# MKS system of units

The **MKS system of units** is a physical system of measurement that uses the metre, kilogram, and second (MKS) as base units. It forms the base of the International System of Units (SI), though SI has since been redefined by different fundamental constants.

## History

By the 19th century, there was a demand by scientists to define a coherent system of units.[1] A coherent system of units is a system of units where all units are directly derived from a set of base units, without the need of any conversion factors. The United States customary units are an example of a non-coherent set of units.[2] In 1874, the British Association for the Advancement of Science (BAAS) introduced the CGS system, a coherent system based on the centimetre, gram and second. These units were inconvenient for electromagnetic applications, since electromagnetic units derived from these did not correspond to the commonly used *practical units*, such as the volt, ampere and ohm.[1][3] After the Metre Convention of 1875, work started on international prototypes for the kilogram and the metre, which were formally sanctioned by the General Conference on Weights and Measures (CGPM) in 1889, thus formalizing the MKS system by using the kilogram and metre as base units.[4]

In 1901, Giovanni Giorgi proposed to the *Associazione elettrotecnica italiana* (AEI) that the MKS system, extended with a fourth unit to be taken from the practical units of electromagnetism, such as the volt, ohm or ampere, be used to create a coherent system using practical units.[5][3]
This system was strongly promoted by electrical engineer George A. Campbell.[6] The CGS and MKS systems were both widely used in the 20th century, with the MKS system being primarily used in practical areas, such as commerce and engineering.[1] The International Electrotechnical Commission (IEC) adopted Giorgi's proposal as the *M.K.S. System of Giorgi* in 1935 without specifying which electromagnetic unit would be the fourth base unit.[7] In 1939, the Consultative Committee for Electricity (CCE) recommended the adoption of Giorgi's proposal, using the ampere as the fourth base unit. This was subsequently approved by the CGPM in 1954.

The **rmks** system (**rationalized metre–kilogram–second**) combines MKS with rationalization of electromagnetic equations.

The MKS system with the ampere as a fourth base unit, is sometimes referred to as the **MKSA system**. This system was extended by adding the kelvin and candela as base units in 1960, thus forming the International System of Units. The mole was added as a seventh base unit in 1971.[3][4]

## Derived units

#### Mechanical units

Quantity | Quantity symbol | Unit | Unit symbol | MKS equivalent |
---|---|---|---|---|

frequency | f | hertz | Hz | s^{−1} |

force | F | newton | N | kg⋅m⋅s^{−2} |

pressure | p | pascal | Pa | kg⋅m^{−1}⋅s^{−2} |

energy | E | joule | J | kg⋅m^{2}⋅s^{−2} |

power | P | watt | W | kg⋅m^{2}⋅s^{−3} |

#### Electromagnetic units

Quantity | Quantity symbol | Unit | Unit symbol | MKSA equivalent |
---|---|---|---|---|

electric charge | Q | coulomb | C | s⋅A |

voltage | U | volt | V | kg⋅m^{2}⋅s^{−3}⋅A^{−1} |

electric capacitance | C | farad | F | kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} |

electric resistance | R | ohm | Ω | kg⋅m^{2}⋅s^{−3}⋅A^{−2} |

electric conductance | G | siemens | S | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |

magnetic flux | Φ_{B} | weber | Wb | kg⋅m^{2}⋅s^{−2}⋅A^{−1} |

magnetic flux density | B | tesla | T | kg⋅s^{−2}⋅A^{−1} |

electric inductance | I | henry | H | kg⋅m^{2}⋅s^{−2}⋅A^{−2} |

## See also

- Centimeter–gram–second system (CGS)
- Foot–pound–second system (FPS)
- List of metric units
- Meter–tonne–second system (MTS)
- Vacuum permeability § Systems of units and historical origin of value of
*μ*_{0} - Vacuum permittivity § Rationalization of units

## References

- Rowlet, Russ (May 2, 2018). "Units: CGS and MKS". University of North Carolina at Chapel Hill. Retrieved May 4, 2021.
- "What makes a system of units coherent?". Sizes, Inc. 2003. Retrieved May 4, 2021.
- "Brief history of the SI". National Institute of Standards and Technology. December 12, 2017. Retrieved May 4, 2021.
- "The International System of Units (SI)" (PDF). Bureau International des Poids et Mesures. 2006. Retrieved May 4, 2021.
- Giovanni Giorgi (1901), "Unità Razionali de Elettromagnetismo", in
*Atti dell' Associazione Elettrotecnica Italiana*. - Brainerd, John G. (1970). "Some Unanswered Questions".
*Technology and Culture*. JSTOR.**11**(4): 601–603. doi:10.2307/3102695. ISSN 0040-165X. JSTOR 3102695. - Arthur E. Kennelly (1935), "Adoption of the Metre–Kilogram-Mass–Second (M.K.S.) Absolute System of Practical Units by the International Electrotechnical Commission (I.E.C.), Bruxelles, June, 1935",
*Proceedings of the National Academy of Sciences of the United States of America*,**21**(10): 579–583, Bibcode:1935PNAS...21..579K, doi:10.1073/pnas.21.10.579, PMC 1076662, PMID 16577693