What is the de Broglie wavelength?

The de Broglie wavelength is the wavelength associated with a moving particle, proposed by Louis de Broglie in 1924. It is given by lambda = h/p, where h is Planck's constant (6.626e-34 J·s) and p is the particle's momentum.

How is momentum calculated from kinetic energy?

For a non-relativistic particle, kinetic energy KE = p^2 / (2m), so p = sqrt(2 * m * KE). This calculator uses that relation when kinetic energy is provided.

Why are results shown in picometers?

Electrons and similar sub-atomic particles at typical energies have wavelengths on the order of picometers (10^-12 m) to nanometers (10^-9 m), which is comparable to atomic and molecular scales. Picometers are the most natural unit for these magnitudes.

Does this calculator account for relativistic effects?

No. This calculator uses the classical momentum formula p = mv and the non-relativistic kinetic energy relation. For particles moving at a significant fraction of the speed of light, a relativistic treatment is required.

What is Planck's constant used here?

The calculation uses h = 6.626 × 10^-34 J·s (joule-seconds), the standard value of Planck's constant.

De Broglie Wavelength Calculator

Calculate the de Broglie wavelength of a particle from its mass and velocity or kinetic energy.

Input Parameters

Calculation Mode

Particle Preset

Velocity (m/s)

Result

Enter values and click Calculate

De Broglie Wavelength

Parameter	Value

Formula applied

Common Particle Masses

Particle	Mass (kg)	Symbol
Electron	9.109 × 10⁻³¹	e⁻
Proton	1.673 × 10⁻²⁷	p⁺
Neutron	1.675 × 10⁻²⁷	n

Planck's constant h = 6.626 × 10⁻³⁴ J·s

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Summary

Calculate the de Broglie wavelength of a particle from its mass and velocity or kinetic energy.

How it works

Select a calculation mode: velocity + mass or kinetic energy + mass.
Choose a preset particle (electron, proton, neutron) or enter a custom mass in kilograms.
Enter the velocity in meters per second or kinetic energy in electron-volts.
The calculator applies lambda = h/p, where p = mv for velocity mode and p = sqrt(2mKE) for energy mode.
Results appear instantly in both picometers (pm) and nanometers (nm).

Use cases

Verify homework or exam solutions for quantum mechanics courses.
Compare the wavelength of electrons versus heavier particles at the same speed.
Explore how kinetic energy affects the wave nature of sub-atomic particles.
Understand why macroscopic objects have negligibly small de Broglie wavelengths.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu