The Kilogram without a Prototype: How a Kibble Balance Determines Mass

A Definition Is Not Yet a Balance

The International System of Units defines the kilogram through the fixed numerical value of the Planck constant. Together with the definitions of the metre and the second, this establishes a unit of mass that is not tied to a particular object remaining unchanged. This definition is exact. A real experiment that determines a mass in kilograms, by contrast, remains subject to uncertainties. This distinction is essential: constants of nature provide the common foundation, while measuring instruments establish the practical connection to specific objects. A Kibble balance is one such realisation. It uses electromagnetic forces and measurements of motion to relate an unknown mass to electrical quantities. This does not make it an ordinary kitchen scale with a better display, but a carefully controlled metrological apparatus with several separate measurement steps.

Two Operating Modes Circumvent a Difficult Problem

In weighing mode, the gravitational force on an object acts on a coil. An electric current generates an opposing force in the magnetic field until equilibrium is reached. The current alone, however, would not allow the mass to be determined accurately enough, because the effective coil geometry and the magnetic field would have to be known. A second operating mode therefore follows: the coil moves through the same field, and the voltage induced in it is measured along with its velocity. Combining the two measurements allows the shared geometrical and magnetic factor to be eliminated. Electrical quantities are linked to quantum-based references in this process. The frequently used description of this as a comparison of mechanical and electrical power is helpful, but must not obscure the fact that the crucial quantities are recorded in separate operating states and must be carefully matched.

Why the Location Is Measured Too

A Kibble balance initially compares forces. To derive a mass from them, the local acceleration due to gravity must also be known. There are also influences from alignment, vibrations, temperature changes and the properties of the object under investigation. Even an exact constant of nature does not spare researchers this work. The quality of a realisation is therefore demonstrated through documented corrections, independent comparisons and a transparent uncertainty calculation. The physical principle linking mass to electrical measurements is established. Improvements to individual apparatus, by contrast, are experimental achievements whose limits must be examined afresh in each case. In everyday life, such references reach less elaborate scales through calibration chains. The practical benefit therefore does not lie in having a Kibble balance everywhere, but in a shared, reproducible foundation for reliable mass measurements.

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