Table 3. SI derived units with | ||||

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} |

**Continue to **SI prefixes