# International System of Units (SI)

The international system of units is the most widely used system of measurement, and is the modern form of the metric system. At its core, this system is built on seven primary units. This system specifies twenty prefixes to the unit symbols and name to state multiples and fractions of each unit.

The international system of units was introduced to the public in 1960 as a result to earlier research that began in 1948. SI is based on the meter-kilogram second system of units (MKS). SI was created to evolve as time progressed forward. It was intended that units and prefixes were to be created and unit definitions to be modified, on an international level, as the technology of the measuring tools we use on a daily basis continues to become more advanced and more precise. An excellent example of this evolving system would be the 24^{th} and 25^{th} General Conferences on Weights and Measures (CGPM) that took place in 2011 and 2014 where a proposal was introduced to alter the definition of “kilogram”. This was brought up because some began to believe that a kilogram was an invariant of nature rather than a measurement of mass.

As mentioned in the previous section, there was an incredible lack of coordination amongst the various professions in a number of areas across the world. To create unity, SI was born. The CGPM, established by the Meter Convention of 1875, took on the mission of bringing together numerous international organizations to agree upon the definitions and standards of the proposed new system. They were also brought together to agree upon the rules about how this new system would be presented and accepted around the world.

In theory, SI can be used for any type of physical measurement. Despite this, the fact could not be ignored that non-SI units of measurement would still appear in the technical, scientific and commercial literature for the foreseeable future. Furthermore, certain units of measurement have been engrained so deeply in history and certain cultures that they will continue to be used for a long time to come. The CIPM has categorized these units and incorporated them into the SI Brochure.

Below is the international system of 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 |