The name Système International d’Unités (SI Units, in short) was adopted at the 11th General Assembly on Weights and Measures in 1960 (11^{th} CGPM, Conférence Générale des Poids et Mesures), but, in spite of its name, it is not in common use in some places and instances, notably in the USA industry.
Physical sciences are based on measurable magnitudes, i.e. magnitudes that admit unambiguous sizecomparison between those of the same class. Metrology is the science of measurement. Perhaps the crucial milestone in metrology took place in 1799, under the French Revolution, when scientists proposed to unify all different weights and measures into the decimal metric system.
A physical magnitude needs to be specified by three items: a unit of that dimension, a number indicating the ratio between the magnitude and the unit used, and a quantification of the accuracy or uncertainty in the previous number (measuring uncertainties can be reduced but never eliminated). It is common practice to implicitly include the uncertainty information in the number by limiting its number of significant figures accordingly, reducing the three parameters above to just two: the number and the unity, what might be further reduced to one if the unit were unambiguously understood (not several different units for the same magnitude, not multiples and submultiples).
Types of magnitude are length, time, volume, mass, temperature, etc. Quoting e.g. L=2.5 m refers to a magnitude L twoandahalf times the length of the unit metre (m). Notice that the decimal sign is a point (.) in English language but a comma (,) for nonEnglish texts; in any case, if there is no significant figure to the left of the decimal point, a zero must always be placed there (e.g. 0.3 and not .3).
Under the SI Units system, seven magnitudes are chosen to form a basic set (metre, kilogramme, second, ampere, kelvin, mole and candela), and all the others (e.g. hertz, newton, volt, radian) are regarded as being derived from this set by appropriate definitions involving only multiplication, division, differentiation or integration (thus, arguments of functions such as sin(x) or log(x) must be nondimensional; e.g. sin(wt), log(p/p_{0})).
The units quoted below are the basic units of
the Système International d’Unités.
NOTE: see 2019 redefinition of the SI base units (Wiki),
and nonSI units mentioned there (Wiki).
Length: The unit of length called the metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second (17^{th} CGPM, 1983).
Mass: The unit of mass called the kilogramme is the mass of the international prototype which is in the custody of the Bureau International des Poids et Mesures (BIPM) at Sévres, near Paris, France (3^{rd} CGPM, 1901).
Time: The unit of time called the second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom (13^{th} CGPM, 1967).
Temperature: The unit of temperature called the kelvin is the fraction 1/273.16 of the temperature of the triple point of water (13^{th} CGPM, 1967).
Electric current: The unit of electric current called the ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular crosssection, and placed 1 metre apart in a vacuum, would produce a force equal to 2´10^{7} newton per metre of length between these conductors (9^{th} CGPM, 1948).
Luminous intensity: The unit of luminous intensity called the candela is 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 (16^{th} CGPM, 1970).
Amount of substance: The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogramme of carbon 12 (14^{th} CGPM, 1971). When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
All derived units are products or ratios of basic units without numeric factors, most of them are dimensional (but radian, steradian and others are nondimensional) and some have special names (radian, steradian, hertz, newton, pascal, joule, watt, coulomb, volt, farad, ohm, siemens, weber, tesla, henry, degree Celsius, lumen and lux).
All basic units and derived units with special names have special symbols (m, kg, s, A, K, mol, cd, rad, sr, Hz, N, Pa, J, W, C, V, F, W, S, Wb, T, H, ºC, lm and lx).
Symbols for derived units are formed by appropriate combination of the special symbols above (e.g. m/s for velocity).
