Kilogram: How the Planck constant Defines Mass
The kilogram is defined using a fixed numerical value of the Planck constant. Its modern definition also depends on the second and the meter, which are defined through a specific atomic transition frequency and the speed of light. This makes the unit part of a linked system of physical constants rather than a mass assigned to a single metal cylinder. The kilogram is the base unit of mass in the International System of Units, abbreviated SI. Its symbol is kg, and it equals one thousand grams. A properly equipped metrology laboratory can calibrate a mass-measurement instrument as a primary standard.
The formal definition fixes the Planck constant at 6.62607015 times ten to the power of negative thirty-four when expressed in joule-seconds. That unit can also be expressed through kilograms, meters, and seconds. The atomic transition frequency of cesium defines the duration of the second. The speed of light in vacuum, combined with the second, defines the meter. The remaining relationship establishes the kilogram. This arrangement preserves continuity with earlier definitions: the kilogram remains within 30 parts per million of the mass of a liter of water at its maximum density, which occurs at approximately 4 degrees Celsius.
Water had been central to the earliest definitions. In 1793, the grave, a precursor to the kilogram, was defined as the mass of a liter of water. The gram was provisionally defined in 1795 as the mass of a cubic centimeter of water at the melting point of ice. The kilogram's original definition belonged to the French Revolution, with the reference temperature later changed to the point of maximum water density. In 1799, the platinum Kilogramme des Archives became the mass standard. Its mass matched a cubic decimeter of water at maximum density, giving the unit a physical prototype in place of the earlier water reference.
The next metal standard followed the Meter Convention, signed in 1875. The International Prototype of the Kilogram was produced in 1879 and adopted in 1889. This platinum-iridium cylinder remained the standard for 130 years, until the modern definition took effect in 2019. Evidence accumulated over time that its mass and the masses of its replicas were changing. Since manufacture late in the nineteenth century, the prototype had diverged from its replicas by approximately 50 micrograms. That divergence motivated competing efforts to develop sufficiently precise measurement technology for a definition tied directly to fundamental physical constants.
The meter offered an earlier example of the same broad transition. It had once been defined with reference to a platinum-iridium bar bearing two marks. In 1960, its definition moved to the wavelength of a particular krypton light emission and later to the speed of light. The resulting standard could be reproduced independently in different laboratories by following a written specification. In 2005, the International Committee for Weights and Measures recommended a comparable change for the kilogram. By October 2010, the committee voted to submit a resolution expressing an intention to define mass through the Planck constant together with other physical constants.
That resolution was accepted by the General Conference on Weights and Measures in October 2011 and discussed further in 2014. Significant progress had been made, but the data were not yet considered robust enough for adoption. Work continued toward the meeting scheduled for 2018. The revision was approved in November 2018, and the definition took effect on May 20, 2019. In principle, any apparatus capable of delineating the kilogram through the Planck constant can be used if it has sufficient precision, accuracy, and stability. A Kibble balance provides one way of doing so, linking the new definition to practical mass standards.
A Kibble balance had previously been used to measure the Planck constant in terms of the metal prototype. Under the revised definition, it can calibrate secondary standard weights for practical use. Other approaches explored over many years included techniques for reproducibly making new kilogram-mass prototypes using material properties traceable to physical constants. Another group of approaches measured the acceleration or weight of adjusted test masses and expressed those measurements in electrical terms. The latter depended on converting a weight measurement into mass. That conversion requires a precise measurement of the strength of gravity in the laboratory, a task known as gravimetry.
The kilogram's name introduces a separate practical feature of SI notation. It is the only base unit whose name already includes an SI prefix, kilo, meaning one thousand. Because a unit cannot have multiple prefixes, smaller and larger prefixed forms are built from gram instead. A millionth of a kilogram is a milligram, rather than a microkilogram. The shortened word kilo is common in informal use, while scientific and technical SI usage avoids it. The SI Brochure also bars abbreviations of unit names or symbols. For smaller quantities, the distinction between milligrams and micrograms has particular consequences: confusion between them has caused serious medication errors.