Photon Momentum Calculator
Although photons are massless, they carry momentum described by p = h / lambda, where h is Planck's constant and lambda is the photon's wavelength. This was one of the key insights of early quantum mechanics, confirmed by Compton's 1923 scattering experiments. For green light at 550 nm, the momentum per photon is about 1.2 x 10^-27 kg m/s, a tiny but measurable quantity that drives effects like radiation pressure and solar sails. Photon momentum is also directly related to photon energy: E = pc = hf. Enter the photon wavelength in nanometers to compute its momentum in SI units.
Photon momentum formula
p = h / lambda
E = h * c / lambda = p * c
Where h = 6.62607015 x 10^-34 J s (Planck's constant), lambda is the wavelength in meters, and c = 2.99792458 x 10^8 m/s. Energy in eV is obtained by dividing by the elementary charge e = 1.602176634 x 10^-19 C.
Photon momentum in context
- Green light (550 nm): p = 1.205 x 10^-27 kg m/s, E = 2.25 eV.
- Hard X-rays (0.1 nm): p = 6.626 x 10^-24 kg m/s, around 1,000 times greater than visible light.
- Compton scattering shifts photon wavelength by delta lambda = (h/mc)(1 - cos theta) because the photon loses momentum to the recoiling electron.
- Solar radiation pressure on a 1 m^2 perfect reflector near Earth is about 9 micro-Pascals, arising from photon momentum flux.
Photon momentum: frequently asked questions
Do photons have momentum even though they have no rest mass?
Yes. Photons carry momentum p = h/lambda = E/c, where E is the photon energy. This was confirmed by Arthur Compton in 1923, who showed that X-ray photons transfer momentum to electrons during scattering (the Compton effect).
What is the formula for photon momentum?
Photon momentum p = h / lambda, where h is Planck's constant (6.626 x 10^-34 J s) and lambda is the wavelength in meters. Equivalently, p = h f / c where f is frequency and c is the speed of light.
What units does this calculator use?
Enter wavelength in nanometers (nm) for convenience; the calculator converts internally to meters. The output is in kg m/s (SI units). Visible light (400 to 700 nm) yields momenta on the order of 10^-27 kg m/s.
How does radiation pressure relate to photon momentum?
Radiation pressure arises from photon momentum transfer. When a photon is absorbed, it transfers momentum p = h/lambda to the absorber. When reflected, it transfers 2p. Solar sails exploit this: the Sun's radiation pressure exerts a small but continuous force on a reflective sail.
How does photon momentum differ from classical momentum?
Classical momentum is mass times velocity (mv). Photons have zero rest mass but travel at c, so the classical formula breaks down. Relativistic mechanics gives photon momentum as E/c = h/lambda, derived from the energy-momentum relation E^2 = (pc)^2 + (mc^2)^2 with m = 0.
Official sources
- NIST CODATA 2018: Planck Constant.
- OpenStax University Physics Vol. 3: Wave Nature of Electromagnetic Radiation.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.