Instead of using raw numbers and base units (e.g. 6.380´10^{6} m, 0.628´10^{}^{6} m, 0.012 V, 0.1´10^{6} Pa), some multiples or submultiples of the base unit can be used in speech and writing (e.g. 6 380 km, 0.628 µm, 12 mV, 0.1 MPa), although care must be taken not to forget the factors during numerical calculations. In any case, be it as numerical exponents or as multiples of base units, it is recommended to use powers three order of magnitude apart, beginning on the base unit (e.g. 6.380´10^{6} m and not 0.6380´10^{7} m, 0.628´10^{6} m and not 6.28´10^{7} m). The prefix and value for the accepted multiples are:
Prefix
Name  Symbol  Value 
exa  E  10^{18} 
peta  P  10^{15} 
tera  T  10^{12} 
giga  G  10^{9} 
mega  M  10^{6} 
kilo  k  10^{3} 
milli  m  10^{3} 
micro  µ  10^{6} 
nano  n  10^{9} 
pico  p  10^{12} 
fempto  f  10^{15} 
atto  a  10^{18} 
Prefixes are applied to just one symbolunit, and thus any exponent applies to the combination prefixunit (e.g. 5 kN/m^{2}=5´10^{3} N/m^{2}=0.5 N/cm^{2})
One exception to the use of prefixes occurs with the unit kilogramme, where the prefixes are applied to the unit gramme (e.g. 5 mg=5´10^{6} kg).
Unit symbols must be written in normal upright characters without an end period (unless it is the end of the sentence), separated from the numeric quantity by one nonwrapable space, and remain unaltered in the plural (in writing, not in pronunciation).
Derived units which are products of base units must be written with a period in between (e.g. N.m, or better N´m), those which are ratios can be written in one of the three forms shown in the example for speed: m.s^{1}, m/s or , although the first one is preferable. These rules may be extended to more complex grouping but more than one solidus (/) should never be used in the same expression unless parentheses are used to avoid ambiguity.
magnitude 
symbol 
unit 
symbol 
equivalence 
length 
l, L 
metre 
m 

mass 
m 
kilogramme 
kg 

time 
t 
second 
s 

electric current 
i 
ampere 
A 

temperature 
T 
kelvin 
K 

luminous intensity 
I,Iv 
candela 
cd 

amount of substance 
n 
mole 
mol 

angle (plane) 
a,b,g,q,f 
radian 
rad 

solid angle 
w,W 
steradian 
sr 

frequency 
n,f 
hertz 
Hz 
s^{1} 
force 
F 
newton 
N 
kg.m.s^{2} 
pressure 
p 
pascal 
Pa 
N.m^{2} 
energy 
E 
joule 
J 
kg.m^{2}.s^{2} 
power 
P 
watt 
W 
J.s^{1} 
electric charge 
q,Q 
coulomb 
C 
A.s 
el. potential difference 
V,f 
volt 
V 
W.A^{1} 
electric capacitance 
C 
farad 
F 
A.s.V^{1} 
electric resistance 
R 
ohm 
W 
V.A^{1} 
electric conductance 
G 
siemens 
S 
W ^{1} 
magnetic flux 
F 
weber 
Wb 
V.s 
magnetic flux density 
B 
tesla 
T 
Wb.m^{2} 
inductance 
L,M 
henry 
H 
Wb.A^{1} 
degree Celsius 
t 
degree Celsius 
ºC 
^{a)} 
luminous flux 
F 
lumen 
lm 
cd.sr 
illumination 
E,i 
lux 
lx 
lm.m^{2} 
a) There are two possibilities: for single temperature values, t, the numerical equivalence is t ºC=(t+273.15) K, whereas for differences in temperature, t, the numerical equivalence is t ºC=t K. For this reason it is impossible to automatically replace degree Celsius by kelvin in a text.
Other names and symbols that are temporarily accepted, but do not belong to the SI units are:
magnitude  symbol  unit  equivalence 
volume  V  litre  1 l=10^{3} m^{3} 
mass  m  gramme  1 g=10^{3} kg 
mass  m  tonne  1 t=10^{3} kg 
time  t  minute  1 min=60 s 
time  t  hour  1 h=3 600 s 
time  t  day  1 d=86 400 s 
angle  a,b,g,q,f  degree  1 º=p /180 rad 
angle  a,b,g,q,f  minute  1 '=p /10 800 rad 
angle  a,b,g,q,f  second  1 ''=p /648 000 rad 
energy  e  electronvolt  1 eV=1.602´10^{19} J 
length  L  Astronomic unit  1 AU=149.598´10^{9} m 
length  L  parsec  1 pc=30.857´10^{15} m 
mass  m  atomic mass unit  1 u=1.661´10^{27} kg 
Physical equations represent natural laws or define new magnitudes.
