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Mass and related quantities: Unit of mass (kilogram)

Definition agreed by the 26th CGPM (November 2018), implemented 20 May 2019:


    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 6.626 070 15 x 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 DeltanuCs.

    This definition implies the exact relation h = 6.626 070 15 x 10–34 kg m2 s–1. Inverting this relation gives an exact expression for the kilogram in terms of the three defining constants h, DeltanuCs and c:

    which is equal to

    The effect of this definition is to define the unit kg m2 s–1 (the unit of both the physical quantities action and angular momentum). Together with the definitions of the second and the metre this leads to a definition of the unit of mass expressed in terms of the Planck constant h.

    The 1889 definition of the kilogram was simply the mass of the international prototype of the kilogram, an artefact made of platinum-iridium. This was, and still is, kept at the BIPM under the conditions specified by the 1st CGPM when it sanctioned the prototype and declared that "this prototype shall henceforth be considered to be the unit of mass". Forty similar prototypes were made at about the same time and these were all machined and polished to have closely the same mass as the international prototype. At the 1st CGPM (1889), after calibration against the international prototype, most of these "national prototypes" were individually assigned to Member States, and some also to the BIPM. The 3rd CGPM, in a declaration intended to end the ambiguity in common usage concerning the use of the word "weight", confirmed that "the kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram". The complete version of these declarations appears on p. 70 of the above-mentioned CGPM proceedings.

    By the time of the second verification of national prototypes in 1946 it was found that on average the masses of these prototypes were diverging from that of the international prototype. This was confirmed by the third verification carried out from 1989 to 1991, the median difference being about 25 micrograms for the set of original prototypes sanctioned by the 1st CGPM (1889). In order to assure the long-term stability of the unit of mass, to take full advantage of quantum electrical standards and to be of more utility to modern science, a new definition for the kilogram based on the value of a fundamental constant, for which purpose the Planck constant h was chosen, was adopted by Resolution 1 of the 26th CGPM (2018).