International Systems Units 1

International Systems Units
1. SI Base Units
2. SI Derived Units

1. SI Base Units

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.

Table 1. SI base units

Base quantity	Name	Symbol
	SI base unit
length	meter	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
thermodynamic temperature	kelvin	K
amount of substance	mole	mol
luminous intensity	candela	cd

2. SI Derived Units

Derived quantity	Name	Symbol
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
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

For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in Table 3.

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.

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