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Photon Momentum Calculator

Find the momentum and energy of a photon.

How it is calculated

Momentum is p = h / λ and energy is E = h × c / λ. The wavelength λ is entered in nanometres and converted to metres (×10⁻⁹) inside the tool. The constants are the exact SI values: h = 6.62607015×10⁻³⁴ J·s and c = 299,792,458 m/s. Momentum is shown in kg·m/s in scientific notation with four decimals; energy is divided by 1.602176634×10⁻¹⁹ J per eV and shown in electronvolts to four decimals.

The wavelength must be greater than zero, otherwise no result appears. The tool treats the photon in vacuum; in a medium the wavelength and the speed of light change, so enter the vacuum wavelength.

Worked example

Green light at λ = 500 nm, which is 5×10⁻⁷ m. Momentum: 6.62607015×10⁻³⁴ / 5×10⁻⁷ = 1.3252 × 10⁻²⁷ kg·m/s. Energy in joules: h × c / λ is about 3.973×10⁻¹⁹ J. Divide by 1.602×10⁻¹⁹ J per eV to get 2.4797 eV. Halving the wavelength would double both values.

Try this example →

Common mistakes

  • Entering the wavelength in metres or micrometres. The box takes nanometres, so 5×10⁻⁷ m must be typed as 500.
  • Entering a frequency instead of a wavelength. Convert with λ = c / f first.
  • Expecting a long wavelength to carry more energy. Both momentum and energy are inversely proportional to the wavelength, so red light carries less than blue.
  • Reading the energy in joules. The tool prints electronvolts, and the momentum, not the energy, is in SI units.
  • Applying the result to a photon inside glass or water, where the wavelength differs from its vacuum value.

Sources

About this calculator

This calculator finds a photon's momentum, p = h/λ, where h is Planck's constant and λ is the photon's wavelength, along with its energy, E = hc/λ (equivalently E = pc). Unlike massive particles, a photon's momentum comes entirely from its wave nature rather than from mv — a direct consequence of treating light as discrete quanta, as Einstein did to explain the photoelectric effect.

Physicists use this relationship throughout quantum mechanics and spectroscopy, where a photon's wavelength (color, in the visible range) directly tells you its energy and momentum. Photonics and optics engineers apply it when designing solar sails and studying radiation pressure — the tiny but real push light exerts on matter — and researchers use it when interpreting spectral lines from atoms or distant stars. Physics students studying wave-particle duality and quantum theory use this calculator to connect a photon's wavelength to its measurable physical properties.

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Comments (1)

  • Editorial team

    For a fast cross-check without a calculator, photon energy in electronvolts is close to 1239,84 divided by the wavelength in nanometres, so 500 nm should land near 2,48 eV. Remember the input is in nanometres, not metres or micrometres, and that the formulas describe a single photon, not a beam. Which part of the spectrum are you working in, ultraviolet, visible or infrared?

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