What is the de Broglie wavelength?

The de Broglie wavelength is the wavelength associated with any moving particle. Louis de Broglie proposed in 1924 that matter has wave-like properties, with wavelength λ = h/p = h/(mv), where h is Planck's constant and p = mv is the particle's momentum.

Why is the de Broglie wavelength only significant for tiny particles?

Because Planck's constant h ≈ 6.626 × 10⁻³⁴ J·s is extremely small, the wavelength is negligibly small for macroscopic objects. For a 1 kg ball moving at 1 m/s, λ ≈ 6.6 × 10⁻³⁴ m — far too small to detect. For an electron (9.1 × 10⁻³¹ kg) at 1 × 10⁶ m/s, λ ≈ 0.7 nm, which is comparable to atomic spacings.

What value of Planck's constant does this calculator use?

This calculator uses the 2019 SI-defined value: h = 6.62607015 × 10⁻³⁴ J·s (joule-seconds), which is exact by definition.

Can I calculate the wavelength for relativistic speeds?

This calculator uses the classical momentum p = mv. For velocities approaching the speed of light (> ~10% of c ≈ 3 × 10⁷ m/s), the relativistic momentum p = γmv should be used. A warning is shown when your input exceeds 10% of the speed of light.

What are the preset particles?

The presets include an electron (9.10938 × 10⁻³¹ kg), a proton (1.67262 × 10⁻²⁷ kg), a neutron (1.67493 × 10⁻²⁷ kg), and an alpha particle (6.64424 × 10⁻²⁷ kg). These cover the most common quantum mechanics problems.

De Broglie Wavelength Calculator

Enter a particle mass and velocity to compute its de Broglie wavelength using λ = h/mv.

Particle Parameters

Preset Particle

Mass (kg)

Use scientific notation: e.g. 9.109e-31

Velocity (m/s)

Enter a mass and velocity, then click Calculate.

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Summary

The de Broglie wavelength describes the wave-like nature of any particle with momentum. Using the relation λ = h/mv (where h is Planck's constant, m is mass, and v is velocity), this calculator shows how quantum mechanical wavelengths vary with particle mass and speed. Results are displayed in meters, nanometers, and picometers for easy comparison with atomic and molecular scales.

How it works

Enter the particle mass in kilograms (or select a preset particle like an electron or proton).
Enter the particle velocity in meters per second.
Click "Calculate" — the tool applies λ = h / (m × v) with h = 6.62607015 × 10⁻³⁴ J·s.
Results appear instantly in meters, nanometers, and picometers.
Use the comparison panel to see how the wavelength relates to atomic and molecular sizes.

Use cases

Quantum mechanics homework and exam preparation.
Verifying textbook de Broglie wavelength problems.
Exploring wave-particle duality for electrons and protons.
Comparing matter-wave wavelengths to X-ray and visible light wavelengths.
Physics lab pre-calculations for electron diffraction experiments.
Teaching demonstrations of how mass and velocity affect quantum behavior.
Quick unit conversion between meters, nanometers, and picometers.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu