International System of Units (SI System)

By Steven McFadyen on April 9th, 2012

The International System of Units (abbreviated SI) is the world's most widely used system of units. The system consists of a set of units and prefixes.

Note: this SI system is being revised to define the unit of mass in terms of fundamental constants. In addition the definitions ampere and kelvin will revised.

Several countries have only partially adopted the SI System; the United States being notable in this regard. A full list of SI units, a conversion calculator and conversion tables are maintained at:

myElectrical Unit Conversion

Base Units

There are seven base units, from which all other units are derived. Each base unit is dimensionally independent.

Name	Symbol	Quantity
meter	m	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.
kilogram	kg	The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
second	s	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.
ampere	A	The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length.
kelvin	K	The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
mole	mol	The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 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.
candela	cd	The 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.

Prefixes

Factor	Name	Symbol	Factor	Name	Symbol
10¹	deca	da	10^-1	deci	d
10²	hecto	h	10^-2	centi	c
10³	kilo	k	10^-3	mili	m
10⁶	mega	M	10^-6	micro	μ
10⁹	giga	G	10^-9	nano	n
10¹²	tera	T	10^-12	pico	p
10¹⁵	peta	P	10^-15	femto	f
10¹⁸	exa	E	10^-18	atto	a
10²¹	zetta	Z	10^-21	zepto	z
10²⁴	yotta	Y	10^-24	yocto	y

Derived Units

Mechanical Units

	Symbol	SI Unit	Base Units
Acceleration	a	m s^-2	m s^-2
Angular Frequency	ω	rad s^-1	rad s^-1
Angular Momentum	L	kg m² s^-1	kg m² s^-1
Area	A, S	m²	m²
Density	ρ	kg m^-3	kg m^-3
Energy	E	J (Joule)	m² kg s^-2
Force	F	N (Newton)	m kg s^-2
Frequency	v, f	Hz (Hertz)	s^-1
Momentum	p	kg m s^-1	kg m s^-1
Moment of Inertia	I, J	kg m²	kg m²
Pressure	P	Pa (Pascal)	m^-1 kg s^-2
Power	P	W (Watt)	m² kg s^-3
Speed, linear	u	m s^-1	m s^-1
Speed, rotational	ω	rad s^-1	rad s^-1
Stress	p	Pa	m^-1 kg s^-2
Surface Tension	λ	N m^-1	kg s^-2
Torque	T	N m^-1	kg s^-2
Velocity	u, v	m s^-1	m s^-1
Viscosity: kinematic		m^{2 s^-1}	m^{2 s^-1}
Viscosity: dynamic	μ, v	Pa s	m^-1 kg s^-1
Work	We	J	m² kg s^-2

Electrical & Magnetic Units

	Symbol	SI Unit	Base Units
Admittance	Y	S (Siemens)	m^-2 kg^-1 s³ A²
Capacitance	C	F (Farad)	m^-2 kg^-1 s⁴ A²
Charge	Q	C (Coulomb)	s A
Charge density, area	ρ	C m^-3	m^-3 s A
Conductance	G	S (Siemens)	m^-2 kg^-1 s³ A²
Conductivity	σ	S m^-1	m^-3 kg^-1 s³ A²
Current (base unit)	I, I	A (Ampere)	A
Current density	J	A m^-2	A m^-2
Electric field strength	E	V m^-1	m kg s^-3 A^-1
Electric flux	ψ	C (coulomb)	s A
Electric flux density	D	C m^-2	m^-2 s A
Electromotive force (e.m.f.)	E, e	V	m² kg s^-3 A^-1
Frequency	F	Hz (Hertz)	s^-1
Impedance	Z	Ω	m² kg s^-3 A^-2
Inductance, mutual	M	H	m² kg s^-2 A^-2
Inductance, self	L	H (Henry)	m² kg s^-2 A^-2
Magnetic field strength	H	A m^-1	A m^-1
Magnetic flux	Φ, φ	Wb (Weber)	m² kg s^-2 A^-1
Magnetic flux density	B	T (Tesla)	kg s^-2 A^-1
Magnetic flux linkage	ψ	Wb	m² kg s^-2 A^-1
Magnetomotive force	F	A (ampere)	A
		At (ampere-turns)	A-turns
Permeability, absolute	μ	H m^-1	m kg s^-2 A^-2
Permeability, free space	μ_o	H m^-1	m kg s^-2 A^-2
Permeability, relative	μ_r
Permittivity, absolute	ε	F m^-1	m^-3 kg^-1 s⁴ A²
Permittivity, free space	ε_o	F m^-1	m^-3 kg^-1 s⁴ A²
Permittivity, relative	ε_r
Potential difference	U, V	V (Volt)	m² kg s^-3 A^-1
Power, active	P	W(Watt)	m² kg s^-3
Power, apparent	S	VA	m² kg s^-3
Power, reactive	Q	var	m² kg s^-3
Reactance	X	Ω	m² kg s^-3 A^-2
Reactive volt-ampere	Q	var
Reluctance	S	A Wb^-1	m^-2 kg^-1 s² A²
Resistance	R	Ω (Ohm)	m² kg s^-3 A^-2
Resistivity	Ω.m	m3 kg s^-3 A^-2
Susceptance	B	S (Siemens)	m^-2 kg^-1 s³ A²
Volt-ampere		VA	V A
Voltage	U, V	V	m² kg s^-3 A^-1
Wavelength	λ	m	m

Heat Units

	Symbol	SI Unit	Base Units
Critical pressure	p_c	P_a (Pascal)	m^-1 kg s^-2
Critical temperature	T_c	K	K
Critical volume	V_c	m³	m³
Cubic expansivity	γ	K^-1	K^-1
Heat capacity	C	J K^-1	m² kg s^-1 K^-1
Linear expansivity	α	K^-1	K^-1
Molar heat capacity	C_m	J mol^{-1 K^-1}	m² kg s^-2 mol^-1 K^-1
Quantity of heat	Q	J (Joule)	m² kg s^-2
Specific heat capacity	c_p, c_v	J kg^-1 K^-1	m² s^-2 K^-1
Specific latent heat	l	J kg^-1	m2 s^-2
Temperature	t, θ, T	K	K
Thermal conductivity	λ	J m^-1 s^-1 K^-1	m kg s^-3 K^-1
		W m-¹ K^-1

Photometric Optical Units

	Symbol	SI Unit	Base Units
Illuminance	E	lx (Lux)	m^-2 cd sr
Luminance	L	cd m^-2	cd m^-2
Luminous flux	Φ, φ	lm (Lumen)	cd sr
Luminous efficacy		lm W^-1	cd sr m^-2 kg^-1 s³

Acoustical Units

	Symbol	SI Unit	Base Units
Frequency	f	Hz (Hertz)	s^-1
Intensity	I	W m^-2	kg s^-3
Power ratio		dB
Reverberation time		s	s

Writing Style

symbols – roman upright type, lowercase, un-capitalised (unless derived from a proper name), no full stop, not pluralised

space – a space separates number and the symbol, i.e. 124 kg, 2500 A

derived – units derived are expressed with space, dot and/or solidus (/), i.e. N m, N·m, m/s, m s^-1, m·s^-1

External Links

Bureau International des Poids et Mesures (official site)

Fundamentals, Standards, SI System, Units

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Steven McFadyen

Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

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