# International System of Units (SI System)

The International System of Units (abbreviated SI) is the world's most widely used system of units. The system consists of a set of units and prefixes.

Note: this SI system is being revised to define the unit of mass in terms of fundamental constants. In addition the definitions ampere and kelvin will revised.

Several countries have only partially adopted the SI System; the United States being notable in this regard. A full list of SI units, a conversion calculator and conversion tables are maintained at:

## Base Units

There are seven base units, from which all other units are derived. Each base unit is dimensionally independent.

Name | Symbol | Quantity |
---|---|---|

meter | m | The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. |

kilogram | kg | The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. |

second | s | The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. |

ampere | A | The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length. |

kelvin | K | The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. |

mole | mol | The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. |

candela | cd | The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. |

## Prefixes

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} | mili | 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 |

## Derived Units

### Mechanical Units

Symbol | SI Unit | Base Units | |
---|---|---|---|

Acceleration | a | m s^{-2} | m s^{-2} |

Angular Frequency | ω | rad s^{-1} | rad s^{-1} |

Angular Momentum | L | kg m² s^{-1} | kg m² s^{-1} |

Area | A, S | m² | m² |

Density | ρ | kg m^{-3} | kg m^{-3} |

Energy | E | J (Joule) | m² kg s^{-2} |

Force | F | N (Newton) | m kg s^{-2} |

Frequency | v, f | Hz (Hertz) | s^{-1} |

Momentum | p | kg m s^{-1} | kg m s^{-1} |

Moment of Inertia | I, J | kg m² | kg m² |

Pressure | P | Pa (Pascal) | m^{-1} kg s^{-2} |

Power | P | W (Watt) | m² kg s^{-3} |

Speed, linear | u | m s^{-1} | m s^{-1} |

Speed, rotational | ω | rad s^{-1} | rad s^{-1} |

Stress | p | Pa | m^{-1} kg s^{-2} |

Surface Tension | λ | N m^{-1} | kg s^{-2} |

Torque | T | N m^{-1} | kg s^{-2} |

Velocity | u, v | m s^{-1} | m s^{-1} |

Viscosity: kinematic | m^{2 s-1 } | m^{2 s-1 } | |

Viscosity: dynamic | μ, v | Pa s | m^{-1} kg s^{-1} |

Work | We | J | m² kg s^{-2} |

### Electrical & Magnetic Units

Symbol | SI Unit | Base Units | |
---|---|---|---|

Admittance | Y | S (Siemens) | m^{-2} kg^{-1} s³ A² |

Capacitance | C | F (Farad) | m^{-2} kg^{-1} s^{4} A² |

Charge | Q | C (Coulomb) | s A |

Charge density, area | ρ | C m^{-3} | m^{-3} s A |

Conductance | G | S (Siemens) | m^{-2} kg^{-1} s³ A² |

Conductivity | σ | S m^{-1} | m^{-3} kg^{-1} s³ A² |

Current (base unit) | I, I | A (Ampere) | A |

Current density | J | A m^{-2} | A m^{-2} |

Electric field strength | E | V m^{-1} | m kg s^{-3} A^{-1} |

Electric flux | ψ | C (coulomb) | s A |

Electric flux density | D | C m^{-2} | m^{-2} s A |

Electromotive force (e.m.f.) | E, e | V | m² kg s^{-3} A^{-1} |

Frequency | F | Hz (Hertz) | s^{-1} |

Impedance | Z | Ω | m² kg s^{-3} A^{-2} |

Inductance, mutual | M | H | m² kg s^{-2} A^{-2} |

Inductance, self | L | H (Henry) | m² kg s^{-2} A^{-2} |

Magnetic field strength | H | A m^{-1} | A m^{-1} |

Magnetic flux | Φ, φ | Wb (Weber) | m² kg s^{-2} A^{-1} |

Magnetic flux density | B | T (Tesla) | kg s^{-2} A^{-1} |

Magnetic flux linkage | ψ | Wb | m² kg s^{-2} A^{-1} |

Magnetomotive force | F | A (ampere) | A |

At (ampere-turns) | A-turns | ||

Permeability, absolute | μ | H m^{-1} | m kg s^{-2} A^{-2} |

Permeability, free space | μ_{o} | H m^{-1} | m kg s^{-2} A^{-2} |

Permeability, relative | μ_{r} | ||

Permittivity, absolute | ε | F m^{-1} | m^{-3} kg^{-1} s^{4} A² |

Permittivity, free space | ε_{o} | F m^{-1} | m^{-3} kg^{-1} s^{4} A² |

Permittivity, relative | ε_{r} | ||

Potential difference | U, V | V (Volt) | m² kg s^{-3} A^{-1} |

Power, active | P | W(Watt) | m² kg s^{-3} |

Power, apparent | S | VA | m² kg s^{-3} |

Power, reactive | Q | var | m² kg s^{-3} |

Reactance | X | Ω | m² kg s^{-3} A^{-2} |

Reactive volt-ampere | Q | var | |

Reluctance | S | A Wb^{-1} | m^{-2} kg^{-1} s² A² |

Resistance | R | Ω (Ohm) | m² kg s^{-3} A^{-2} |

Resistivity | Ω.m | m3 kg s^{-3} A^{-2} | |

Susceptance | B | S (Siemens) | m^{-2} kg^{-1} s³ A² |

Volt-ampere | VA | V A | |

Voltage | U, V | V | m² kg s^{-3} A^{-1} |

Wavelength | λ | m | m |

### Heat Units

Symbol | SI Unit | Base Units | |
---|---|---|---|

Critical pressure | p_{c} | P_{a} (Pascal) | m^{-1} kg s^{-2} |

Critical temperature | T_{c} | K | K |

Critical volume | V_{c} | m³ | m³ |

Cubic expansivity | γ | K^{-1} | K^{-1} |

Heat capacity | C | J K^{-1} | m² kg s^{-1} K^{-1} |

Linear expansivity | α | K^{-1} | K^{-1} |

Molar heat capacity | C_{m} | J mol^{-1 K-1 } | m² kg s^{-2} mol^{-1} K^{-1} |

Quantity of heat | Q | J (Joule) | m² kg s^{-2} |

Specific heat capacity | c_{p}, c_{v} | J kg^{-1} K^{-1} | m² s^{-2} K^{-1} |

Specific latent heat | l | J kg^{-1} | m2 s^{-2} |

Temperature | t, θ, T | K | K |

Thermal conductivity | λ | J m^{-1} s^{-1} K^{-1} | m kg s^{-3} K^{-1} |

W m-^{1} K^{-1 } |

### Photometric Optical Units

Symbol | SI Unit | Base Units | |
---|---|---|---|

Illuminance | E | lx (Lux) | m^{-2} cd sr |

Luminance | L | cd m^{-2} | cd m^{-2} |

Luminous flux | Φ, φ | lm (Lumen) | cd sr |

Luminous efficacy | lm W^{-1} | cd sr m^{-2} kg^{-1} s³ |

### Acoustical Units

Symbol | SI Unit | Base Units | |
---|---|---|---|

Frequency | f | Hz (Hertz) | s^{-1} |

Intensity | I | W m^{-2} | kg s^{-3} |

Power ratio | dB | ||

Reverberation time | s | s |

## Writing Style

symbols– roman upright type, lowercase, un-capitalised (unless derived from a proper name), no full stop, not pluralised

space– a space separates number and the symbol, i.e. 124 kg, 2500 A

derived– units derived are expressed with space, dot and/or solidus (/), i.e. N m, N·m, m/s, m s^{-1}, m·s^{-1}

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