# Base units Terms Explained

Derived units are formed by powers, products or quotients of the base units and are unlimited in number; Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and distance which, in SI, has the dimensions metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.

Some derived units have special names, for example the unit of force is the newton. Coherent units (such as those in SI) are derived units that contain no numerical factor other than 1: in the example above, *one* newton is the force required to accelerate a mass of *one* kilogram by *one* metre per second squared. Since the SI units of mass and acceleration are kg and m⋅s^{−2}respectively and *F* ∝ *m* × *a*, the units of force (and hence of newtons) is formed by multiplication to give kg⋅m⋅s^{−2}. Since the newton is part of a coherent set of units, the constant of proportionality is 1.

Name | Symbol | Quantity | Expressed in terms of other SI units | Expressed in terms of SI base units |
---|---|---|---|---|

radian | rad | angle | 1 | m/m |

steradian | sr | solid angle | 1 | m^{2}/m^{2} |

hertz | Hz | frequency | s^{−1} | |

newton | N | force, weight | kg⋅m⋅s^{−2} | |

pascal | Pa | pressure, stress | N/m^{2} | kg⋅m^{−1}⋅s^{−2} |

joule | J | energy, work, heat | N⋅m | kg⋅m^{2}⋅s^{−2} |

watt | W | power, radiant flux | J/s | kg⋅m^{2}⋅s^{−3} |

coulomb | C | electric charge or quantity of electricity | s⋅A | |

volt | V | voltage (electrical potential difference), electromotive force | W/A | kg⋅m^{2}⋅s^{−3}⋅A^{−1} |

farad | F | electric capacitance | C/V | kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} |

ohm | Ω | electric resistance, impedance, reactance | V/A | kg⋅m^{2}⋅s^{−3}⋅A^{−2} |

siemens | S | electrical conductance | A/V | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |

weber | Wb | magnetic flux | V⋅s | kg⋅m^{2}⋅s^{−2}⋅A^{−1} |

tesla | T | magnetic field strength | Wb/m^{2} | kg⋅s^{−2}⋅A^{−1} |

henry | H | inductance | Wb/A | kg⋅m^{2}⋅s^{−2}⋅A^{−2} |

degree Celsius | °C | temperature relative to 273.15 K | K | |

lumen | lm | luminous flux | cd⋅sr | cd |

lux | lx | illuminance | lm/m^{2} | m^{−2}⋅cd |

becquerel | Bq | radioactivity (decays per unit time) | s^{−1} | |

gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |

sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |

katal | kat | catalytic activity | s^{−1}⋅mol | |

Notes 1. The radian and steradian, once given special status, are now considered dimensionless derived units.2. The ordering of this table is such that any derived unit is based only on base units or derived units that precede it in the table. |