Version: 1.0 Beta, last update: 2024-02-14


The kilogram, symbol $\rm{kg}$, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant, ${h}$, to be $6.626\:070\:15 \times 10^{-34}$ when expressed in the unit ${\rm{J}}\ {\rm{s}}$, which is equal to ${\rm{kg}}\ {\rm{m}}^{2}\ {\rm{s}}^{-1}$, where the metre and the second are defined in terms of $c$ and $\Delta\nu_{\rm{Cs}}$.

This definition is valid from 2019-05-20
Unit kilogram
Symbol kg
Quantity mass
Defining Constant Planck constant
Defining Resolution
CGPM Resolution 1 (2018)
Unit Type SI base unit
Defining Equation $$1\;{\rm{kg}} = \left(\frac{{h}}{6.626\:070\:15 \times 10^{-34}}\right) {\rm{m}}^{-2}\;{\rm{s}}$$
  1. This definition implies the exact relation ${{h}} = {6.626\:070\:15 \times 10^{-34}}\ {{\rm{kg}}\ {\rm{m}}^{2}\ {\rm{s}}^{-1}}$. Inverting this relation gives an exact expression for the kilogram in terms of the three defining constants ${h}$, $\Delta\nu_{\rm{Cs}}$ and $c$: $$1\;{\rm{kg}} = \left(\frac{{h}}{6.626\:070\:15 \times 10^{-34}}\right)\ {{\rm{m}}^{-2}\ {\rm{s}}}$$ which is equal to $$1\;{\rm{kg}} = \frac{(299\:792\:458)^{2}}{(6.626\:070\:15 \times 10^{-34})({9\:192\:631\:770})} \frac{{h}\,\Delta\nu_{\rm{Cs}}}{c^{2}} \approx 1.475\:5214 \times 10^{40} \frac{{h}\,\Delta\nu_{\rm{Cs}}}{c^{2}}$$.
  2. The effect of this definition is to define the unit ${\rm{kg}}\ {\rm{m}}^{2}\ {{\rm{s}}^{-1}}$ (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 ${h}$.
  3. The previous definition of the kilogram fixed the value of the mass of the international prototype of the kilogram, ${m(\mathcal{K})}$, to be equal to one kilogram exactly and the value of the Planck constant ${h}$ had to be determined by experiment. The present definition fixes the numerical value of ${h}$ exactly and the mass of the prototype has now to be determined by experiment.
  4. The number chosen for the numerical value of the Planck constant in this definition is such that at the time of its adoption, the kilogram was equal to the mass of the international prototype, ${{m(\mathcal{K})}} = 1\ {\rm{kg}}$, with a relative standard uncertainty of $1 \times 10^{-8}$, which was the standard uncertainty of the combined best estimates of the value of the Planck constant at that time.
  5. Note that with the present definition, primary realizations can be established, in principle, at any point in the mass scale.