Planck constant

The Planck constant, or Planck's constant, denoted by ${\textstyle h}$, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.

Planck constant
Common symbols	${\displaystyle h}$
SI unit	joule per hertz (joule seconds)
Other units	electronvolt per hertz (electronvolt seconds)
Dimension	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-1}}$
Value	6.62607015×10−34 J⋅Hz−1 4.135667696...×10−15 eV⋅Hz−1

Reduced Planck constant
Common symbols	${\displaystyle \hbar }$
SI unit	joule-seconds
Other units	electronvolt-seconds
Derivations from other quantities	${\displaystyle \hbar {=}h/(2\pi )}$
Dimension	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-1}}$
Value	1.054571817...×10−34 J⋅s 6.582119569...×10−16 eV⋅s

The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation. Planck later referred to the constant as the "quantum of action". In 1905, Albert Einstein associated the "quantum" or minimal element of the energy to the electromagnetic wave itself. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

In metrology, the Planck constant is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value ${\displaystyle h}$ = 6.62607015×10⁻³⁴ J⋅Hz⁻¹. It is often used with units of electronvolt (eV), which corresponds to the SI unit per elementary charge.