De Broglie Wavelength Calculator

It is the wavelength associated with a moving particle, equal to Planck constant divided by the particle momentum. It expresses the wave-like nature of matter that underpins quantum mechanics.

Large objects have enormous momentum compared with Planck constant, so their de Broglie wavelength is far too small to measure. Only tiny particles like electrons have wavelengths large enough to show diffraction.

Use SI units: mass in kilograms and velocity in meters per second, so momentum comes out in kg-m/s and the wavelength in meters. The calculator also reports the result in nanometers for convenience.

For a non-relativistic particle, momentum relates to kinetic energy by p = √(2mE), so the wavelength is λ = h / √(2mE), where E is the kinetic energy in joules, m is the mass in kilograms, and h is Planck's constant. This is handy when you know an electron's accelerating voltage: E = qV gives the energy, then λ follows. Example: a 100 eV electron (E ≈ 1.6×10⁻¹⁷ J) has λ = h / √(2mE) ≈ 1.2×10⁻¹⁰ m, about 0.12 nm.

Not exactly. λ = h/(mv) uses the non-relativistic momentum p = mv, which breaks down as the speed approaches that of light. For fast particles you must use the relativistic momentum p = γmv, with γ = 1 / √(1 − v²/c²), which makes the true wavelength shorter than the simple formula predicts. The high-energy electrons in electron microscopes, for example, need this relativistic correction.