They must be written in terms of physical magnitudes, that is, by means of symbols that represent at the same time a unit and a number.
All numeric factors appearing in a physical equation must be nondimensional.
When physical equations have empirical coefficients with dimensions, they must be represented by physical constants (symbols, comprising the unit and the number, made explicit apart).
Symbols for physical magnitudes should preferably be formed by one latin or greek letter, sometimes with subindices and other modifiers and must be printed in italic characters (symbols for units must be printed in normal upright font). A period should not follow to a symbol except for grammatical rules. To help on reading numbers with many figures, a small space may be used to separate groups of three figures at either side of the decimal sign (but never used a comma or a point).
Some nondimensional physical magnitudes are traditionally represented by a twoletter symbol (e.g. Re, Nu) and care must be taken not to take it as a product of two oneletter symbols in physical equations (a small space should be used). Notice that Re is in italics if it refers to the variable called Reynolds number but in upright Re if it refers to the function named real part.
Subindices can be used to distinguish different physical magnitudes with the same letter (e.g. c_{p}, c_{v}) or to represent the same physical magnitude applied to different systems or different times (e.g. m_{1}, m_{2}, for the mass of gas, m_{H2O}). As shown above, literal names and numbers used as subindices are printed upright, but if variables are used to represent them (e.g. m_{i}) they must be printed in italic.
Numbers must be printed in upright characters using a point at the baseline as decimal sign (a comma in nonEnglish texts). The multiplication sign for numbers is a cross (e.g. 6.02´10^{23}) for English texts and a midpoint or a cross for nonEnglish texts (e.g. 6,02× 10^{23} or 6.02´10^{23}).
Coefficients and factors (e.g. thermal expansion coefficient, a , dV/V=a dT are used to name dimensional magnitudes that appear in physical equations that show proportional dependence of the form A =KB.
Parameters, ratios and numbers (e.g. thermal capacity ratio g =c_{p}/c_{v}, Reynolds number Re=VL/n ) are used to name nondimensional magnitudes.
Fractions (e.g. mole fraction, x_{i}) are used to name nondimensional magnitudes that are lower than unity.
Constants (e.g. Boltzmann constant, k=R/N_{A}) are used to name dimensional magnitudes that do not vary with experimental circumstances. A bad usage occurs in the so called "chemical equilibrium constant", which is dependent on temperature.
Concentrations (e.g. mass concentration of a component B, r _{B}=m_{B}/V) are used to name a dimensional magnitude in a mixture divided by the volume of the mixture.
Densities (e.g. charge density, r =dQ/dV) are used to name a dimensional magnitude in a sufficiently small system divided by the volume of that system..
Flux densities (e.g. thermal flux density, ) are used to name the dimensional magnitude obtained by division of a flux magnitude (one that pierces a control surface) by the area of the surface.
The adjective "specific" (e.g. specific volume, v=V/m) refers to the original magnitude divided by the mass of the system.
The adjective "molar" (e.g. molar volume, v=V/n) refers to the original magnitude divided by the amount of substance in the system.
Miscellaneous units and conversion values
The units listed below are grouped in:
 Light and thermal radiation units.
