Planck constant

The Planck constant (denoted h) is a fundamental physical constant from quantum mechanics, equal to 6.62607015 × 10⁻³⁴ joule-seconds exactly. It appears in the energy of a photon (E = hν), the Heisenberg uncertainty principle (Δx · Δp ≥ ℏ/2, where ℏ = h/2π is the reduced Planck constant), and the de Broglie wavelength (λ = h/p) that links any particle’s momentum to a wave description.

Max Planck introduced the constant in 1900 to explain blackbody radiation — the spectrum of light emitted by a heated object. Classical physics predicted infinite energy at short wavelengths (the “ultraviolet catastrophe”); Planck’s assumption that energy comes in discrete packets E = nhν resolved the divergence and inadvertently launched quantum mechanics. Einstein extended the idea in 1905 to explain the photoelectric effect, for which he received the 1921 Nobel Prize.

Since May 2019, the Planck constant defines the kilogram in the SI system. The 2019 SI redefinition moved several base units (kilogram, ampere, kelvin, mole) from dependence on physical artefacts to dependence on fundamental constants. Before 2019, the kilogram was defined by a platinum-iridium cylinder stored in a vault outside Paris (the International Prototype of the Kilogram, IPK); after 2019, it’s defined via Planck’s constant and laboratory-realizable apparatus called a Kibble balance (formerly “watt balance”), which equates mechanical and electrical power to determine mass from h.

The practical effect for everyday measurements: nothing. The new definition was chosen so that 1 kg under the new SI equals 1 kg under the old SI to within measurement precision. Your kitchen scale and the mass on the side of a flour bag haven’t changed. What did change is the chain of traceability: national metrology institutes (NIST in the US, NPL in the UK, PTB in Germany) can now realise the kilogram independently from first principles, rather than calibrating against a copy of the Paris cylinder. Source: BIPM — SI base units, as of 2026-05.

Worked example: photon energy

A green photon at λ = 550 nm has frequency ν = c/λ = (3.00 × 10⁸) / (5.50 × 10⁻⁷) = 5.45 × 10¹⁴ Hz. Its energy is E = hν = (6.626 × 10⁻³⁴) × (5.45 × 10¹⁴) = 3.61 × 10⁻¹⁹ J, or about 2.25 eV. A 1-watt green laser therefore emits roughly 1 / 3.61 × 10⁻¹⁹ ≈ 2.8 × 10¹⁸ photons per second. Because h is so small, individual photon energies are minuscule in joules but enormous as a fraction of a chemical bond — which is why visible light can drive photosynthesis and UV light can damage DNA, but radio waves cannot.

Why the redefinition matters

Tying the kilogram to h eliminated a single point of failure. The Paris cylinder had drifted by tens of micrograms relative to its sister copies over a century — a problem when pharmaceutical dosing, semiconductor metrology, and force standards all chain up to that one artefact. With h fixed, any sufficiently equipped lab can realise the kilogram from electrical quantities measurable to parts in 10⁸. The same principle now anchors the ampere (to the elementary charge e) and the kelvin (to the Boltzmann constant k). See also kilogram and the NIST SI redefinition overview.