Definition
Planck's constant h ≈ 6.626 × 10⁻³⁴ joule-seconds is the fundamental constant of quantum mechanics. It relates the energy of a photon to its frequency (E = hf), gives the smallest meaningful unit of action in any physical process, and sets the boundary below which classical physics no longer describes nature.
The reduced form ℏ = h/(2π) appears in most quantum equations.
Why it matters
How it works
Planck's 1900 derivation of the blackbody spectrum required assuming that a cavity wall could exchange energy with its radiation field only in integer multiples of hf, where f is the frequency. He treated the assumption as a mathematical trick. Five years later Einstein used the same quantum to explain the photoelectric effect, treating it as physically real: light itself comes in packets of energy E = hf.
From there h surfaces throughout quantum mechanics. The de Broglie relation p = h/λ links momentum to wavelength. Bohr's quantization condition fixes electron orbits at multiples of ℏ in angular momentum. The Schrödinger equation contains ℏ in its time-evolution operator. The Heisenberg uncertainty relations Δx·Δp ≥ ℏ/2 are statements about how much smaller than ℏ the product of two complementary uncertainties can be (the answer is: not at all).
Numerically h is tiny in everyday units, which is why classical physics works at human scales: the action of a swinging pendulum is enormous compared to h, so quantum effects are invisible. At atomic scales the action becomes comparable to h and quantum mechanics takes over.
Combining h with the speed of light c and the gravitational constant G gives the Planck length √(ℏG/c³) ≈ 1.6 × 10⁻³⁵ m and the Planck time ≈ 5.4 × 10⁻⁴⁴ s — the scales at which gravity must be treated quantum-mechanically. Beyond those scales, an unknown theory of quantum gravity (string theory, loop quantum gravity, or something else) is required.