NonSI units of length 
name 
symbol 
equivalence 
1 angstrom 
Å 
= 10^{10} m  
1 astronomical unit 
AU 
= 1.496´10^{11} m  
1 foot international 
ft (or ') 
= 0.3048 m  
1 inch 
in (or '') 
= 0.0254 m  
1 light year 
ly 
= 9.4605´10^{15} m  
1 micron 
µ 
= 10^{6} m  
1 mil  = 2.54´10^{}^{5} m  
1 geographical mile 
mi 
= 1.853 184´10^{3} m  
1 imperial mile 
mi 
= 1.609 344´10^{3} m  
1 imperial nautical mile 
mi 
= 1.853 184´10^{3} m  
1 international nautical mile 
mi 
= 1.852´10^{3} m  
1 sea mile 
mi 
= 1.8288´10^{3} m  
1 parsec 
pc 
= 3.085 72´10^{16} m  
1 yard 
yd 
= 0.9144 m  
NonSI units of area  
1 square foot 
ft^{2} 
= 0.092 903 m^{2}  
1 square inch 
in^{2} 
= 6.4516´10^{}^{4} m^{2}  
NonSI units of volume  
1 cubic foot 
ft^{3} 
= 0.028 316 8 m^{3}  
1 cubic inch 
in^{3} 
= 1.638 71´10^{}^{5} m^{3}  
1 imperial gallon , UK 
gal 
= 4.546 091´10^{}^{3} m^{3}  
1 dry gallon USA 
gal 
= 4.404 883 77´10^{}^{3} m^{3}  
1 liquid gallon USA 
gal 
= 3.785 411´10^{3} m^{3}  
1 litre, liter 
l (or L) 
= 1.0´10^{}^{3} m^{3}  
NonSI units of angle (plane)  
1 degree 
º 
= 0.017 453 3 rad  
1 minute 
' 
= 2.908 88´10^{}^{4} rad  
1 second 
'' 
= 4.848 14´10^{}^{6} rad  
NonSI units of solid angle  
1 hemisphere  = 6.283 185 3 sr  
NonSI units of time  
1 day solar mean 
d 
= 8.6400´10^{4} s  
1 day sideral 
d 
= 8.6164´10^{4} s  
1 minute solar mean 
min 
= 60 s  
1 second sidereal 
s 
= 0.997 269 56 s  
1 year solar mean, tropical 
yr 
= 3.155 692 6´10^{7} s  
1 year sidereal 
yr 
= 3.155 815´10^{7} s  
1 year calendar (365 mean solar days) 
yr 
= 3.1536´10^{7} s  
NonSI units of velocity (linear)  
1 foot per second 
ft.s^{1} 
= 0.3048 m.s^{1}  
1 inch per second 
in.s^{1} 
= 0.0254 m.s^{1}  
1 kilometre per hour 
km.h^{1} (or km/h) 
= 0.277 778 m.s^{1}  
1 knot international 
kn 
= 0.514 444 m.s^{1}  
1 knot UK 
kn 
= 0.514 773 m.s^{1}  
1 mile per hour 
mi.h^{1} or (mph) 
= 0.447 04 m.s^{1}  
NonSI units of velocity (angular)  
1 cycle per second 
rev.s^{1} 
= 6.283 185 rad.s^{1}  
1 hertz 
(Hz) 
= 6.283 185 rad.s^{1}  
1 revolution per minute 
rev.min^{1 }(or rpm) 
= 0.104 720 rad.s^{1}  
NonSI units of frequency  
1 radian per second 
rad.s^{1} 
= 0.159 155 Hz  
1 revolution per minute 
rev.min^{1} (or rpm) 
= 0.016 667 Hz  
NonSI units of acceleration  
1 foot per square second 
ft.s^{2} 
= 0.304 800 m.s^{2}  
1 gravity, free fall standard 
g 
= 9.806 650 m.s^{2}  
1 Galileo 
Gal 
= 0.010 m.s^{2}  
1 inch per square second 
in.s^{2} 
= 0.025 400 m.s^{2}  
NonSI units of mass  
1 atomic mass unit 
u 
= 1.661´10^{}^{27} kg  
1 pound 
lb (or lbm) 
= 0.453 592 kg  
1 slug  = 14.593 881 kg  
1 long ton, UK 
ton 
= 1.016 046´10^{3} kg  
1 metric tonne 
t 
= 1.0´10^{3} kg  
NonSI units of force  
1 dyne 
dyn 
= 1.0´10^{}^{5} N  
1 kilogrammeforce or kilopond 
kgf (or kp) 
= 9.806 N  
1 poundforce 
lbf 
= 4.448 22 N  
