ConverterHub

Photon Momentum Calculator

Find the momentum and energy of a photon.

Result

1.3252e-27 kg·m/s
2.4797 eV

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 = 1.3252e-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.

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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