Planck constant

Planck constant
Common symbols	${\displaystyle h}$
SI unit	joule per hertz (J/Hz)
In SI base units	kg⋅m2⋅s−1
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-second (J·s)
In SI base units	kg⋅m2⋅s−1
Derivations from other quantities	${\displaystyle \hbar ={\frac {h}{2\pi }}}$
Dimension	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-1}}$
Value	1.054571817...×10−34 J⋅s 6.582119569...×10−16 eV⋅s

The Planck constant, or Planck's constant, denoted by ${\displaystyle h}$, 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 a particle's momentum is equal to the wavenumber of the associated matter wave (the reciprocal of its wavelength) multiplied by the Planck constant.

The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation.^[1] Planck later referred to the constant as the "quantum of action".^[2] 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.^[3] The SI units are defined such that it has the exact value ${\displaystyle h}$ = 6.62607015×10⁻³⁴ J⋅Hz⁻¹‍^[4] when the Planck constant is expressed in SI units.

The closely related reduced Planck constant, denoted ${\textstyle \hbar }$ (h-bar), equal to the Planck constant divided by 2π: ${\textstyle \hbar ={\frac {h}{2\pi }}}$, is commonly used in quantum physics equations. It relates the energy of a photon to its angular frequency, and the linear momentum of a particle to the angular wavenumber of its associated matter wave. As ${\displaystyle h}$ has an exact defined value, the value of ${\textstyle \hbar }$ can be calculated to arbitrary precision: ${\displaystyle \hbar }$ = 1.054571817...×10⁻³⁴ J⋅s.^[5] As a proportionality constant in relationships involving angular quantities, the unit of ${\textstyle \hbar }$ may be given as J·s/rad, with the same numerical value, as the radian is the natural dimensionless unit of angle.