NonSI units of pressure  
1 atmosphere 
atm 
= 1.013 25´10^{5} Pa  
1 bar 
bar 
= 10^{5} Pa  
1 atmosphere technical 
at 
= 0.980 665´10^{5 }Pa  
1 barye 
dyn.cm^{2} 
= 0.1 Pa  
1 inch of water at 4 ºC 
inH_{2}O 
= 249.089 Pa  
1 inch of mercury at 32 ºF 
inHg 
= 3.386 39´10^{3} Pa  
1 millibar 
mbar 
= 100.0 Pa  
1 millimetre of mercury 
mmHg 
= 133.322 Pa  
1 millimetre of water 
mmH_{2}O 
= 9.806 65 Pa  
1 poundforce per square inch 
psi 
= 6.894 76´10^{3} Pa  
1 torricelli 
tor 
= 133.322 Pa  
NonSI units of viscosity (dynamic)  
1 centipoise 
cP 
= 10^{3} Pa.s  
NonSI units of viscosity (kinematic)  
1 centistokes 
cSt 
= 100 m2.s^{1}  
NonSI units of surface tensión  
1 dyne per centimetre 
dyn.cm^{1} 
= 10^{3} N.m^{1}  
NonSI units of energy, heat and work  
1 British thermal unit international 
Btu 
= 1.055 75´10^{3} J  
1 calorie thermal international 
cal_{IT} 
= 4.1868 J  
1 kilocalorie 
kcal 
= 4.1868´10^{3} J  
1 gross calorie 
Cal 
= 4.1868´10^{3} J  
1 electronvolt 
eV 
= 1.602 1917´10^{}^{19} J  
1 erg 
erg 
= 1.0´10^{}^{7} J  
1 frigorie 
fr 
= 4.1855´10^{3 }J  
1 therm  = 1.055´10^{8} J  
1 thermie 
th 
= 4.1868´10^{6} J  
1 ton of refrigeration, US 
ton 
= 3.038 318´10^{8} J  
NonSI units of power  
1 British thermal unit per hour 
Btu/h 
= 0.293071 W  
1 horsepower electric 
hp 
= 746.00 W  
1 horsepower imperial 
hp 
= 745.70 W  
1 horsepower metric 
hp 
= 735.499 W  
1 horsepower water 
hp 
= 746.043 W  
1 kilocalorie per hour 
kcal/h 
= 1.1630 W  
1 ton of refrigeration per day, US 
ton 
= 3.516 85´10^{3} W  
NonSI units of specific energy  
1 British thermal unit per pound 
Btu/lb 
= 2.326´10^{3} J.kg^{1}  
1 calorie (I.T.) per gramme 
cal_{IT}/g 
= 4.1868´10^{3} J.kg^{1}  
1 kilocalorie (I.T.) per kilogramme 
kcal_{IT}/kg 
= 4.1868´10^{3} J.kg^{1}  
NonSI units of heat flux density  
1 British thermal unit per square foot hour 
Btu.ft^{2}.h^{1} 
= 3.15459 W.m^{2}  
1 kilocalorie (I.T.) per square metre hour 
kcal_{IT}.m^{2}.h^{1} 
= 1.163 W.m^{2}  
NonSI units of temperature  
t degree Celsius 
ºC 
= t + 273.15 K  
t degree Fahrenheit 
ºF 
= 5t/9 + 459.67 K  
t degree Rankine 
ºR 
= 5t/9 K  
NonSI units of specific heat capacity  
1 British thermal unit per pound degree Celsius 
Btu.lb^{1}.ºC^{1} 
= 2.326´10^{3} J.kg^{1}.K^{1}  
1 British thermal unit per pound degree Fahrenheit 
(Btu.lb^{1}.ºF^{1}) 
=4.1868´10^{3 }J.kg^{1}.K^{1}  
1 kilocalorie per kilogramme kelvin 
kcal_{IT}.kg^{1}.K^{1} 
= 4.1868´10^{3 }J.kg^{1}.K^{1}  
NonSI units of thermal conductivity  
1 British thermal unit per foot second degree Fahrenheit 
Btu.ft^{1}.s^{1}.ºF^{1} 
=6.23064´10^{3} W.m^{1}.K^{1}  
1 British thermal unit per inch hour degree Fahrenheit 
Btu.in^{1}.h^{1}.ºF^{1} 
= 20.7688 W.m^{1}.K^{1}  
1 kilocalorie (I.T.) per metre hour degree Celsius 
kcal.m^{1}.h^{1}.ºC^{1} 
= 1.1630 W.m^{1}.K^{1}  
