Organization of the SI

The International System of Units (Systeme International d'Unites, SI) consists of three classes of units:

• seven base units,
• two supplementary units, and
• a number of derived units.

These units together form a coherent system of units which are officially known as SI units. Those units which do not form part of this system are known as out-of-system units.

SI Base Units

Phyiscal quantity	Dimension	Name	Symbol
Mass	M	kilogram	kg
Length	L	metre	m
Time	T	second	s
Temperature	Θ	kelvin	K
Amount of substance	N	mole	mol
Electric current intensity	I	ampere	A
Luminous intensity	J	candela	cd

The official defintion of seven SI base units is given in the following table.

meter (metre)		The meter is the length of the path travelled by light in vacuum during a time interval of \(\frac{1}{299792458}\)[s]. (17th CGPM (1983), Resolution 1)
kilogram		The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogra. [1st CGPM (1889), 3rd CGPM (1901)]
second		The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels (\(F=4, m_F = 0\) to \(F=3, m_F = 0\)) of the ground state of the cesium 133 atom (13th CGPM (1967)).
amper		The amper is that constant current which, if maintained in two straight parallel conductors of infinite length of negligible circular corss-section and placed 1 meter apart in vacuum, would produce between these conductors a force equalt ot \(2 \times 10^{-7} [\frac{N}{m}]\) (9th CGPM (1948), Resolution 2 and 7).
kelivn		The kelvin, unit of thermodynamic temperature, is the fraction \(\frac{1}{273.16}\) of the thermodynamic temperature of the triple point of water (13th CGPM (1967), Resolution 4).
mole		(I) The mole is the amount of substance of a system which conatains as many elementary entities as there are atoms in 0.012 [kg] of carbon 12. (II) when the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particle, or specified groups of such particles (14th CGPM (1971), Resolution 3). In this defintion, it is understood that the carbon 12 atoms are unbound, at rest and in their ground state.
candela		The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency \(540\times 10^{12}\)[Hz] and that has a radiant intesity in that direction of \(\frac{1}{683}\) [\(\frac{W}{sr}\)] (16th CGPM (1979), Resolution 3).

SI Supplementary Units

Besides the seven SI base units, the SI has two supplementary units, and these are the radian for plane angle, and the steradian for solid angle. Both units are dimensionless i.e. in a dimension equation they have the value of unity. However, they are sometimes included in dimensional equations using an arbitrary dimensional symbol, for example, the Greek letter \(\alpha\) or a Roman capital \(A\) for plane angle while the Greek letter \(\Omega\) for the solid angle. Since this notation is non-official these symbols can be omitted from a dimensional equation in cases where this does not cause ambiguity. The two supplementary units are listed in the following table.

Physical quantity	Dimnesion	Name	Symbol
Plane angle	\(\alpha\)	radian	rad
Solid angle	\(\Omega\)	steradian	sr

SI Derived Units

The SI derived uints are those units that are defined by the simple equation which relates two or more basic SI units. There are twenty derived units with special names and symbols and these units are listed in the following table.

Name	Symbol	Physical qunatity	Dimension	Equivalent in SI base units
becquerel	Bq	radioactivity	\(T^{-1}\)	\(1 [Bq] = 1 [s^{-1}]\)
coulomb	C	quantity of electricity, electric charge	IT	\(1 [C] = 1 [A\cdot s]\)
farad	F	electric capacitance	\(M^{-1}L^{-2}T^4I^2\)	\(1 [F] = 1 [kg^{-1}\cdot m^{-2}\cdot s^4\cdot A^2]\)
gray	Gy	absorbed dose of radiation, kerma, specific energy imparted	\(L^2T^{-2}\)	\(1[Gy] = 1[m^2\cdot s^{-2}]\)
henry	H	electric inductance	\(ML^2T^{-2}I^{-2}\)	\(1 [H] = 1 [kg\cdot m^2\cdot s^{-2}\cdot A^{-2}]\)
hertz	Hz	frequency	\(T^{-1}\)	\(1 [Hz] = 1 [s^{-1}]\)
joule	J	energy, work, heat	\(ML^2T^{-2}\)	\(1 [J] = 1 [kgm^2s^{-2}]\)
katal	kt	enzymatic activity	\(NT^{-1}\)	\(1 [kt] = 1 [mol\cdot s^2]\)
lumen	lm	luminous flux	\(J\Omega\)	\(1 [lm] = 1 [cd\cdot sr]\)
lux	lx	illuminance	\(J\Omega L^{-2}\)	\(1 [lx] = 1 [cd\cdot sr \cdot m^{-2}]\)
newton	N	force,weight	\(MLT^{-2}\)	\(1 [N] = 1 [kg\cdot m \cdot s^{-2}]\)
ohm	\(\Omega\)	electric resistance	\(ML^2T^{-3}I^{-2}\)	\(1 [\Omega] = 1 [kg\cdot m^2 \cdot s^{-3}\cdot A^{-2}]\)
pascal	Pa	pressure, stress	\(ML^{-1}T^{-2}\)	\(1 [Pa] = 1 [kg\cdot m^{-1}\cdot s^{-2}]\)
poiseuille (pascal-second)	Po	absolute viscosity, dynamic viscosity	\(ML^{-1}T^{-1}\)	\(1 [Po] = 1 [kg\cdot m^{-1} \cdot s^{-1}]\)
siemens	S	electric conductance	\(M^{-1}L^{-2}T^3I^2\)	\(1 [S] = 1 [kg^{-2}\cdot m^{-2}\cdot s^3 \cdot A^2]\)
sievert	Sv	dose equivalent, dose equivalent index	\(L^2T^{-2}\)	\(1 [Sv] = 1 [m^2\cdot s^{-2}]\)
tesla	T	induction field, magnetic flux density	\(MT^{-2}I^{-1}\)	\(1 [T] = 1 [kg\cdot A^{-1} \cdot s^{-2}]\)
volt	V	electric potential, electromotive force, potential difference	\(ML^2T^-3I^-1\)	\(1 [V] = 1 [kg \cdot m^2 \cdot s^{-3}\cdot A^{-1}]\)
watt	W	power, radiant flux	\(ML^2T^{-3}\)	\(1 [W] = 1 [kg \cdot m^2 \cdot s^{-3}]\)
weber	Wb	induction magnetic flux	\(ML^2T^{-2}I^{-1}\)	\(1 [Wb] = 1 [kg\cdot m^2 \cdot s^{-2} \cdot A^{-1}]\)