De Broglie Wavelength Calculator

Background.

In 1924 Louis de Broglie proposed that everything that moves has a wavelength: λ = h/p, Planck's constant over momentum. Three years later Davisson and Germer scattered electrons off a nickel crystal and watched them diffract exactly as X-rays of that predicted wavelength would — matter really does interfere with itself. The proposal earned de Broglie the 1929 Nobel Prize and sits at the foundation of wave mechanics.

This page evaluates the nonrelativistic form λ = h/(mv) from a particle's mass and speed. Planck's constant has been exact by definition since the 2019 SI: h = 6.626 070 15×10⁻³⁴ J·s, so the only uncertainty in the result is the uncertainty in your inputs.

The formula explains a striking asymmetry in nature. An electron at a million metres per second carries so little momentum that its wavelength, 0.73 nm, is larger than an atom — comparable to crystal lattice spacings, which is why electron diffraction and electron microscopy work. A 0.145 kg baseball at 40 m/s has λ ≈ 1.1×10⁻³⁴ m, some twenty orders of magnitude below a proton's radius; no conceivable experiment resolves it, which is why baseballs travel in trajectories rather than interference patterns. Quantum behaviour is not switched off for large objects — it is merely scaled beyond all observability by h's smallness.

The nonrelativistic momentum p = mv underneath this page is accurate to about 1% up to roughly 14% of light speed (electrons of a few keV). Faster than that, relativistic momentum γmv is required — the scope note beside the result marks the boundary.

What is de broglie wavelength calculator?

The de Broglie wavelength is the wavelength of the quantum matter wave associated with any moving particle: λ = h/p, where h is Planck's constant and p the particle's momentum — in this nonrelativistic implementation, p = mv. It is not a metaphor: the wavelength predicts real interference fringes and diffraction angles, confirmed for electrons, neutrons, whole atoms, and molecules as large as C₆₀ and beyond. Because h ≈ 6.6×10⁻³⁴ J·s is so small, only microscopic momenta yield wavelengths large enough to detect.

How to use this calculator.

1. 01Enter the particle's mass in kilograms — electron 9.109×10⁻³¹, proton 1.673×10⁻²⁷, neutron 1.675×10⁻²⁷ kg.
2. 02Enter its speed in m/s; if you know kinetic energy instead, convert with v = √(2E/m) first — substituting energy for momentum directly is a dimensional error the page cannot catch for you.
3. 03Check the relativity boundary before trusting the output: below ≈4×10⁷ m/s (≈14% of c) the nonrelativistic form stays within 1%.
4. 04Compare the resulting λ with the feature size that would diffract it — crystal spacings run 0.2–0.5 nm — to judge whether wave behaviour is observable in your setup.
5. 05For thermal neutrons or gas atoms, use the thermal speed for a first estimate: room-temperature neutrons near 2,200 m/s give λ ≈ 0.18 nm, matching lattice spacings — the basis of neutron diffraction.

The formula.

De Broglie's relation λ = h/p unifies two earlier surprises: Einstein's photon momentum p = h/λ (light behaving as particles) read in reverse (particles behaving as waves). With nonrelativistic momentum p = mv the page's form λ = h/(mv) follows. Wavelength shrinks inversely with both mass and speed — double either and the wavelength halves — which is the entire reason quantum effects vanish at everyday scales: h/(mv) with kilogram masses is smaller than any physically meaningful length. The relation is exact in the momentum form; what is approximate here is only p = mv, which understates true momentum as speed climbs (by 1% at 0.14c, by 15% at 0.5c). Electron microscopists exploit the inverse-speed scaling deliberately — accelerating electrons to shrink λ below atomic spacing is what gives a TEM its resolution. The engine divides the exact 2019-SI Planck constant by the mass-speed product in Decimal arithmetic, rounding once to twelve significant digits.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST, 2022 CODATA Recommended Values of the Fundamental Physical Constants.
2. [2]OpenStax, University Physics Volume 3, chapter 6, Photons and Matter Waves.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.