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- International System of Units (SI)
- SI base units | SI derived units | SI derived units with special names | SI unit multiples
# SI base units

- The International System of Units (SI) is the internationally agreed basis for expressing measurements at all levels of precision and in all areas of science, technology, and human endeavour.
- There are two classes of units in the SI, base units and derived units. The seven base units of the SI provide the reference used to define all the measurement units of the International System.

Base quantity | SI base unit | |
---|---|---|

Name | Symbol | |

length | metre | m |

mass | kilogram | kg |

time, duration | second | s |

electric current | ampere | A |

thermodynamic temperature | kelvin | K |

amount of substance | mole | mol |

luminous intensity | candela | cd |

# SI derived units

- Derived units are expressed algebraically in terms of base units or other derived units. The symbols for derived units are obtained by means of the mathematical operations of multiplication and division. For example, the derived unit for the derived quantity molar mass — mass divided by amount of substance — is the kilogram per mole, symbol kg/mol.

Derived quantity | SI coherent derived unit | |
---|---|---|

Name | Symbol | |

area | square metre | m^{2} |

volume | cubic metre | m^{3} |

speed, velocity | metre per second | m/s |

acceleration | metre per second squared | m/s^{2} |

wavenumber | reciprocal metre | m^{-1} |

density, mass density | kilogram per cubic metre | kg/m^{3} |

surface density | kilogram per square metre | kg/m^{2} |

specific volume | cubic metre per kilogram | m^{3}/kg |

current density | ampere per square metre | A/m^{2} |

magnetic field strength | ampere per metre | A/m |

amount concentration^{(a)}, concentration | mole per cubic metre | mol/m^{3} |

mass concentration | kilogram per cubic metre | kg/m^{3} |

luminance | candela per square metre | cd/m^{2} |

refractive index^{(b)} | one | 1 |

relative permeability^{(b)} | one | 1 |

(a) In the field of clinical chemistry this quantity is also called substance concentration. | ||

(b) These are dimensionless quantities, or quantities of dimension one, and the symbol "1" for the unit (the number "one") is generally omitted in specifying the values of dimensionless quantities. |

# SI Derived units with special names

- Some derived units are given a special name, this being simply a compact form for the expression of combinations of base units that are used frequently. There are 22 special names for units approved for use in the SI.

Derived quantity | SI coherent derived unit ^{(a)} | |||
---|---|---|---|---|

Name | Symbol | Expressed in terms of SI base units | ||

1 | plane angle | radian ^{(b)} | rad | m/m = 1 |

2 | solid angle | steradian ^{(b)} | sr^{(c)} | m^{2}/m^{2}=1 |

3 | frequency | hertz ^{(a)} | Hz | s^{-1} |

4 | force | newton | N | m kg s^{-2} |

5 | pressure, stress | pascal | Pa | N/m^{2} = m^{-1} kg s^{-2} |

6 | energy, work, amount of heat | joule | J | N m = m^{2} kg s^{-2} |

7 | power, radiant flux | watt | W | J/s = m^{2} kg s^{-3} |

8 | electric charge, amount of electricity | coulomb | C | s A |

9 | electric potential difference, electromotive force | volt | V | W/A = m^{2} kg s^{-3} A^{-1} |

10 | capacitance | farad | F | C/V = m^{-2} kg^{-1} s^{4} A^{2} |

11 | electric resistance | ohm | Ω | V/A = m^{2} kg s^{-3} A^{-2} |

12 | electric conductance | siemens | S | A/V = m^{-2} kg^{-1} s^{3} A^{2} |

13 | magnetic flux | weber | Wb | V s = m^{2} kg s^{-2} A^{-1} |

14 | magnetic flux density | tesla | T | Wb/m^{2} = kg s^{-2} A^{-1} |

15 | inductance | henry | H | Wb/A = m^{2} kg s^{-2} A^{-2} |

16 | Celsius temperature | degree Celsius ^{(e)} | °C | K |

17 | luminous flux | lumen | lm | cd sr ^{(c)} = cd |

18 | illuminance | lux | lx | lm/m^{2} = m^{-2} cd |

19 | activity referred to a radionuclide ^{(f)} | becquerel ^{(d)} | Bq | s^{-1} |

