The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent.

SI derived units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

Table 3.  SI derived units with special names and symbols
	SI derived unit
Derived quantity	Name	Symbol	Expression   in terms of   other SI units	Expression in terms of SI base units
plane angle	radian (a)	rad	-	m·m-1 = 1 (b)
solid angle	steradian (a)	sr (c)	-	m2·m-2 = 1 (b)
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, quantity of heat	joule	J	N·m	m2·kg·s-2
power, radiant flux	watt	W	J/s	m2·kg·s-3
electric charge, quantity 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		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 (c)	m2·m-2·cd = cd
illuminance	lux	lx	lm/m2	m2·m-4·cd = m-2·cd
activity (of a radionuclide)	becquerel	Bq	-	s-1
absorbed dose, specific energy (imparted), kerma	gray	Gy	J/kg	m2·s-2
dose equivalent (d)	sievert	Sv	J/kg	m2·s-2
catalytic activity	katal	kat		s-1·mol
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4. (b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted. (c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units. (d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

Note on degree Celsius. The derived unit in Table 3 with the special name degree Celsius and special symbol °C deserves comment. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T₀ = 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation

t= T- T₀.

The unit of Celsius temperature is the degree Celsius, symbol °C. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by

t/°C = T/K - 273.15.

It follows from the definition of t that the degree Celsius is equal in magnitude to the kelvin, which in turn implies that the numerical value of a given temperature difference or temperature interval whose value is expressed in the unit degree Celsius (°C) is equal to the numerical value of the same difference or interval when its value is expressed in the unit kelvin (K). Thus, temperature differences or temperature intervals may be expressed in either the degree Celsius or the kelvin using the same numerical value. For example, the Celsius temperature difference t and the thermodynamic temperature difference T between the melting point of gallium and the triple point of water may be written as t = 29.7546 °C = T = 29.7546 K.

The special names and symbols of the 22 SI derived units with special names and symbols given in Table 3 may themselves be included in the names and symbols of other SI derived units, as shown in Table 4.

Table 4.  Examples of SI derived units whose names and symbols include SI derived units with special names and symbols
	SI derived unit
Derived quantity	Name	Symbol
dynamic viscosity	pascal second	Pa·s
moment of force	newton meter	N·m
surface tension	newton per meter	N/m
angular velocity	radian per second	rad/s
angular acceleration	radian per second squared	rad/s2
heat flux density, irradiance	watt per square meter	W/m2
heat capacity, entropy	joule per kelvin	J/K
specific heat capacity, specific entropy	joule per kilogram kelvin	J/(kg·K)
specific energy	joule per kilogram	J/kg
thermal conductivity	watt per meter kelvin	W/(m·K)
energy density	joule per cubic meter	J/m3
electric field strength	volt per meter	V/m
electric charge density	coulomb per cubic meter	C/m3
electric flux density	coulomb per square meter	C/m2
permittivity	farad per meter	F/m
permeability	henry per meter	H/m
molar energy	joule per mole	J/mol
molar entropy, molar heat capacity	joule per mole kelvin	J/(mol·K)
exposure (x and rays)	coulomb per kilogram	C/kg
absorbed dose rate	gray per second	Gy/s
radiant intensity	watt per steradian	W/sr
radiance	watt per square meter steradian	W/(m2·sr)
catalytic (activity) concentration	katal per cubic meter	kat/m3

The 20 SI prefixes used to form decimal multiples and submultiples of SI units are given in Table 5.

It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names of Table 5 are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.

Because the SI prefixes strictly represent powers of 10, they should not be used to represent powers of 2. Thus, one kilobit, or 1 kbit, is 1000 bit and not 2¹⁰ bit = 1024 bit. To alleviate this ambiguity, prefixes for binary multiples have been adopted by the International Electrotechnical Commission (IEC) for use in information technology.

Units outside the SI

Certain units are not part of the International System of Units, that is, they are outside the SI, but are important and widely used. Consistent with the recommendations of the International Committee for Weights and Measures (CIPM, Comité International des Poids et Mesures), the units in this category that are accepted for use with the SI are given in Table 6.

Table 6.  Units outside the SI that are accepted for use with the SI
Name	Symbol	Value in SI units
minute (time)	min	1 min = 60 s
hour	h	1 h = 60 min = 3600 s
day	d	1 d = 24 h = 86 400 s
degree (angle)	°	1° = ( /180) rad
minute (angle)		1 = (1/60)° = (/10 800) rad
second (angle)		1 = (1/60) = (/648 000) rad
liter	L	1 L = 1 dm3 = 10-3 m3
metric ton (a)	t	1 t = 103 kg
neper	Np	1 Np = 1
bel (b)	B	1 B = (1/2) ln 10 Np (c)
electronvolt (d)	eV	1 eV = 1.602 18 x 10-19 J, approximately
unified atomic mass unit (e)	u	1 u = 1.660 54 x 10-27 kg, approximately
astronomical unit (f)	ua	1 ua = 1.495 98 x 1011 m, approximately
(a) In many countries, this unit is called "tonne.'' (b) The bel is most commonly used with the SI prefix deci: 1 dB = 0.1 B. (c) Although the neper is coherent with SI units and is accepted by the CIPM, it has not been adopted by the General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures) and is thus not an SI unit. (d) The electronvolt is the kinetic energy acquired by an electron passing through a potential difference of 1 V in vacuum. The value must be obtained by experiment, and is therefore not known exactly. (e) The unified atomic mass unit is equal to 1/12 of the mass of an unbound atom of the nuclide 12C, at rest and in its ground state. The value must be obtained by experiment, and is therefore not known exactly. (f) The astronomical unit is a unit of length. Its value is such that, when used to describe the motion of bodies in the solar system, the heliocentric gravitation constant is (0.017 202 098 95)2 ua3·d-2. The value must be obtained by experiment, and is therefore not known exactly.

The liter in Table 6 deserves comment. This unit and its symbol l were adopted by the CIPM in 1879. The alternative symbol for the liter, L, was adopted by the CGPM in 1979 in order to avoid the risk of confusion between the letter l   and the number 1 . Thus, although both  l and L are internationally accepted symbols for the liter, to avoid this risk, the preferred symbol for use is L. Neither a lowercase script letter l nor an uppercase script letter L are approved symbols for the liter.

Other units outside the SI that are currently accepted for use with the SI by NIST are given in Table 7. These units, which are subject to future review, should be defined in relation to the SI in every document in which they are used; their continued use is not encouraged. The CIPM currently accepts the use of all of the units given in Table 7 with the SI except for the curie, roentgen, rad, and rem. Because of the continued wide use of these units in the United States, NIST still accepts their use with the SI.