Photon Momentum Calculator
Enter frequency or wavelength to compute the photon momentum p = h/λ = E/c (and the equivalent mass).
Input Data
Results
At a glance:Even though photons are massless, they carry momentum p = h/λ = h·f/c = E/c (from special relativity E² = p²c² + m²c⁴ with m=0). This momentum is the basis of radiation pressure: a beam of power P delivers force F = P/c (doubled if fully reflected). It explains the Compton effect (photon–electron momentum exchange), solar sails and laser cooling. The 'equivalent mass' m_eq = E/c² is the inertial mass corresponding to the photon's energy (not a rest mass). This tool returns p, E and m_eq from f or λ.
Formula
p = h/λ = h·f/c = E/c
Equivalent mass: m_eq = E/c²
$$p = \frac{h}{\lambda}, \quad E = \frac{hc}{\lambda} = hf, \quad E = pc$$How to Use
- Enter frequency f (Hz) or wavelength λ (nm).
- The calculator returns momentum p, energy E and equivalent mass m_eq.
Case Studies
Solar sail
λ = 500 nm, flux gives p per photon ≈ 1.3e-27 kg·m/s.
Force ≈ P/c for absorbed light.
Large sails accumulate measurable thrust in vacuum.
FAQ
How can a massless particle have momentum?
Relativity gives momentum to energy even without rest mass: p = E/c. For light this is well established (radiation pressure, Compton scattering).
What is radiation pressure?
The force per area from photons: absorbed light exerts P/c, reflected light 2P/c. It is tiny but drives solar sails over large areas.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.