SI - INTERNATIONAL SYSTEM OF UNITS

The name Système International d'Unités, (International System of Units) and the abbreviation SI, were established by the 11th General Conference on Weights and Measures (CGPM) in 1960.

The base quantities used in the SI are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The base quantities are by convention assumed to be independent. The corresponding base units of the SI were chosen by the CGPM to be the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. The derived units of the SI are then formed as products of powers of the base units, according to the algebraic relations that define the corresponding derived quantities in terms of the base quantities. When the product of powers includes no numerical factor other than one, the derived units are called coherent derived units.

Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets. Note that symbols for quantities are only recommendations, in contrast to symbols for units whose style and form is mandatory.

The value of a quantity is expressed as the product of a number and a unit, and the number multiplying the unit is the numerical value of the quantity expressed in that unit. The numerical value of a quantity depends on the choice of unit. Thus the value of a particular quantity is independent of the choice of unit, although the numerical value will be different for different units. The same value of a speed v = dx/dt of a particle might be given by either of the expressions v = 25 m/s = 90 km/h, where 25 is the numerical value of the speed in the unit metres per second, and 90 is the numerical value of the speed in the unit kilometres per hour.

SI base units

 

Examples of coherent derived units in the SI expressed in terms of base units

Derived quantity		SI coherent derived unit
Name	Symbol	Name	Symbol
area	A	square metre	m2
volume	V	cubic metre	m3
speed, velocity	v	metre per second	m s-1
acceleration	a	metre per second squared	m s-2
wavenumber	σ	reciprocal metre	m-1
density, mass density	ρ	kilogram per cubic metre	kg m-3
surface density	ρA	kilogram per square metre	kg m-2
specific volume	v	cubic metre per kilogram	m3kg-1
current density	j	ampere per square metre	A m-2
magnetic field strength	H	ampere per metre	A m-1
amount concentration, concentration	c	mole per cubic metre	mol m-3
mass concentration	ρ, γ	kilogram per cubic metre	kg m-3
luminance	Lv	candela per square metre	cd m-2
refractive index	n	(the number) one	1
relative permeability	μr	(the number) one	1

 

Coherent derived units in the SI with special names and symbols

	SI coherent derived unit
Derived quantity	Name	Symbol	Expressed in terms of other SI units	Expressed in terms of SI base units
plane angle	radian	rad	1	m m-1
solid angle	steradian	sr	1	m2 m-2
frequency	hertz	Hz		s-1
force	newton	N		m kg s-2
pressure, stress	pascal	Pa	N/m2	m-1 kg s-2
energy, work, amount of heat	joule	J	N m	m2 kg s-2
power, radiant flux	watt	W	J/s	m2 kg s-3
electric charge, amount of electricity	coulomb	C		s A
electric potential difference, electromotive force	volt	V	W/A	m2 kg s-3 A-1
capacitance	farad	F	C/V	m-2 kg-1 s4 A2
electric resistance	ohm	Ω	V/A	m2 kg s-3 A-2
electric conductance	siemens	S	A/V	m-2 kg-1 s3 A2
magnetic flux	weber	Wb	V s	m2 kg s-2 A-1
magnetic flux density	tesla	T	Wb/m2	kg s-2 A-1
inductance	henry	H	Wb/A	m2 kg s-2 A-2
Celsius temperature	degree Celsius	°C		K
luminous flux	lumen	lm	cd sr	cd
luminance	lux	lx	lm/m2	m-2 cd
activity referred to a radionuclide	becquerel	Bq		s-1
absorbed dose, specific energy (imparted), kerma	gray	Gy	J/kg	m2 s-2
dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent	sievert	Sv	J/kg	m2 s-2
catalytic activity	katal	kat		s-1 mol

 

Examples of SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols

		SI coherent derived unit
Derived quantity	Name	Symbol	Expressed in terms of SI base units
dynamic viscosity	pascal second	Pa s	m-1 kg s-1
moment of force	newton metre	N m	m2 kg s-2
surface tension	newton per metre	N/m	kg s-2
angular velocity	radian per second	rad/s	m m-1 s-1 = s-1
angular acceleration	radian per second squared	rad/s2	m m-1 s-2 = s-2
heat flux density, irradiance	watt per square metre	W/m2	kg s-3
heat capacity, entropy	joule per kelvin	J/K	m2 kg s-2 K-1
specific heat capacity, specific entropy	joule per kilogram kelvin	J/(kg K)	m2 s-2 K-1
specific energy	joule per kilogram	J/kg	m2 s-2
thermal conductivity	watt per metre kelvin	W/(m K)	m kg s-3 K-1
energy density	joule per cubic metre	J/m3	m -1 kg s-2
electric field strength	volt per metre	V/m	m kg s-3 A-1
electric charge density	coulomb per cubic metre	C/m3	m-3 s A
surface charge density	coulomb per square metre	C/m2	m-2 s A
electric flux density, electric displacement	coulomb per square metre	C/m2	m-2 s A
permittivity	farad per metre	F/m	m-3 kg-1 s4 A2
permeability	henry per metre	H/m	m kg s-2 A-2
molar energy	joule per mole	J/mol	m2 kg s-2 mol-1
molar entropy, molar heat capacity	joule per mole kelvin	J/(mol K)	m2 kg s-2 K-1 mol-1
exposure (x- and γ-rays)	coulomb per kilogram	C/kg	kg-1 s A
absorbed dose rate	gray per second	Gy/s	m2 s-3
radiant intensity	watt per steradian	W/sr	m4 m-2 kg s-3 = m2 kg s-3
radiance	watt per square metre steradian	W/(m2 sr)	m2 m-2 kg s-3 = kg s-3
catalytic activity concentration	katal per cubic metre	kat/m3	m-3 s-1 mol

