The SI / metric system

SI base units
Some SI Derived Units with special names
Some fundamental physical constants
Some astronomical constants
Some conversions of NON-SI Units to SI Units
SI related links

SI (Système International d'Unités) is the modernized version of the metric system. It is used on an international basis and in science and mathematical areas.

There are critics opposing this standard, but it has been widely accepted around the world. I personally have nothing against this system, but I would like to point out that the system itself is basically ok (more or less, I guess), but it seems administration of the system are leaving much for improvement and maybe should be more strict and precise in order to support its scientific and practical value.

SI base units

Unit Type Unit Name Symbol Definition
Lengthmeterm1/299,792,458 of the distance travelled by light in a vacuum in one second
Unit of masskilogramkgA kilogram is equal to the mass of the international Platinum-Iridium prototype kept in Paris.
TimesecondsDefined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the Caesium-133 atom.
Electric Current ampere A The amount of current that if maintained in two parallel rectilinear conductors (of infinite length and negligible circular cross-section) placed 1 metre apart in a vacuum, would produce a force between these conductors equal to 2 * 10-7 newton per metre.
TemperaturekelvinKThe fraction 1/273.16 of the thermodynamic temperature at the triple point of water.
Amount of Substance mole mol The amount of substance which contains as many elementary units as there are atoms in 0.012 kg of pure Carbon-12.
Luminous Intensity candela cd One candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Supplementary units:

Unit Type Unit Name Symbol Definition
plane angle radian rad m*m-1 = 1
solid angle steradian sr m2*m-2 = 1


All metric units can be used as fractions or multiples by using prefixes. Note the case of the letters, and its significance. M ismega while m is milli, and k is kilo while K is kelvin etc. Here are some examples of the most common prefixes:

Prefix NameSymbolFactor   Prefix NameSymbolFactor
yottaY1024   decid10-1
zettaZ1021   centic10-2
exaE1018   millim10-3
petaP1015   microµ10-6
teraT1012   nanon10-9
gigaG109   picop10-12
megaM106   femtof10-15
kilok103   attoa10-18
hectoh102   zeptoz10-21
dekada101   yoctoy10-24

Some SI Derived Units with special names

Physical Quantity Name of Unit Symbol Definition
frequency hertz Hz 1/s
energy joule J kg*m2/s2
force newton N kg*m/s2
pressure pascal Pa kg/m*s2
power watt W kg*m2/s3
electric charge coulomb C A*s
electric potential volt V kg*m2/A*s3
electric resistance ohm Ω kg*m2/A2*s3
capacitance farad F A2*s4/kg*m2
inductance henry H kg*m2/A2*s2
magnetic flux weber Wb kg*m2/A*s2
magnetic flux density tesla T kg/A*s2

Some fundamental physical constants:

Constant Symbol Value
speed of light in a vacuum c 299,792,458 m/s
gravitational constant G 6.67*10-11m3/kg*s2
Avogadro constant NA 6.022*1023 mol-1
universal gas constant R 8.31 J/mol * K
Boltzmann's constant k 1.38*10-23 J/K
elementary charge e 1.60*10-19 C
permittivity of free space ε0 8.85*10-12C2/N*m2
permeability of free space μo 4π*10-7 T*m/A
electron mass me 9.11*10-31 kg
proton mass mp 1.67*10-27 kg
neutron mass mn 1.67*10-27 kg
Planck's constant   6.63*10-34 J*s
electron charge-to-mass ratio -e/me -1.76*1011 C/kg
proton-electron mass ratio mp/me 1840
molar volume of ideal gas at STP   22400 cm3/mol
Bohr magneton µB 9.27*10-24 J/T
magnetic flux quantum Φ0 = h/2e 2.07*10-15 Wb
Rydberg constant R 1.10*107 m-1

Some astronomical constants

Constant Symbol Value
standard gravity at earth's surface g 9.80665 m/s2
equatorial radius of earth Re 6.374*106 m
mass of earth Me 5.976*1024 kg
mass of moon   7.350*1022 kg = 0.0123 Me
mean radius of moon's orbit around earth   3.844*108 m
mass of sun   1.989*1030 kg
mean radius of earth's orbit around the sun AU 1.496*1011 m
period of earth's orbit around sun yr 3.156*107 s
diameter of our galaxy   7.5*1020 m
mass of our galaxy   2.7*1041 kg = ( 1.4*1011 ) * Mass of sun

Some conversions of NON-SI Units to SI Units


1 electron-volt (eV) = 1.6022 * 10-19 J
1 erg = 10-7 J
1 British thermal unit (BTU) = 1055 J
1 calorie (cal) = 4.186 J
1 kilowatt-hour (kWh) = 3.6 * 106 J


1 gram (g) = 10-3 kg
1 atomic mass unit (u) = 931.5 MeV/c2 = 1.661 * 10-27 kg
1 MeV/c2 = 1.783 * 10-30 kg


1 dyne = 10-5 N
1 pound (lb or #) = 4.448 N


1 centimeter (cm) = 10-2 m
1 kilometer (km) = 103 m
1 fermi = 10-15 m
1 Angstrom (Å) = 10-10 m
1 inch (in or ") = 0.0254 m
1 foot (ft) = 0.3048 m
1 mile (mi) = 1609.3 m
1 astronomical unit (AU) = 1.496 * 1011 m
1 light-year (ly) = 9.46 * 1015 m
1 parsec (ps) = 3.09 * 1016 m


1 degree (°) = 1.745 * 10-2 rad
1 min (') = 2.909 * 10-4 rad
1 second (") = 4.848 * 10-6 rad


1 liter (L) = 10-3 m3


1 kilowatt (kW) = 103 W
1 horsepower (hp) = 745.7 W


1 bar = 105 Pa
1 atmosphere (atm) = 1.013 * 105 Pa
1 pound per square inch (lb/in2) = 6.895 * 103 Pa


1 year = 3.156 * 107 s
1 day (d) = 8.640 * 104 s
1 hour (h) = 3600 s
1 minute (min) = 60 s


1 mile per hour (mi/h) = 0.447 m/s

Magnetic field:

1 gauss = 10-4 T

SI related links

Bureau International des Poids et Mesures - The SI system
NIST SI related - Current definitions and similar