Planck constant, h

The constant that links a photon’s energy to its frequency, E = hf, and sets the scale of every quantum effect. It has been exact since 2019, when fixing its value became the definition of the kilogram.

h = 6.62607015 × 10⁻³⁴ J·s

Exact by definition, so it has no uncertainty at all.

In other units

Values marked … are exact, but their decimals run on, so they stop at ten significant figures instead of being rounded.

Planck constant in SI units and in other units
Quantity	Value
h	6.62607015 × 10⁻³⁴ J·s
h	4.135667696… × 10⁻¹⁵ eV·s
hc	1.986445857… × 10⁻²⁵ J·m
hc	1239.841984… eV·nm

h in eV·s

6.62607015 × 10⁻³⁴ J·s ÷ (1.602176634 × 10⁻¹⁹ J/eV)
= 4.135667696… × 10⁻¹⁵ eV·s

hc in J·m

6.62607015 × 10⁻³⁴ J·s × 299,792,458 m/s
= 1.986445857… × 10⁻²⁵ J·m

hc in eV·nm

hc = 1.986445857… × 10⁻²⁵ J·m
= 1.986445857… × 10⁻²⁵ ÷ (1.602176634 × 10⁻¹⁹ J/eV) × 10⁹ nm/m
= 1239.841984… eV·nm

Divide by a wavelength in nanometres to get a photon’s energy in electronvolts.

Where the value comes from

Until 2019 the Planck constant was measured against the kilogram, by two very different experiments: Kibble balances, which weigh a mass against an electromagnetic force, and counts of the atoms in near-perfect spheres of silicon. Once they agreed closely enough, the 2019 revision fixed h at the value they pointed to.

The dependency then ran the other way. A joule-second is kg·m²/s, so with h, the metre and the second fixed, the kilogram follows, and a Kibble balance now realises a mass from h instead of calibrating h against a metal cylinder.

Which form to use

With energy in joules and frequency in hertz, use 6.626 × 10⁻³⁴ J·s. With energy in electronvolts, use 4.136 × 10⁻¹⁵ eV·s and skip the conversion at the end.

For a photon given by its wavelength, combine h and c once: hc = 1239.84 eV·nm, so a 500 nm photon carries 2.48 eV. The common shortcut of 1240 eV·nm is 0.013 percent high.

The same constant turns a momentum into a wavelength for matter as well as light: the de Broglie wavelength of a particle is λ = h/p.

Common mistakes

Using h with angular frequency. E = hf needs f in hertz; with ω in radians per second the relation is E = ℏω, and mixing the two is an error of exactly 2π.
Leaving the wavelength in nanometres in E = hc/λ while h and c are in SI units, which makes the energy 10⁹ times too small.
Quoting h with an uncertainty. Tables from before 2019 give one, because h was measured then; the value in use now is exact.

Tools that use it

Photon Energy Calculator computes E = hf and E = hc/λ with it.
Wavelength and Frequency Calculator shows the photon energy that goes with each frequency.
Electromagnetic Spectrum Explorer gives the photon energy at every point of the spectrum, E = hf.
Photoelectric Effect Simulator gives each photon its energy hf and draws the stopping potential against frequency, a line of slope h/e.
De Broglie Wavelength Calculator turns a particle’s momentum into its matter wavelength, λ = h/p.
Bohr Model and Hydrogen Spectrum Simulator finds each photon’s frequency from the energy of the jump, f = ΔE/h.

Related constants

Reduced Planck constant, ℏ = 1.054571817… × 10⁻³⁴ J·s
Speed of light in vacuum, c = 299,792,458 m/s
Elementary charge, e = 1.602176634 × 10⁻¹⁹ C
Stefan-Boltzmann constant, σ = 5.670374419… × 10⁻⁸ W/(m²·K⁴)