Planck's constant
/ PLAHNK /
Every measuring system has a basic unit that sets its grain — a currency has its smallest coin, a ruler its finest mark. The quantum world has such a unit too, a single tiny number that sets how coarse nature's graininess is. It links the energy a packet of light carries to how fast that light wiggles, and it fixes how big the unavoidable fuzziness of the uncertainty principle is. That number is Planck's constant, written h.
More precisely, Planck's constant is the fundamental constant of quantum mechanics. It is the proportionality factor connecting a photon's energy to its frequency: energy equals h times frequency. It also appears in the de Broglie wavelength, in the uncertainty principle, and in the Schrödinger equation. Its value is extremely small, about 6.626 × 10⁻³⁴ joule-seconds, and that smallness is precisely why quantum effects are hidden in everyday life.
The honest point is that h is not just a conversion factor; it is the size of the quantum world itself. If h were zero, energy would be smooth, the uncertainty principle would vanish, and physics would collapse back to the classical picture. Because h is small but genuinely not zero, the graininess is real yet invisible at human scale. Since 2019 its value is fixed exactly by definition and is used to define the kilogram.
A single photon of green light, with a frequency near 5.5 × 10¹⁴ cycles per second, carries an energy of h times that frequency — about 3.7 × 10⁻¹⁹ joules. It takes the combined energy of millions of such photons to register as anything noticeable, which is why we never sense light arriving in lumps.
h converts a light wave's frequency into the energy of its photons.
You will often meet a relative, the reduced Planck constant ħ ('h-bar'), which is just h divided by 2π. It is the version that appears most naturally in equations involving angular quantities, such as the uncertainty principle and spin.