 

Non-SI units accepted for use with the International System of Units

Quantity	Name of unit	Symbol for unit	Value in SI units
time, duration	minute	min	1 min = 60 s
	hour	h	1 h = 60 min = 3 600 s
	day	d	1 d = 24 h = 86 400 s
plane angle	degree	°	1° = (π/180) rad
	minute	'	1' = (1/60)° = (π/10 800) rad
	second	"	1" = (1/60)' = (π/648 000) rad
area	hectare	ha	1 ha = 1hm2 = 104 m2
volume	litre	L, l	1 L = 1 dm3 = 10-3 m3
mass	tonne	t	1 t = 103 kg

 

Non-SI units whose values in SI units must be obtained experimentally

Quantity	Name of unit	Symbol for unit	Value in SI units
Units accepted for use with the SI
energy	electronvolt	eV	1 eV = 1.602 176 53(14)×10-19 J
mass	dalton	Da	1 Da = 1.660 538 86(28)×10-27 kg
	unified atomic mass unit	u	1 u = 1 Da
length	astronomical unit	ua	1 ua = 1.495 978 706 91(6)×1011 m
Natural units (n.u.)
speed, velocity	natural unit of speed (speed of light in vacuum)	co	299 792 458 m s-1
action	natural unit of action (reduced Planck constant)	ℏ	1.054 571 68(18)×10-34 Js
mass	natural unit of mass (electron mass)	me	9.109 382 6(16)×10-31 kg
time, duration	natural unit of time	ℏ/(meco2)	1.288 088 667 7(86)×10-21 s
Atomic units (a.u.)
charge	atomic unit of charge, (elementary charge)	e	1.602 176 53(14)×10-19 C
mass	atomic unit of mass, (electron mass)	me	9.109 382 6(16)×10-31 kg
action	atomic unit of action, (reduced Planck constant)	ℏ	1.054 571 68(18)×10-34 Js
length	atomic unit of length, bohr (Bohr radius)	ao	0.529 177 210 8(18)×10-10 m
energy	atomic unit of energy, hartree (Hartree energy)	Eh	4.359 744 17(75)×10-18 J
time, duration	atomic unit of tim	ℏ/Eh	2.418 884 326 505(16)×10-17 s

 

Other non-SI units

Quantity	Name of unit	Symbol for unit	Value in SI units
pressure	bar	bar	1 bar = 0.1 MPa = 105 Pa
	millimetre of mercury	mmHg	1 mmHg ≈ 133.322 Pa
length	angström	Å	1 Å = 0.1 nm = 10-10 m
distance	nautical mile	M	1 M = 1852 m
area	barn	b	1 b = 100 fm2 = 10-28 m2
speed, velocity	knot	kn	1 kn = (1852/3600) m s-1
logarithmic ratio quantities	neper	Np
	bel	B
	decibel	dB

 

Non-SI units associated with the CGS system of units

Quantity	Name of unit	Symbol for unit	Value in SI units
energy	erg	erg	1 erg = 10-7 J
force	dyne	dyn	1 dyn = 10-5 N
dynamic viscosity	poise	P	1 P = 1 dyn s cm-2 = 0.1 Pa s
kinematic viscosity	stokes	St	1 St = 1 cm2 s-1 = 10-4 m2 s-1
luminance	stilb	sb	1 sb = 1 cd cm-2 = 104 cd m-2
illuminance	phot	ph	1 ph = 1 cd sr cm-2 = 104 lx
acceleration	gal	Gal	1 Gal = 1 cm s-2 = 10-2 m s-2
magnetic flux	maxwell	Mx	1 Mx = 1 G cm2 = 10-8 Wb
magnetic flux density	gauss	G	1 G = 1 Mx cm-2 = 10-4 T
magnetic field	œrsted	Oe	1 Oe ≙ (103/4π) A m-1

 

SI prefixes

 

Names and symbols for decimal multiples and submultiples of the unit of mass are formed by attaching prefix names to the unit name 'gram', and prefix symbols to the unit symbol 'g'.

These SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (for example, one kilobit represents 1000 bits and not 1024 bits). The names and symbols for the prefixes corresponding to 2¹⁰, 2²⁰, 2³⁰, 2⁴⁰, 2⁵⁰, and 2⁶⁰ are, respectively: kibi, Ki; mebi, Mi; gibi, Gi; tebi, Ti; pebi, Pi; and exbi, Ei. Thus, for example, one kibibyte would be written: 1 KiB = 2¹⁰ B = 1024 B, where B denotes a byte. Although these prefixes are not part of the SI, they should be used in the field of information technology to avoid the incorrect usage of the SI prefixes.

 

Bibliography:

1. "The International System of Units (SI)." Bureau International des Poids et Mesures. 30 Nov 2010. <https://www.bipm.org/en/home>.
2. "The International System of Units from NIST." Oct 2000. National Institute of Standards and Technology. 30 Nov 2010. <http://physics.nist.gov/cuu/Units/>.