

SI Base Units & Derived Units  The data presented here is derived from publications of NIST, so it is in the public domain. However, this HTML implementation is not in the public domain. It is provided to make for easier access.
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
  SI base unit
 Base quantity  Name  Symbol 

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 


For detailed information on the SI base units, see Definitions of the SI base units and their Historical context.
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  m^{2}  volume  cubic meter  m^{3}  speed, velocity  meter per second  m/s  acceleration  meter per second squared  m/s^{2}  wave number  reciprocal meter  m^{1}  mass density  kilogram per cubic meter  kg/m^{3}  specific volume  cubic meter per kilogram  m^{3}/kg  current density  ampere per square meter  A/m^{2}  magnetic field strength  ampere per meter  A/m  amountofsubstance concentration  mole per cubic meter  mol/m^{3}  luminance  candela per square meter  cd/m^{2}  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)}    m^{2}·m^{2 }= 1 ^{(b)}  frequency  hertz  Hz    s^{1}  force  newton  N    m·kg·s^{2}  pressure, stress  pascal  Pa  N/m^{2}  m^{1}·kg·s^{2}  energy, work, quantity of heat  joule  J  N·m  m^{2}·kg·s^{2}  power, radiant flux  watt  W  J/s  m^{2}·kg·s^{3}  electric charge, quantity of electricity  coulomb  C    s·A  electric potential difference, electromotive force  volt  V  W/A  m^{2}·kg·s^{3}·A^{1}  capacitance  farad  F  C/V  m^{2}·kg^{1}·s^{4}·A^{2}  electric resistance  ohm   V/A  m^{2}·kg·s^{3}·A^{2}  electric conductance  siemens  S  A/V  m^{2}·kg^{1}·s^{3}·A^{2}  magnetic flux  weber  Wb  V·s  m^{2}·kg·s^{2}·A^{1}  magnetic flux density  tesla  T  Wb/m^{2}  kg·s^{2}·A^{1}  inductance  henry  H  Wb/A  m^{2}·kg·s^{2}·A^{2}  Celsius temperature  degree Celsius  °C    K  luminous flux  lumen  lm  cd·sr ^{(c)}  m^{2}·m^{2}·cd = cd  illuminance  lux  lx  lm/m^{2}  m^{2}·m^{4}·cd = m^{2}·cd  activity (of a radionuclide)  becquerel  Bq    s^{1}  absorbed dose, specific energy (imparted), kerma  gray  Gy  J/kg  m^{2}·s^{2}  dose equivalent ^{(d)}  sievert  Sv  J/kg  m^{2}·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. 

For a graphical illustration of how the 22 derived units with special names and symbols given in Table 3 are related to the seven SI base units, see relationships among SI units.
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 T_{0 }= 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 T_{0}.
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/s^{2}  heat flux density, irradiance  watt per square meter  W/m^{2}  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/m^{3}  electric field strength  volt per meter  V/m  electric charge density  coulomb per cubic meter  C/m^{3}  electric flux density  coulomb per square meter  C/m^{2}  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/(m^{2}·sr)  catalytic (activity) concentration  katal per cubic meter  kat/m^{3} 
 






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