NonSI units of thermal conductance  
1 British thermal unit per square foot hour degree Fahrenheit 
Btu.ft^{2}.h^{1}.ºF^{1} 
= 5.67826 W.m^{2}.K^{1}  
1 kilocalorie (I.T.) per square metre hour kelvin 
kcal.m^{2}.h^{1}.K^{1} 
= 1.1630 W.m^{2}.K^{1}  
NonSI units of thermal diffusivity  
1 foot squared per hour 
ft^{2}.h^{1} 
= 2.58064´10^{}^{5} m^{2}.s^{1}  
1 inch squared per hour 
in^{2}.h^{1} 
= 1.79211´10^{}^{7} m^{2}.s^{1}  
NonSI units of luminance, brightness, illumination  
1 lux, lumen per square metre 
lx (or lm.m^{2}) 
= 0.159 155 cd.m^{2}  
NonSI units of luminous flux  
1 candle power spherical 
cd 
= 12.566 lm  
1 watt of maximum visible radiation 
W 
= 683 lm  
1 watt of solar radiation 
W 
= 96 lm  
1 watt of 0.632 µm laser light 
W 
= 140 lm  
1 watt of incandescent lamp at 300 K 
W 
= 15 lm  
NonSI units of luminous intensity  
1 lumen of spherical luminous flux 
lm 
= 0.079 577 cd  
1 lumen per steradian 
lm.sr^{1} 
= 1 cd  
NonSI units of illuminance, illumination  
1 candle per square meter 
cd.m^{2} 
= 6.283 185 lx 
^{a}The above conversion applies to single temperature values, when dealing with differences in temperature, the relationship is 1 K = 1 ºC = 9/5 ºF = 9/5 ºR.
Fundamental physical constants
Quantity 
Symbol 
Value 
Unit 
Uncertainty (ppm) 
atomic mass unit 
m_{u} 
1.660 565 5´10^{27} 
kg 
5 
Avogadro constant 
N_{A} 
6.022 045´10^{23} 
mol^{1} 
5 
Boltzmann constant 
k 
1.380 662´10^{23} 
J.K^{1} 
8.5 
proton charge 
e 
1.602 189 2´10^{19} 
C 
3 
curie 
Ci 
3.7´10^{10 } 
disintegrations.s^{1} 
exact 
Einstein constant 
c^{2} 
8.987 551 79´10^{16} 
J.kg^{1} 
exact 
electron rest mass 
m_{e} 
9.109 534´10^{31} 
kg 
0.6 
electronvolt 
eV 
1.602 189 2´10^{19} 
J 
3 
electronic charge 
e 
1.602 189 2v10^{19} 
C 
3 
Faraday constant 
F 
9.648 456´10^{4} 
C.mol^{1} 
3 
fine structure constant 
a 
7.297 350 6´10^{3} 
 
0.6 
first radiation constant 
c_{1} 
3.741 832´10^{16} 
W.m^{2} 
0.6 
gas constant 
R 
8.314 41 
J.mol^{1}.K^{1} 
40 
gravitational acceleration 
g_{0} 
9.806 65 
m.s^{2} 
exact 
universal gravitational constant 
G 
6.672´10^{}^{11} 
N.m^{2}.kg^{2} 
600 
icepoint temperature 
T_{st} 
273.15 
K 
exact 
Planck constant 
h 
6.626 076´10^{}^{34} 
J.s 
0.6 
proton rest mass 
m_{p} 
1.672 648 5´10^{}^{27} 
kg 
0.6 
second radiation constant 
c_{2} 
0.014 387 86 
m.K 
8.5 
speed of light in vacuum 
c 
2.997 924 58´10^{8} 
m.s^{1} 
exact 
standard acceleration of free fall 
g_{0} 
9.806 65 
m.s^{2} 
exact 
standard molar volume of ideal gas (at T_{st} and p_{st}) 
V_{st} 
0.022 413 83 
m^{3}.mol^{1} 
0.6 
standard pressure 
p_{st} 
1.013 25´10^{5} 
Pa 
exact 
standard temperature 
T_{st} 
273.15 
K 
exact 
StefanBoltzmann constant 
s 
5.670 32´10^{}^{8} 
W.m^{2}.K^{4} 
34 
triple point of water 
T_{tr} 
273.16 
K 
exact 
Wien’s radiation constant 
c_{3} 
2.897 790´10^{}^{3} 
m.K 
0.6 