≡ 1 BTUIT/min
BTU (International Table) per second BTUIT/s≡ 1 BTUIT/s=
calorie (International Table) per second calIT/s≡ 1 calIT/s=
erg per second erg/s≡ 1 erg/s=
foot-pound-force per hour ft⋅lbf/h≡ 1 ft lbf/h
foot-pound-force per minute ft⋅lbf/min≡ 1 ft lbf/min=
foot-pound-force per second ft⋅lbf/s≡ 1 ft lbf/s=
horsepower (boiler) hp-->≈ 34.5 lb/h × 970.3 BTUIT/lb
horsepower (European electrical) hp≡ 75 kp⋅m/s=
horsepower (electrical) hp≡ 746 W=
horsepower (mechanical) hp≡ 550 ft⋅lbf/s=
horsepower (metric) hp or PS≡ 75 m⋅kgf/s=
litre-atmosphere per minute L·atm/min≡ 1 atm × 1 L/min=
litre-atmosphere per second L·atm/s≡ 1 atm × 1 L/s=
lusec lusec≡ 1 L·μmHg/s
p≡ 100 m⋅kgf/s=
square foot equivalent direct radiation sq ft EDR≡ 240 BTUIT/h
ton of air conditioning ≡ of ice melted / 24 h
ton of refrigeration (imperial) ≡ × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F
ton of refrigeration (IT) ≡ × iceIT / 24 h: iceIT = 144 °F × 2326 J/kg⋅°F
watt (SI unit) WThe power which in one second of time gives rise to one joule of energy.= = 1 J/s = 1 N⋅m/s = 1 kg⋅m2/s3

Action

Action!Name of unit!Symbol!Definition!Relation to SI units
au≡ ℏ ≡ [32]

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)
pound per foot second lb/(ft⋅s)≡ 1 lb/(ft⋅s)
pound-force second per square foot lbf⋅s/ft2≡ 1 lbf⋅s/ft2
pound-force second per square inch lbf⋅s/in2≡ 1 lbf⋅s/in2

Kinematic viscosity

Kinematic viscosity!Name of unit!Symbol!Definition!Relation to SI units
square foot per second ft2/s≡ 1 ft2/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

Definition!Relation to SI units
ampere (SI base unit) A≡ one coulomb of charge going past a given point per second.(SI base unit)
electromagnetic unit
abampere (CGS unit)
abamp≘ 10 A= 10 A
esu per second; statampere (CGS unit) esu/s≘ (10 A⋅cm/s) / c

Electric charge

Electric charge!Name of unit!Symbol!Definition!Relation to SI units
abcoulomb
electromagnetic unit (CGS unit)
abC; emu≘ 10 C= 10 C
aue=
C≡ charge of exactly 1/ elementary charges[33] = 1 C = 1 A⋅s
F≡ 1 mol × NAe
mA⋅h≡ 0.001 A × 1 h= 3.6 C
statcoulomb
franklin; electrostatic unit (CGS unit)
statC; Fr; esu≘ (10 A⋅cm) / c

Electric dipole

Electric dipole!Name of unit!Symbol!Definition!Relation to SI units
atomic unit of electric dipole moment ea0
coulomb-meter C⋅m= 1 C⋅m
D≡ 10−10 esu⋅Å[34]

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) statVc⋅(1 μJ/A⋅m)=
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.= 1 V = 1 W/A = 1 J/C

Electrical resistance

Electrical resistance!Name of unit!Symbol!Definition!Relation 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.= 1 Ω = 1 V/A

Capacitance

Capacitor's ability to store charge!Name of unit!Symbol!Definition!Relation 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.= 1 F = 1 C/V

Magnetic flux

Magnetic flux!Name of unit!Symbol!Definition!Relation to SI units
maxwell (CGS unit)Mx≘ 10−8 Wb= 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.= 1 Wb = 1 V⋅s

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) GMx/cm2 ≘ 10−4 T= 10−4 T [35]
tesla (SI unit) TWb/m2= 1 T = 1 Wb/m2

Inductance

Inductance!Name of unit!Symbol!Definition!Relation 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.= 1 H = 1 Wb/A

Temperature

Temperature!Name of unit!Symbol!Definition!Relation to SI units
°C[°C] ≡ [K] − 273.15[K] ≡ [°C] + 273.15
°De[K] = 373.15 − [°De] ×
°F[°F] ≡ [°C] × + 32[K] ≡ ([°F] + 459.67) ×
°N[K] = [°N] × + 273.15
°R;[°R] ≡ [K] × [K] ≡ [°R] × 5/9
°Ré[K] = [°Ré] × + 273.15
°Rø[K] = ([°Rø] − 7.5) × + 273.15
GM[°F] ≡ [GM] × 25 + 250[K] ≡ [GM] × + 394.26
kelvin (SI base unit) K≡ change in the thermodynamic temperature that results in a change of thermal energy by 1.380 649 × 10−23 J.[36] (SI base unit)

