Kilogram

The kilogram, symbol kg, is the base unit of mass in the International System of Units (SI), equal to 1,000 grams. Since May 20, 2019, its definition has been based on a fixed numerical value of the Planck constant, rather than on the mass of a particular metal object. This makes the unit independent of a single physical artifact while preserving continuity with earlier mass measurements. (nist.gov)

Definition and physical meaning

The kilogram is defined by assigning the Planck constant $h$ the exact value

The joule, symbol J, is the SI unit of energy. Because a joule-second can be expressed in kilograms, meters, and seconds, fixing $h$, together with the definitions of the meter and second, establishes the kilogram. The meter depends on the exact speed of light in vacuum; the second depends on a specified transition frequency of the cesium-133 atom. (bipm.org)

The definition specifies a unit, not a mandatory measuring instrument. A laboratory may realize it through any valid method that links a measured mass to the SI defining constants and provides an appropriate uncertainty evaluation. Although the defining value of $h$ is exact, experimental realizations remain subject to measurement uncertainty. Exact definition therefore does not mean that every measurement in kilograms is exact. (bipm.org)

Mass and weight

The kilogram measures mass, not weight. In scientific usage, weight is a force associated with gravity, commonly expressed as $W=mg$, where $g$ is the local gravitational acceleration. Its SI unit is the newton, equal to kg·m·s⁻². Thus an unchanged object can have the same mass but different weights in different gravitational environments. (nist.gov)

At the conventional standard gravitational acceleration of 9.80665 m·s⁻², a mass of 1 kg has a weight of 9.80665 N. The kilogram-force is a separate, non-SI force unit based on this convention; it must not be confused with the kilogram. Everyday expressions such as “weighs five kilograms” report mass using ordinary language rather than the technical meaning of weight. (nvlpubs.nist.gov)

Historical development

The kilogram originated in the decimal metric system developed in France during the late eighteenth century. Early proposals connected mass standards to the mass of a specified volume of water. A platinum kilogram standard, the Kilogramme des Archives, was established in 1799, translating the water-based scale into a durable reference object. Water remained historically important, but it is not part of the modern kilogram definition. (nist.gov)

In 1889, the General Conference on Weights and Measures adopted the International Prototype of the Kilogram (IPK) as the defining standard. This cylinder consisted of an alloy containing 90 percent platinum and 10 percent iridium. It was kept by the International Bureau of Weights and Measures (BIPM) in Sèvres, France; national prototypes and working standards transmitted its mass scale to other laboratories. (nist.gov)

Comparisons revealed changes in the relative masses of the IPK and its copies. Under the artifact definition, the IPK itself necessarily remained exactly one kilogram: comparisons alone could not establish which object had changed in an absolute sense. This limitation motivated a definition independent of material stability. The conference approved the revised SI on November 16, 2018, with implementation on May 20, 2019. (nist.gov)

Practical realization

One principal realization method uses a Kibble balance, an electromechanical instrument formerly called a watt balance. In one operating mode, an electromagnetic force balances the weight of a test mass. In another, moving the coil through a magnetic field generates a voltage. Combining the measurements eliminates a difficult-to-determine magnetic and geometric factor, giving an idealized relationship

where $v$ is velocity, $U$ voltage, and $I$ current. The two modes are performed separately; the equation compares equivalent mechanical and electrical power. (nist.gov)

Electrical measurements using the Josephson effect and quantum Hall effect connect the result to fundamental constants, including $h$. Before redefinition, a known mass enabled the apparatus to measure the Planck constant. With $h$ now fixed, the relationship is reversed to determine mass. (nist.gov)

A complementary method uses highly characterized spheres enriched in the isotope silicon-28. Measurements of sphere volume and crystal lattice spacing establish the number of atoms, with corrections for surface layers and crystal imperfections. Combining atom counting with atomic-mass relationships permits realization of the kilogram without reference to the IPK. (nist.gov)

Notation and dissemination

For historical reasons, the kilogram is the only SI base unit whose name already contains a prefix. Additional decimal multiples and submultiples are formed by attaching prefixes to gram, not to kilogram. Thus 1 mg equals $10^{-6}$ kg, and the appropriate symbol is “mg,” not “μkg.” The symbol kg is lowercase, unchanged in the plural, and separated from the numerical value by a space: 5 kg, not 5 kgs. (nist.gov)

In metrology, practical access to the kilogram still commonly depends on calibrated physical weights. National laboratories transfer the unit from primary realizations to reference standards, which support further calibrations. This establishes metrological traceability: a documented connection between a measurement and the SI through a calibration chain. Replacing the defining artifact did not eliminate physical mass standards; it changed the foundation to which their assigned values are linked. (bipm.org)