Basic and supplementary units – Units SI

The International System of Units SI is based on nine physical quantities.

Physical Quantity	Unit name	Unit Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Plane Angle	radian	rad
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cd
Solid angle	steradian	sr
Thermodynamic temperature	kelvin	K

 

Derived units

By dimensionally appropriate multiplication and/or division of the units shown above, derived Units SI are obtained. Some of these are given special names.

Physical Quantity	Unit name	Unit Symbol	Derivation
Electric Capacitance	farad	F	(A2s4)(kgm2)
Electric charge	coulomb	C	As
Electric Conductance	siemens	S	(A2s3)/(kgm2)
Electric potential difference	volt	V	(kgm2)/(As3)
Electric resistance	ohm	Ω	(kgm2)/ (A2s3)
Energy	joule	J	(kgm2)/s2
Force	newton	N	(kg m)/s2
Frequency	hertz	Hz	1/s
Illuminance	lux	lx	(cd sr)/m2
Inductance	henry	H	(kgm2)/ (A2s2)
Luminous flux	lumen	lm	cd sr
Magnetic flux	weber	Wb	(kgm2)/ (As2)
Magnetic flux density	tesla	T	kg/ (As2)
Power	watt	W	(kgm2)/s3
Pressure	pascal	Pa	kg/ (ms2)

 

Some other derived Units SI not having special names.

Physical Quantity	Unit	Unit symbol
Acceleration	metre per second squared	m/s2
Angular velocity	radian per second	rad/s
Area	square metre	m2
Current density	ampere per square metre	A/m2
Density	kilogram per cubic metre	kg/m3
Dynamic viscosity	pascal second	Pa s
Electric charge density	coulomb per cubic metre	C/m3
Electric field strength	volt per metre	V/m
Energy density	joule per cubic metre	J/m3
Heat capacity	joule per kelvin	J/K
Heat flux density	watt per square metre	W/m2
Kinematic viscosity	square metre per second	m2/s
Luminance	candela per square metre	cd/m2
Magnetic field strength	ampere per metre	A/m
Moment of force	newton metre	N m
Permeability	henry per metre	H/m
Permittivity	farad per metre	F/m
Specific volume	cubic metre per kilogram	m3/kg
Surface tension	newton per metre	N/m
Thermal conductivity	watt per metre kelvin	W/(mK)
Velocity	meter per second	m/s
Volume	cubic metre	m3

 

Units: not SI (Units SI)

Some of the units which are not part of the SI system, but which are recognized for continued use with the SI system, are as shown

Physical quantity	Unit name	Unit symbol	Definition
Angle	degree	°	(π/180)rad
Angle	minute	′	(π/10,800)rad
Angle	second	′′	(π/648000)rad
Celsius temperature	degree Celsius	°C	K -273.2(For K see 1.3.1)
Dynamic viscosity	poise	P	10-1Pa s
Energy	calorie	cal	≈4.18J
Fahrenheit temperature	degree Fahrenheit	°F	(9/8)°C+32
Force	kilogram force	kgf	≈9.807 N
Kinematic viscosity	stokes	St	10-4m2/s
Length	inch	in	2.54×10-2m
Length	micron	μm	10-6m
Mass	pound	lb	≈0.454kg
Mass	tonne	t	103kg
Pressure	atmosphere	atm	101.325 Pa
Pressure	bar	bar	105Pa
Pressure	millimeter of mercury	mm Hg	≈133.322Pa
Pressure	torr	torr	≈133.322Pa
Thermodynamic temperature	degree Rankine	°R	°F + 459.7
Time	minute	min	60 s
Time	hour	h	3600 s
Time	day	d	86400 s

 

Notes on writing symbols 

(a) Symbols should be in roman type lettering: thus cm, not cm.

(b) Symbols should remain unaltered in the plural: thus cm, not cms.

(c) There should be a space between the product of two symbols: thus N m, not Nm.

(d) Index notation may be used: thus m/s may be written as m s^-1and W/(m K) as W m^-1 K^-1

 

Decimal multiples of units.

For quantities which are much larger or much smaller than the units so far given, decimal multiples of units are used.

Internationally agreed multiples are as shown.

 

For small quantities

Multiple	Prefix	Symbol
10-1	deci	d
10-2	centi	c
10-3	milli	m
10-6	micro	μ
10-9	nano	n
10-12	pico	p
10-15	femto	f
10-18	atto	a

 

For large quantities

Multiple	Prefix	Symbol
10	deca	da
102	hector	h
103	kilo	k
106	mega	M
109	giga	G
1012	tera	T
1015	peta	P
1018	exa	E

 

Notes 

(a) A prefix is used with the gram, not the kilogram: thus Mg, not kkg.

(b) A prefix may be used for one or more of the unit symbols: thus kN m, N mm and kN mm are all acceptable.

(c) Compound prefixes should not be used: thus ns, not mμs.