Other meanings of Planck constant
Physics constant
The Planck constant is a fundamental physical constant relating photon energy to frequency, named after Max Planck. It sets the scale at which quantum effects become significant and is central to modern definitions of mass, energy, frequency, and electromagnetic radiation.
The Planck constant connects the energy of a photon with its frequency through E = hν. Here, E is energy, ν is frequency, and h is the Planck constant. Its SI unit, the joule-second, is equivalent to kilogram metre squared per second. The constant also relates a particle’s momentum to its wavelength through the de Broglie relation p = h/λ, showing why wave-like behavior appears for electrons and other microscopic objects. Its small numerical value explains why quantum effects are usually imperceptible in everyday mechanics, while remaining decisive in atomic, molecular, solid-state, and nuclear physics.1
The reduced Planck constant, written ℏ or “h-bar,” is h/(2π). It is especially convenient for rotational motion, angular momentum, wave functions, and quantum field theory.
The constant emerged from Max Planck’s 1900 analysis of black-body radiation. Planck introduced discrete energy elements to reproduce the observed spectrum, initially treating quantization as a formal device; the idea became a foundation of quantum theory when Albert Einstein applied it to the photoelectric effect.2 Subsequent work by Niels Bohr, Louis de Broglie, Werner Heisenberg, Erwin Schrödinger, and others extended quantization to atoms, matter waves, and mechanics.
For much of the twentieth century, the value of h was measured experimentally through relationships involving electrical standards, spectroscopy, and precision balances. The 2019 revision of the International System of Units assigned the Planck constant an exact value, making it one of the constants that defines the SI rather than a quantity whose uncertainty is continually adjusted.3
The exact value of the Planck constant is 6.62607015 × 10−34 joule seconds. This fixed value helps define the kilogram: a precise realization of the kilogram can be linked to mechanical power through a Kibble balance, which compares mechanical and electrical quantities. Electrical measurements in that balance depend on quantum electrical phenomena, including the Josephson and quantum Hall effects.3
Fixing h does not mean that every laboratory directly weighs an object by counting Planck constants. Instead, it provides a chain of definitions and measurements connecting mass to frequency, voltage, current, and time. Because the second is defined using the cesium-133 atomic transition and the metre is tied to the speed of light, these linked constants support highly reproducible measurements across national metrology institutes.4
The Planck constant is more than a conversion factor for light: it establishes the characteristic scale of action, the product of energy and time or momentum and distance. Quantization is therefore expressed in many apparently different settings, from atomic angular momentum to the spacing of energy levels in solids. The uncertainty principle can be written using ℏ, as in ΔxΔp ≥ ℏ/2, although the constant itself does not impose a simple universal minimum uncertainty for every pair of measurements.
A related historical quantity, the Planck length, is constructed from h or more precisely ℏ, the speed of light, and the gravitational constant. It is a dimensional scale used in theories of quantum gravity, not a directly observed “smallest possible length.” The same caution applies to the Planck time and Planck energy: they are natural units, not automatically confirmed physical boundaries.5
The symbol h denotes the Planck constant; ℏ denotes the reduced Planck constant h/(2π).
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