# The International System of Units (SI)

The International System of Units, often abbreviated SI from the French Le Système international d'unités, is the most popular and widely used system of measurements today. It is based on the metric system and used in everyday human affairs, commerce and science. It is the preferred system in most countries in the world with the most notable exception being the United States.

The system resides on seven base units from which an additional 22 units are derived and named.

## SI base units

Maxwell introduced the concept of a coherent system of units in the 19th century. The idea is that a minimum number of units are declared base units and other measurable physical quantities then can be derived from these base units. The SI system has chosen the seven base units described in the table below. Important to understand is that the choice of these units are arbitrary and not something that is inevitable when analyzing the possible physical quantities. Instead of choosing the kilogram as a base unit of mass and Newton as the derived unit of force defined as the a function of base units N = kg×m×/s2, we could had rearranged to have Newton as a base unit and derive the kilogram from base units as kg = N×s2/m.

Unit name Unit symbol Quantity measured Dimension symbol Definition
metre m length L Since 1983: The distance traveled by light during 1/299792458 second in vacuum.
kilogram kg mass M Since 1889: The mass of the International prototype kilogram located in Sèvres, France
second s time T Since 1967: 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 isotope.
ampere A electric current I Since 1946: The constant current flowing through two straight parallel conductors of infinite length and negligible cross-sections separated by one metre in vacuum, which would produce a force of 2 x 10-7 newtons per metre between the two conductors.
kelvin K thermodynamic temperature Θ Since 1967: 1/273.16 of the thermodynamic temperature of the triple point of water.
mole mol amount of substance N Since 1967: The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of carbon 12.
candela cd luminous intensity J Since 1979: The luminous intensity 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.

Sometimes these seven units are divided into primary fundamental units which are the three units needed to describe all kinematical and mechanical systems, the metre, second and kilogram. The other four are then called auxiliary fundamental units. Claims could be made that temperature should not be considered a fundamental unit of SI at all since temperature is an emergent quantity expressing the energy per freedom of degree of a particle, which could be expressed in terms of energy, or equivalent in mass, length and time.

## Derived SI units

From these seven fundamental units another 22 units are defined in the SI system as derived units.

Unit name Unit symbol Quantity measured In terms of other SI units In terms of SI base units
steradian sr solid angle 1 m1/m1
hertz Hz frequency s-1
newton N force, weight kg×m×s-2
pascal Pa pressure, stress N/m2 kg×m-1×s-2
joule J energy, work, heat N×m kg×m2×s-2
watt W power J/s kg×m2×s-3
coulomb C electric charge s×A
volt V electric potential difference W/A kg×m2×s-3×A-1
farad F electric capacitance C/V kg-1×m-2×s4×A2
ohm Ω electric resistance, impedance, reactance V/A kg×m2×s-3×A-2
siemens S electric conductance A/V kg-1×m-2×s3×A2
weber Wb magnetic flux V×s kg×m-2×s-2×A-1
tesla T magnetic field strength Wb/m2 kg×s-2×A-1
henry H inductance Wb/A kg×m2×s-2×A-2
degree Celsius °C temperature relative to 273.15 K K
lumen lm luminous flux cd×sr cd
lux lx illuminance lm/m2 m-2×cd
becquerel Bq radioactivity (decays per unit of time) s-1
gray Gy absorbed dose of ionizing radiation J/kg m2×s-2
sievert Sv equivalent dose of ionizing radiation J/kg m2×s-2
katal kat catalytic activity s-1×mol