GATE: Physics: SI Unit System
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 below, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.
Examples of SI derived units
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 
amountofsubstance 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 
SI Derived Units
For ease of understanding and convenience, 22 SI derived units have been given special names and symbols
SI derived units with special names and symbols
Derived quantity  Name  Symbol  Expression in terms of other SI units  Expression in terms of SI base units 
plane angle  radian (a)  rad  N/A  m x m − 1 = 1 (b) 
solid angle  steradian (a)  sr (c)  N/A  m2 × m − 2 = 1 (b) 
frequency  hertz  Hz  N/A  s − 1 
force  newton  N  N/A  m x kg x s − 2 
pressure, stress  pascal  Pa  N/m2  m − 1 x kg x s − 2 
energy, work, quantity of heat  joule  J  N x m  m2 x kg x s − 2 
power, radiant flux  watt  W  J/s  m2 x kg x s − 3 
electric charge, quantity of electricity  coulomb  C  N/A  s x A 
electric potential difference, electromotive force  volt  V  W/A  m2 x kg x s − 3 × A − 1 
capacitance  farad  F  C/V  m − 2 x kg1 × s4 x A2 
electric resistance  ohm  V/A  N/A  m2 x kg x s − 3 × A − 2 
electric conductance  siemens  S  A/V  m − 2 x kg1 × s3 x A2 
For ease of understanding and convenience, 22 SI derived units have been given special names and symbols
Derived quantity  Name  Symbol  Expression in terms of other SI units  Expression in terms of SI base units 
magnetic flux  weber  Wb  V x s  m2 x kg x s − 2 × A − 1 
magnetic flux density  tesla  T  Wb/m2  kg x s − 2 × A − 1 
inductance  henry  H  Wb/A  m2 x kg x s − 2 × A − 2 
Celsius temperature  degree Celsius  ° C  N/A  K 
luminous flux  lumen  lm  cd x sr (c)  m2 × m − 2 x cd = cd 
illuminance  lux  lx  lm/m2  m2 × m − 4 x cd = m − 2 x cd 
activity (of a radionuclide)  becquerel  Bq  N/A  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  N/A  s − 1 x mol 

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.

In practice, the symbols rad and sr are used where appropriate, but the derived unit “1” is generally omitted.

In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.

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 above table 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 = TT0.
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.