# IAS: Physics: SI Unit System

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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 |

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 |

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 kg-1 × 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 kg-1 × 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 = 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.