20 | absorbed dose, specific energy (imparted), kerma | gray | Gy | J/kg = m^{2} s^{-2} |

21 | dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent | sievert (g) | Sv | J/kg = m^{2} s^{-2} |

22 | catalytic activity | katal | kat | s^{-1} mol |

(a) The SI prefixes may be used with any of the special names and symbols, but when this is done the resulting unit will no longer be coherent. | ||||

(b) The radian and steradian are special names for the number one that may be used to convey information about the quantity concerned. In practice the symbols rad and sr are used where appropriate, but the symbol for the derived unit one is generally omitted in specifying the values of dimensionless quantities. | ||||

(c) In photometry the name steradian and the symbol sr are usually retained in expressions for units. | ||||

(d) The hertz is used only for periodic phenomena, and the becquerel is used only for stochastic processes in activity referred to a radionuclide. | ||||

(e) The degree Celsius is the special name for the kelvin used to express Celsius temperatures. The degree Celsius and the kelvin are equal in size, so that the numerical value of a temperature difference or temperature interval is the same when expressed in either degrees Celsius or in kelvins. | ||||

(f) Activity referred to a radionuclide is sometimes incorrectly called radioactivity. | ||||

(g) The name gray should be used instead of joules per kilogram for the unit of absorbed dose D of ionizing radiation, and the name sievert instead of joules per kilogram for the unit of dose equivalent H, which is the product of the absorbed dose D and the dimensionless quality factor Q. |

# Decimal multiples and sub-multiples of SI units

- A set of multiple and sub-multiple prefixes have been adopted for use with the SI units. They may be used with any of the base units and with any of the derived units with special names. When the prefixes are used, the prefix name and the unit name are combined to form a single word, and similarly the prefix symbol and the unit symbol are written without any space to form a single symbol, which may itself be raised to any power.

Multiples | Submultiples | ||||
---|---|---|---|---|---|

Factor | Name | Symbol | Factor | Name | Symbol |

10^{1} | deca | da | 10^{-1} | deci | d |

10^{2} | hecto | h | 10^{-2} | centi | c |

10^{3} = (10^{3})^{1} | kilo | k | 10^{-3} = (10^{3})^{-1} | milli | m |

10^{6} = (10^{3})^{2} | mega | M | 10^{-6} = (10^{3})^{-2} | micro | μ |

10^{9} = (10^{3})^{3} | giga | G | 10^{-9} = (10^{3})^{-3} | nano | n |

10^{12} = (10^{3})^{4} | tera | T | 10^{-12} = (10^{3})^{-4} | pico | p |

10^{15} = (10^{3})^{5} | peta | P | 10^{-15} = (10^{3})^{-5} | femto | f |

10^{18} = (10^{3})^{6} | exa | E | 10^{-18} = (10^{3})^{-6} | atto | a |

10^{21} = (10^{3})^{7} | zetta | Z | 10^{-21} = (10^{3})^{-7} | zepto | z |

10^{24} = (10^{3})^{8} | yotta | Y | 10^{-24} = (10^{3})^{-8} | yocto | y |

- For example, we may write: kilometre, km; microvolt, μV; 50 V/cm = 50 V (10
^{-2}m)^{-1}= 5000 V/m. - The kilogram, kg, is an exception, because although it is a base unit the name already includes the prefix kilo, for historical reasons. Multiples and sub-multiples of the kilogram are written by combining prefi xes with the gram: thus we write milligram, mg, not microkilogram, μkg.

Sources: *The International System of Units (SI)*, 8th edition, 2006. BIPM - Bureau International des Poids et Mesures / International Bureau of Weights and Measures [http://www.bipm.org/].

*Guide for the Use of the International System of Units (SI)*, NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology, US Dept of Commerce [http://www.nist.gov/].