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Kilogram

Metric unit of mass

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Set of cast iron metric weights. Since these weights have moveable handles, they are no longer valid for trade.
Coyau · CC BY-SA 3.0

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The kilogram is an SI base unit, defined ultimately in terms of three defining constants of the SI, namely a specific transition frequency of the caesium-133 atom, the speed of light, and the Planck constant. A properly equipped metrology laboratory can calibrate a mass measurement instrument such as a Kibble balance as a primary standard for the kilogram mass.

The kilogram was originally defined in 1795 during the French Revolution as the mass of one litre of water (originally at 0 °C, later changed to the temperature of its maximum density, approximately 4 °C). The current definition of a kilogram agrees with this original definition to within 30 parts per million (0.003%). In 1799, the platinum Kilogramme des Archives replaced it as the standard of mass. In 1889, a cylinder composed of platinum–iridium, the International Prototype of the Kilogram (IPK), became the standard of the unit of mass for the metric system and remained so for 130 years, before the current definition was adopted in 2019.

Definition

The kilogram is defined in terms of three defining constants:

  • a specific atomic transition frequency ΔνCs, which defines the duration of the second,
  • the speed of light in vacuum c, which when combined with the second, defines the length of the metre,
  • and the Planck constant h, which when combined with the metre and second, defines the mass of the kilogram.

The formal definition according to the General Conference on Weights and Measures (CGPM) is:

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.

— CGPM

Defined in term of those units, the kg is formulated as:

kg = ⁠(299792458)2/(6.62607015×10−34)(9192631770)⁠⁠hΔνCs/c2⁠ ≈ (1.4755214×1040)⁠hΔνCs/c2⁠.

This definition is generally consistent with previous definitions: the kilogram remains within 30 parts per million (0.003%) of the mass of one litre of water at the temperature of its maximum density (approximately 4 °C), with the density of water at that temperature very close to 1 kg/L.

Timeline of previous definitions

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