Planck constant (h)

The Planck constant, written h, is the fundamental number that sets the scale of all quantum effects. It is breathtakingly small — about 6.6 × 10⁻³⁴ joule-seconds — which is exactly why the strange features of quantum mechanics stay hidden in everyday life and only show up for atoms, electrons, and single particles of light. Where h is negligible, the world looks classical.

Its job is to convert between things classical physics kept separate. Multiply a light wave's frequency by h and you get the energy of one of its photons; this is the relation E = hf. The constant carries units of energy times time, the units of a quantity called action, and it is in this sense the basic 'grain size' of nature: action does not come in arbitrarily small amounts but in steps measured by h.

Physicists very often use the reduced Planck constant, ħ (pronounced 'h-bar'), which is simply h divided by 2π. It appears throughout quantum mechanics — in the uncertainty principle, the Schrödinger equation, and the rules for angular momentum and spin. Since 2019 h has been fixed to an exact value by definition and used to define the kilogram, a fitting promotion for the number that ushered in the quantum era.