Measurement Fundamentals

# International System of Units (SI)

The principle behind the International System of Units is to provide the same values for measurements such as length, weight, and time no matter where in the world measurement is performed. The units used in this system are referred to as “SI units.” The system was established at the 1960 General Conferences on Weights and Measures (CGPM). The abbreviation “SI” stands for “Le Système International d'Unités.”

The International System of Units comprises the following three categories.

- Base units
- Supplementary units
- Derived units

## Base Units

Amount | Unit name | Unit symbol | Definition |
---|---|---|---|

Length | Meter | m | The distance traveled by light in a vacuum in 1/299792458 second. |

Weight | Kilogram | kg | This is the unit for weight. The mass of the international prototype kilogram. |

Time | Second | s | The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. |

Current | Ampere | A | The 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 2×10^{-7} newtons per meter of length. |

Thermodynamic temperature | Kelvin | K | 1/273.16 of the thermodynamic temperature of the triple point of water. |

Substance amount | Mole | mol | The amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. (Limited to objects with clarified composition.) Elementary entities are subatomic particles that compose matter and energy. |

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

## Supplementary Units

Amount | Unit name | Unit symbol | Definition |
---|---|---|---|

Plane angle | Radian | rad | Radian describes the plane angle subtended by an arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. |

Solid angle | Steradian | sr | A steradian is a solid angle at the center of a sphere subtending a section on the surface equal in area to the square of the radius of the sphere. |

## Derived Units

Derived units are a combination of base units and supplementary units and the mathematical symbols of multiplication and division.

Amount | Unit name | Unit symbol |
---|---|---|

Area | Square meter | m^{2} |

Volume | Cubic meter | m^{3} |

Speed | Meter per second | m/s |

Acceleration | Meter per second squared | m/s^{2} |

Wavenumber | Reciprocal meter | m^{-1} |

Density | Kilogram per cubic meter | kg/m^{3} |

Current density | Ampere per square meter | A/m^{2} |

Magnetic field strength | Ampere per meter | A/m |

Concentration (of amount of substance) | Mole per cubic meter | mol/m^{3} |

Specific volume | Cubic meter per kilogram | m^{3}/kg |

Luminance | Candela per square meter | cd/m^{2} |

Some derived units are given unique names.

Amount | Unit name | Unit symbol | Composition |
---|---|---|---|

Frequency | Hertz | Hz | 1Hz=1s^{-1} |

Force | Newton | N | 1N=1kg･m/s^{2} |

Pressure, stress | Pascal | Pa | 1Pa=1N/m^{2} |

Energy, work, amount of heat | Joule | J | 1J=1N･m |

Power, radiant flux | Watt | W | W=1J/s |

Electric charge, amount of electricity | Coulomb | C | 1C=1A･s |

Electric potential/electric potential difference, voltage, electromotive force | Volt | V | 1V=1J/C |

Resistance (electrical) | Ohm | Ω | 1Ω=1V/A |

Conductance (electrical) | Siemens | S | 1S=1Ω^{-1} |

Magnetic | Weber | Wb | 1Wb=1V･s |

Magnetic flux density, magnetic induction | Tesla | T | 1T=1Wb/m^{2} |

Inductance | Henry | H | 1H=1Wb/A |

Celsius temperature | Degree Celsius | ℃ | 1t=T-To |

Luminous flux | Lumen | lm | 1lm=1cd･sr |

Illuminance | Lux | lx | 1lx=1lm/m^{2} |

## Reference Information

SI unit prefixes indicating integer powers of ten

Factor | Prefix | Symbol | Factor | Prefix | Symbol |
---|---|---|---|---|---|

10^{18} |
exa | E | 10^{-1} |
deci | d |

10^{15} |
peta | P | 10^{-2} |
centi | c |

10^{12} |
tera | T | 10^{-3} |
milli | m |

10^{9} |
giga | G | 10^{-6} |
micro | µ |

10^{6} |
mega | M | 10^{-9} |
nano | n |

10^{3} |
kilo | k | 10^{-12} |
pico | p |

10^{2} |
hecto | h | 10^{-15} |
femto | f |

10 | deka | da | 10^{-18} |
atto | a |

Non-SI units

Amount | Unit name | Unit symbol | Definition |
---|---|---|---|

Time | Minute | min | 1min=60s |

Hour | h | 1h=60min | |

Day | d | 1d=24h | |

Plane angle | Degree | ° | 1°= (π/180) rad |

Minute | ′ | 1′= (1/60) ° | |

Second | ″ | 1″= (1/60) ′ | |

Volume | Liter | l, L | 1l=1dm^{3} |

Weight | Metric ton | t | 1t=10^{3}kg |