De Broglie Wavelength Calculator
The de Broglie wavelength of a particle from its mass and speed — the scale on which it behaves as a wave — with its momentum, the equivalent frequency, and how the wavelength compares with an atom.
Every moving object has a wavelength: Planck's constant over its momentum.
How the de broglie wavelength calculator works
Every moving object has a wavelength: Planck's constant over its momentum. For an electron at a few per cent of light speed that is a fraction of a nanometer — comparable to atomic spacing, which is why electrons diffract from crystals and why electron microscopes resolve atoms. For anything you can hold, the wavelength is so far below any measurable scale that the wave nature never shows.
Above about a tenth of light speed the momentum needs the relativistic factor, which the page applies.
Formula: λ = h / p, p = γ m v
Worked examples
| Inputs | De Broglie wavelength (m) | Note |
|---|---|---|
| An electron at 1,000 km/s | 7.2739e-10 | 0.73 nm |
| A thermal neutron | 1.7982e-10 | 0.18 nm — crystal scale |
| A dust grain | 6.6261e-19 | immeasurably short |
FAQFrequently asked questions
What is the de Broglie wavelength?
The wavelength associated with any moving particle: Planck's constant divided by its momentum. Louis de Broglie proposed it in 1924 and electron diffraction confirmed it three years later.
Why do we not see wave behaviour in everyday objects?
Because their momentum is enormous on this scale. A thrown ball has a wavelength around 10⁻³⁴ meters — smaller than anything can ever measure.
Why do electron microscopes see atoms?
Because electrons at tens of kilovolts have wavelengths of picometers, thousands of times shorter than visible light. Resolution is limited by wavelength.
What are thermal neutrons?
Neutrons slowed to room-temperature speeds, about 2.2 km/s, whose wavelength of 0.18 nm matches crystal spacings. Neutron diffraction maps structures that X-rays miss.
When does relativity matter?
Above about a tenth of light speed the momentum grows faster than mv. The page uses the full relativistic momentum, so it is right at any speed below c.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.