Calculate the de Broglie wavelength of any particle using the de Broglie equation λ = h / (m × v). Select a particle type (electron, proton, etc.) or enter a custom mass, then provide either velocity or kinetic energy to get the matter wave wavelength in your preferred unit (m, nm, Å, pm).
de Broglie Wavelength (λ)
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Wavelength in Meters
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Momentum (p = m × v)
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Particle Mass Used
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The de Broglie equation states that every moving particle has an associated wavelength given by λ = h / (m × v), where h is Planck's constant (6.626 × 10⁻³⁴ J·s), m is the particle's mass, and v is its velocity. This relationship, proposed by Louis de Broglie in 1924, introduced the concept of wave-particle duality — the idea that matter can behave both as a particle and as a wave.
An electron has a mass of approximately 9.1094 × 10⁻³¹ kg. At a velocity of 1 × 10⁶ m/s, its de Broglie wavelength is roughly 0.727 nm — on the scale of atomic spacings. This is why electron diffraction can be used to study crystal structures, similar to how X-rays are used.
If you know the kinetic energy (KE) rather than velocity, you can derive velocity from v = √(2 × KE / m), then substitute into λ = h / (m × v). This simplifies to λ = h / √(2 × m × KE). This calculator supports direct kinetic energy input in units of eV, keV, MeV, or joules.
For a photon, which has no rest mass, the de Broglie wavelength is calculated using its energy: λ = h × c / E, where c is the speed of light. Alternatively, since a photon's momentum is p = E/c, you can use λ = h / p. This is directly equivalent to the standard formula for the wavelength of electromagnetic radiation.
The de Broglie wavelength is a length, so its SI unit is the meter (m). In practice, matter waves are extremely small, so results are more conveniently expressed in nanometers (nm), angstroms (Å, where 1 Å = 0.1 nm), or picometers (pm). This calculator lets you choose your preferred output unit.
Because de Broglie wavelength is inversely proportional to mass and velocity, large objects have wavelengths so incredibly small (far smaller than any atomic nucleus) that wave effects are completely undetectable. Wave-particle duality is only practically observable for subatomic particles like electrons, protons, and neutrons.
Wave-particle duality, formalized by de Broglie, is a cornerstone of quantum mechanics. It explains phenomena like electron diffraction, quantum tunneling, and the behavior of particles in double-slit experiments. It also underpins modern technologies such as electron microscopes and semiconductor devices.
Yes. Select from preset particles including the proton (1.6726 × 10⁻²⁷ kg) and hydrogen atom (1.6735 × 10⁻²⁷ kg), or enter any custom mass in kilograms. Heavier particles like protons have much shorter wavelengths than electrons at the same velocity, due to the inverse relationship between mass and wavelength.