Fundamental physical constant that sets the scale of quantum mechanical quantization.The Planck constant (symbol h) is a fundamental physical constant that defines the quantum of action—the smallest possible amount of change in a physical system. It sets the scale at which quantum effects become significant: for macroscopic objects, h is so small that quantum behavior is negligible, but for particles like electrons, it governs the quantization of energy, angular momentum, and other properties. It appears in the de Broglie wavelength of matter, the energy of a photon (E = hν), and the uncertainty principle.
Max Planck introduced the constant in 1900 to explain the spectrum of blackbody radiation, postulating that energy is emitted in discrete quanta proportional to frequency. This marked the birth of quantum theory.
The constant has the units of action (energy × time) and a value of approximately 6.626 × 10⁻³⁴ joule-seconds. In quantum mechanics, it relates the frequency of a wave to the energy of its associated particle, and it sets the minimum uncertainty in simultaneous measurements of position and momentum. It also defines the Planck scale, where quantum gravitational effects are expected to become important.
The Planck constant is used in defining the kilogram in the International System of Units (via the Kibble balance), in quantum computing, and in the calibration of semiconductor devices.
The Planck constant is so small that if you tried to measure the energy of a baseball pitch with quantum precision, the uncertainty in its position would be far smaller than the size of a proton.
| E | variable | Energy of a photon — energy joule |
| f | variable | Frequency of the electromagnetic wave — frequency hertz |
| h | constant | Fundamental constant relating energy to frequency in quantum mechanics — planck constant = 6.62607015e-34 joule second |
| E | variable | Energy of a photon — energy joule |
| ν | variable | Frequency of the photon — frequency hertz |
| h | constant | Fundamental constant relating energy and frequency of a quantum — planck constant = 6.62607015e-34 joule second |
| p | variable | canonical momentum — momentum kilogram metre per second |
| q | variable | canonical coordinate — position metre |
| n | variable | quantum number (integer) — quantum number |
| h | constant | fundamental constant relating energy to frequency — planck constant = 6.62607015e-34 joule second |
| ∮ | operator | integral over one full period of the motion — closed line integral |
| F | variable | frequency of magnetic oscillation — frequency hertz |
| A | variable | extremal cross-sectional area of Fermi surface — area square metre |
| h | constant | planck constant = 6.62607015e-34 joule second |
| e | constant | elementary charge = 1.602176634e-19 coulomb |
| AB | variable | Molecule composed of atoms A and B — molecule |
| A | variable | Atom A produced — atom |
| B | variable | Atom B produced — atom |
| h | constant | Relates photon energy to frequency — planck constant = 6.62607015e-34 joule second |
| \nu | constant | Frequency of the incident photon — photon frequency = variable hertz |
| + | operator | Combines photon with molecule — addition operator |
| \rightarrow | operator | Indicates transformation — reaction arrow |
| \lambda | variable | de Broglie wavelength of the particle — wavelength metre |
| p | variable | momentum of the particle — momentum kilogram metre per second |
| h | constant | Planck constant, the quantum of action — planck constant = 6.62607015e-34 joule second |
