**Image**

"*The SI is an evolving system that reflects the best current practices in measurement *"

Extract from the SI brochure, CIPM's Consultative Committee for Units, 9th edition, 2018

## The SI's base units

The International System of Units (SI, abbreviated from the French "*Système international (des unités)*") is the set of units of measurement consisting of the 7 base units associated with the 7 base quantities. It is completed by derived units and prefixes.

The seven basic quantities are: length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. The base units are the base on which all the units used to quantitatively express the measured quantities are built. Standards and measurement references are materializations of the measured quantity.

To date, their definitions, are as follows:

### The metre

**Symbol** : m

**Quantity** : length

**Definition **: The metre is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m·s^{−1}, where the second is defined in terms of the caesium frequency Δν_{Cs}.

#### Metre derived units

Quantity | Unit | Expressed in SI based units |
---|---|---|

area | square meter | m^{2} |

volume | cubic meter | m^{3} |

plane angle | radian (rad) | m.m^{-1} |

solid angle | steradian (sr) | m^{2}.m^{-2} |

absorbed dose | gray (Gy) | m^{2}.s^{-2} |

### The kilogram

**Symbol** : kg

**Quantity** : mass

**Definition **: The kilogram is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 ×10^{−34} when expressed in the unit J·s, which is equal to kg·m^{2}·s^{−1}, where the metre and the second are defined in terms of c and Δν_{Cs}.

#### Kilogram derived units

Quantity | Unit | Expressed in terms of SI based units |
---|---|---|

force | newton (N) | m.kg.s^{-2} |

pressure | pascal (Pa) | m^{-1}.kg.s^{-2} |

electric potential difference | volt (V) | m^{2}.kg.s^{-}^{3}.A^{-}^{1} |

energy | joule (J) | m^{2}.kg.s^{-2} |

power, radiant flux | watt (W) | m^{2}.kg.s^{-3} |

### The second

**Symbol** : s

**Quantity** : time

**Definition : **The second is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency Δν_{Cs}, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s^{−1}.

#### Second derived units

Quantity | Unit | Expressed in terms of SI based units |
---|---|---|

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

activity refered to a radionucleide | becquerel (Bq) | s^{-1} |

dose equivalent | sievert (Sv) | m ^{2}.s^{-2} |

absorbed dose | gray (Gy) | m^{2}.s^{-2} |

### The ampere

**Symbol** : A

**Quantity** : electric current

**Definition : **The ampere is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10^{−19} when expressed in the unit C, which is equal to A·s, where the second is defined in terms of Δν_{Cs}.

#### Ampere derived units

Quantity | Unit | Expressed in terms of SI based units |
---|---|---|

electric charge | coulomb (C) | s.A |

electric potential difference | volt (V) | m^{2}.kg.s^{−3}.A^{−1} |

electric resistance | ohm (Ω) | m^{2}.kg.s^{−3}.A^{−2} |

capacitance | farad (F) | m^{−2}.kg^{−1}.s^{4}.A^{2} |

inductance | henry (H) | m^{2}.kg.s^{−2}.A^{−2} |

magnetic flux density | tesla (T) | kg.s^{−2}.A^{−1} |

### The kelvin

**Symbol** : K

**Quantity** : thermodynamic temperature

**Definition : **The kelvin is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10^{−23 }when expressed in the unit J·K^{−1}, which is equal to kg·m^{2}·s^{−2}·K^{−1}, where the kilogram, metre and second are defined in terms of h, c and Δν_{Cs}.

#### Kelvin derived units

Quantity | Unit | Expressed in terms of SI based units |
---|---|---|

Celsius temperature t/°C |
degré Celsius (°C) |
K T/K – 273,15 |

thermal conductivity | watt per metre kelvin | m.kg.s^{-3}.K^{-1} |

surface thermal resistance | square-metre kelvin per watt | kg^{-1}.s^{3}.K |

heat capacity | joule per kelvin | kg.m^{2}.s^{-2}.K^{-1} |

### The mole

**Symbol** : mol

**Quantity** : amount of substance

**Definition : **The mole is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 10^{23} elementary entities. This number is the fixed numerical value of the Avogadro constant, N_{A}, when expressed in the unit mol^{-1} and is called the Avogadro number.

#### Mole derived units

Quantity | Unit | Expressed in terms of SI based units |
---|---|---|

molar concentration | mole per cubic metre |
mol.m |

catalytic activity | katal (kat) | mol.s^{-1} |

### The candela

**Symbol** : cd

**Quantity** : luminous intensity

**Definition : **The candela is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10^{12} Hz, K_{cd}, to be 683 when expressed in the unit lm·W^{−1}, which is equal to cd·sr·W^{−1}, or cd·sr·kg^{−1}·m^{−2}·s^{3}, where the kilogram, metre and second are defined in terms of h, c and Δν_{Cs}.

#### Candela derived units

Quantity | Unit | Expressed in terms of SI based units |
---|---|---|

luminous flux | lumen (lm) | cd^{.}sr = m^{2}.m^{-2}.cd |

illuminance | lux (lx) | lm^{.}m^{-2} = m^{-2}.cd |

## Multiples and sub-multiples

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

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

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

10^{3} |
kilo | k | 10^{-3} |
milli | m |

10^{6} |
mega | M | 10^{-6} |
micro | µ |

10^{9} |
giga | G | 10^{-9} |
nano | n |

10^{12} |
tera | T | 10^{-12} |
pico | p |

10^{15} |
peta | P | 10^{-15} |
femto | f |

10^{18} |
exa | E | 10^{-18} |
atto | a |

10^{21} |
zetta | Z | 10^{-21} |
zepto | z |

10^{24} |
yotta | Y | 10^{-24} |
yocto | y |