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


Table 1: SI base units

Quantity Name Symbol   Definition

  meter m   The meter 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.
Unit of time  second s   periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Unit of
electric current  
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 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.
Unit of
thermodynamic  
temperature
kelvin K   The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Unit of
amount of
substance
mole  mol   1.  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
       2. 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.
Unit of
luminous
intensity
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.

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 2.  Examples of SI derived units

  SI derived unit
Derived quantity Name Symbol
area square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared   m/s2
wave number reciprocal meter m-1
mass density kilogram per cubic meter kg/m3
specific volume cubic meter per kilogram m3/kg
current density ampere per square meter A/m2
magnetic field
strength
ampere per meter A/m
amount-of-substance
concentration
mole per cubic meter mol/m3
luminance candela per square meter cd/m2
mass fraction kilogram per kilogram, which may be represented by the number 1 kg/kg = 1


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 Omega 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.

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 gamma 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.


Table 5.  SI prefixes
Factor Name  Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
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
10-21 zepto z
10-24 yocto y

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.

Example 1: 10-6 kg = 1 mg (one milligram), but not 10-6 kg = 1 µkg (one microkilogram)
Example 2: Consider the earlier example of the height of the Washington Monument. We may write hW = 169 000 mm = 16 900 cm = 169 m = 0.169 km using the millimeter (SI prefix milli, symbol m), centimeter (SI prefix centi, symbol c), or kilometer (SI prefix kilo, symbol k).

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° = ( pi/180) rad
minute (angle) ' 1' = (1/60)° = (pi/10 800) rad
second (angle) '' 1'' = (1/60)' = (pi/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.


Table 7.  Other units outside the SI that are currently accepted for use with the SI, subject to further review
Name Symbol    Value in SI units
nautical mile   1 nautical mile = 1852 m
knot   1 nautical mile per hour = (1852/3600) m/s
are a 1 a = 1 dam2 = 102 m2
hectare  ha 1 ha = 1 hm2 = 104 m2
bar bar 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa
ångström Å 1 Å = 0.1 nm = 10-10 m
barn b 1 b = 100 fm2 = 10-28 m2
curie Ci 1 Ci = 3.7 x 1010 Bq
roentgen R 1 R = 2.58 x 10-4 C/kg
rad rad 1 rad = 1 cGy = 10-2 Gy
rem rem 1 rem = 1 cSv = 10-2 Sv