De Broglie Wavelength Calculator
Find the matter wavelength of a moving particle.
Results update as you type.
How it works
One of the most profound ideas in physics is that matter behaves as waves, and this calculator finds the de Broglie wavelength that quantifies it. You enter a particle's mass and velocity, and it returns its wavelength in meters and nanometers. In 1924, Louis de Broglie proposed that every moving particle has an associated wavelength equal to Planck's constant divided by the particle's momentum, which is its mass times its velocity. This wave-particle duality was soon confirmed by experiments showing that electrons diffract like waves, a cornerstone of quantum mechanics. Because Planck's constant is extraordinarily small, the wavelength is only measurable for very light, fast particles such as electrons, neutrons, and atoms. For an electron moving at a million meters per second, the wavelength is around a nanometer, comparable to atomic spacing, which is why electron waves are used in electron microscopes to image tiny structures beyond the reach of light microscopes. For everyday objects, a person walking or a thrown ball, the wavelength is so vanishingly small that wave behavior is completely undetectable, which is why we do not notice quantum effects at human scales. This calculator makes the abstract concrete, letting you see how wavelength depends on mass and speed. Both must be positive. Enter the mass and velocity to compute the de Broglie wavelength.
λ = h / (m·v)
De Broglie proposed that every moving particle has a wavelength equal to Planck's constant divided by its momentum, the product of mass and velocity. Because Planck's constant is tiny, the wavelength is only significant for very light particles like electrons; for everyday objects it is unimaginably small.
Source:Quantum mechanics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter particle mass and velocity.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Wavelength updates instantly as you type — no button to press.
Frequently asked questions
What is the de Broglie wavelength?
The de Broglie wavelength is the wavelength associated with a moving particle, equal to Planck's constant divided by the particle's momentum. It expresses wave-particle duality, the quantum idea that matter has wave-like properties. The concept, proposed by Louis de Broglie in 1924, is a foundation of quantum mechanics and was confirmed by electron diffraction experiments.
Why don't everyday objects show wave behavior?
Because Planck's constant is extremely small, the de Broglie wavelength of any macroscopic object is unimaginably tiny, far smaller than an atomic nucleus. Wave effects like diffraction only appear when the wavelength is comparable to the size of obstacles or openings, which never happens for large objects, so their wave nature is completely undetectable.
What particles have measurable wavelengths?
Very light, fast particles such as electrons, neutrons, protons, and atoms have de Broglie wavelengths large enough to observe. Electrons in particular have wavelengths near atomic dimensions at typical energies, which is why they diffract off crystals and are used in electron microscopy to resolve details far smaller than visible light can reach.
How is this used in electron microscopy?
Electron microscopes exploit the very short de Broglie wavelength of fast electrons, which is far smaller than the wavelength of visible light. Because resolution is limited by wavelength, using electron waves allows imaging of structures down to the atomic scale, revealing detail impossible with light microscopes. The calculator shows how accelerating electrons shortens their wavelength.
What units should I use?
Enter mass in kilograms and velocity in meters per second to get the wavelength in meters, which the calculator also converts to nanometers for convenience. For subatomic particles, masses are very small; for example, an electron's mass is about 9.109 times ten to the minus 31 kilograms. Using consistent SI units ensures a correct result.