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De Broglie Wavelength Calculator

Find the quantum wavelength of a moving particle.

How it is calculated

The de Broglie relation gives the wavelength of a moving particle from its momentum: λ = h ÷ (m × v). Here h is the Planck constant, fixed in the tool at 6.62607015×10⁻³⁴ J·s, m is the mass in kilograms and v the speed in metres per second. Both must be above zero. The wavelength is shown in metres in scientific notation with three decimals and also in nanometres with four decimals. The formula is the non-relativistic one with momentum p = mv, so it is accurate for speeds well below the speed of light. For everyday objects the wavelength is so small that the nanometre figure shows as 0.0000.

Worked example

An electron has a mass of 9.109e-31 kg and moves at 1,000,000 m/s. The momentum is 9.109e-31 × 1,000,000 = 9.109e-25 kg·m/s. Dividing the Planck constant 6.626e-34 by this gives a wavelength of 7.274e-10 m, which is 0.7274 nm, comparable to the spacing between atoms in a crystal.

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Common mistakes

  • Entering mass in grams or atomic mass units. The tool needs kilograms, so an electron is about 9.109e-31, not 9.109e-28.
  • Using speed in km/s or km/h when metres per second are required.
  • Reading 0.0000 nm for a large object as zero wavelength. A 0.145 kg ball at 40 m/s has 1.142e-34 m, so use the metre value.
  • Applying the formula to speeds close to the speed of light, where relativistic momentum should be used instead of mv.
  • Typing scientific notation incorrectly, for example 9.109*10^-31, instead of 9.109e-31.

About this calculator

This calculator finds the de Broglie wavelength of a moving particle: λ = h/(m·v), where h is Planck's constant, m is the particle's mass, and v is its velocity. This wavelength expresses the wave-like nature that quantum mechanics assigns to all matter, not just light — the smaller and slower the particle, the more its wave nature becomes noticeable relative to its size.

Physics and chemistry students use it to work through quantum mechanics problems, while researchers in electron microscopy rely on the same relationship to determine the resolving power achievable at a given electron energy. Enter the particle's mass and velocity to get its de Broglie wavelength.

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