Information entropy

Information entropy!Name of unit!Symbol!Definition!Relation to SI units!Relation to bits
natural unit of information
nit; nepit
nat
Sh≡ ln(2) × nat= 1 bit
hartley
ban
Hart; ban≡ ln(10) × nat
bit; b= 1 bit
≡ 4 bits= 22 bit
B≡ 8 bits= 23 bit
kilobyte (decimal) kB= bit
kibibyte (kilobyte) KiB= 213 bit = 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)cdThe luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.(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. Approximately 0.981 cd.≈ 0.981 cd

Luminance

Luminance
Name of unitSymbolDefinitionRelation to SI units
candela per square footcd/ft2≡ cd/ft2
candela per square inchcd/in2≡ cd/in2
candela per square metre (SI unit); nit (deprecated)cd/m2≡ cd/m2= 1 cd/m2
footlambertfL≡ (1/π) cd/ft2
lambertL≡ (104/π) cd/m2
stilb (CGS unit)sb≡ 104 cd/m2= 104 cd/m2

Illuminance

Illuminance
Name of unitSymbolDefinitionRelation to SI units
footcandle
lumen per square foot
fc≡ lm/ft2=
lumen per square inchlm/in2≡ lm/in2
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 unitSymbolDefinitionRelation to SI units
becquerel (SI unit) Bq≡ Number of disintegrations per second= 1 Bq = 1/s
Ci[37] =
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.

Radiation – exposure

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

Radiation – absorbed dose

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

Radiation – equivalent dose

Radiation – equivalent dose
Name of unitSymbolDefinitionRelation to SI units
rem≡ 0.01 Sv= 0.01 Sv
sievert (SI unit) Sv≡ 1 J/kg= 1 Sv = 1 J/kg = 1 m2⋅s2
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 = QDwhere 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.

Notes and References

  1. jobs . The astronomical unit gets fixed : Nature News & Comment . Nature . 10.1038/nature.2012.11416 . Nature.com . September 14, 2012. 123424704 . August 31, 2013.
  2. "NIST Reference on Constants, Units, and Uncertainty."(2010). National Institute of Standards and Technology. Retrieved October 17, 2014.
  3. Web site: NIST - National Institute of Standards and Technology. NIST.
  4. Lide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
  5. 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.
  6. Web site: International Astronomical Union - IAU. www.iau.org.
  7. Klein, Herbert Arthur.(1988). The Science of Measurement: a Historical Survey. Mineola, NY: Dover Publications 0-4862-5839-4.
  8. https://www.bipm.org/en/publications/si-brochure/table8 International System of Units,
  9. Book: 2000asqu.book.....C. Cox. Arthur N.. 2000. Allen's Astrophysical Quantities. 4th. AIP Press / Springer. New York. 0387987460.
  10. Book: 2008gady.book.....B. Binney. James. Tremaine. Scott. 2008. Galactic Dynamics. 2nd. 978-0-691-13026-2. Princeton University Press. Princeton, NJ.
  11. P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
  12. Whitelaw, Ian. (2007). A Measure of All Things: The Story of Man and Measurement. New York: Macmillan 0-312-37026-1. p. 152.
  13. 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.
  14. Pasko, Wesley Washington (1894). American dictionary of printing and bookmaking. (1894). New York: Howard Lockwood. p. 521.
  15. 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.
  16. 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".
  17. http://physics.nist.gov/cgi-bin/cuu/Value?ttme|search_for=atomic+unit+of+mass CODATA Value: atomic unit of mass.
  18. The Swiss Federal Office for Metrology gives Zentner on a German language web page Web site: Metas: Masseinheiten - SI-Einheiten . 2006-10-09 . dead . https://web.archive.org/web/20060928011837/http://www.metas.ch/de/scales/systemch.html . 2006-09-28 . and quintal on the English translation of that page Web site: OFMET: Units of measure - SI units . 2006-10-09 . dead . https://web.archive.org/web/20010309033010/http://www.metas.ch/en/scales/systemch.html . 2001-03-09 . ; the unit is marked "spécifiquement suisse !"
  19. see Callippic cycle for explanation of the differences
  20. This is based on the average Gregorian year. See above for definition of year lengths.
  21. 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.
  22. The length of ancient lustral cycles was not constant; see Lustrum for more details
  23. 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.
  24. Web site: CODATA Value: Planck time. physics.nist.gov. 2018-06-20.
  25. 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.
  26. 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)
  27. 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.
  28. Until 1970 the UK Admiralty (and until 1954 the US) used other definitions of the nautical mile and hence the knot. See also
    1. Length
  29. http://physics.nist.gov/cuu/Constants/ CODATA Value: atomic unit of force
  30. 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.
  31. 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.
  32. http://www.bipm.org/en/si/si_brochure/chapter4/table7.html International System of Units,
  33. Web site: SI brochure (2019). BIPM. 132. SI Brochure. May 23, 2019.
  34. Robert G. Mortimer Physical chemistry, Academic Press, 2000, page 677
  35. 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.
  36. Web site: Mise en pratique. BIPM.
  37. 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.
  38. 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.