How this calculator works
Every momentum magnitude p corresponds to de Broglie wavelength h/p. For a massive particle the relativistic momentum is gamma m v. The classical choice uses m v and is accurate only when speed is much smaller than c. A stationary particle has zero momentum and an unbounded wavelength, so wavelength inversion requires positive momentum or speed. Inputs labelled nm and kg m/s use those fixed units. A momentum-only calculation can also describe a photon.
Formula
lambda = h/p; p = gamma m v; gamma = 1/sqrt(1-v²/c²). Classical approximation: p = m v. Relativistic inversion: v = c p/sqrt(p²+m²c²).
Worked example
A momentum of 6.62607015e-34 kg m/s gives a wavelength of 1 m. A classical 1 kg object moving at 1 m/s has wavelength 6.62607015e-34 m.
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Frequently asked questions
Does higher momentum give a shorter wave?
Yes. Doubling momentum halves the wavelength.
When should I use relativistic momentum?
Use it when speed is an appreciable fraction of c. The classical option is for low-speed comparisons.
Can I enter zero speed?
Zero speed would give an infinite wavelength. This finite-result tool requires a positive speed when using mass and speed.