Physics · Quantum · Private, in-browser
De Broglie Wavelength Calculator
Calculate de Broglie wavelength from mass and velocity, kinetic energy, momentum, or accelerating voltage. Use particle presets for electrons and other particles, change units directly, and compare classical and relativistic results when speed or energy is high.
Formula, Variables, and Units
- Core relation:
λ = h / p, where λ is wavelength, h is Planck's constant, and p is momentum.
- Velocity mode: classical
p = mv; relativistic p = γmv.
- Kinetic energy mode: classical
p = sqrt(2mKE); relativistic pc = sqrt(KE² + 2KE mc²).
- Voltage mode: a singly charged particle accelerated through
V volts gains KE = qV. For an electron, volts map directly to electron-volts.
- Momentum mode: enter momentum directly, then the wavelength is simply
λ = h/p.
SI units are used internally. Unit selectors convert kg, grams, atomic mass units, electron masses, m/s, km/s, eV, keV, MeV, GeV, volts, meters, nanometers, angstroms, picometers, and femtometers.
When Relativistic Momentum Matters
The classical shortcut is accurate when v is much smaller than c. Around 0.1c, the correction becomes visible; by electron microscope energies such as 100 keV, it is no longer a rounding detail. Relativistic momentum is larger, so the corrected de Broglie wavelength is shorter than the non-relativistic estimate.
In energy mode the calculator uses pc = sqrt(KE² + 2KE mc²) for the relativistic path. In velocity mode it uses γ = 1/sqrt(1 - v²/c²) and p = γmv. Momentum mode treats your entered momentum as already final.
Electron Examples and Scale
An electron at 1 eV has a wavelength around 1.23 nm, large enough to compare with molecular dimensions. At 100 eV the wavelength is about 0.123 nm, close to atomic and crystal spacings. At 100 keV the relativistic wavelength is a few picometers, which is why high-energy electron beams can probe much smaller structure.
The same formula makes macroscopic matter waves vanish from ordinary experience. A 0.145 kg baseball at 40 m/s has a wavelength around 1.14×10^-34 m, far below nuclear scales.
Photon Caveat and Common Mistakes
- Photons: photons obey
λ = h/p, but they have no rest mass, so do not use the particle mass inputs for light.
- eV vs volts: electron-volts are energy. Volts become energy only after multiplying by particle charge.
- Mass units: atomic mass units and electron masses are mass units, not energies.
- Relativity: do not use
p = mv for fast electrons or high-energy beams when precision matters.
Methodology and Constants
Last reviewed: June 8, 2026. Calculations run locally in your browser and use exact SI constants where available.
- Planck constant:
h = 6.62607015×10^-34 J·s.
- Speed of light:
c = 299,792,458 m/s.
- Elementary charge:
e = 1.602176634×10^-19 C, so 1 eV equals 1.602176634×10^-19 J.
- Particle masses: electron, proton, neutron, alpha particle, muon, C60 fullerene, and baseball presets are stored in kilograms and converted for display.
- Assumptions: voltage mode assumes a singly charged particle unless the alpha preset is selected, where charge number 2 is used. Momentum input is treated as the momentum to use directly.
FAQ
How do you calculate de Broglie wavelength?
Use λ = h/p. For low-speed particles, find momentum from p = mv or from kinetic energy with p = sqrt(2mKE), then divide Planck's constant by that momentum.
What units should I use?
SI units always work, but this calculator also converts common classroom and lab units: eV, keV, MeV, GeV, volts, kg, grams, atomic mass units, electron masses, meters, nanometers, angstroms, picometers, and femtometers.
How do I calculate electron wavelength from eV or voltage?
Select Electron, choose kinetic energy or accelerating voltage, enter the value in eV or V, and read the wavelength. For an electron accelerated through 100 V, the energy is 100 eV.
When do relativistic corrections matter?
Check the relativistic result when speed approaches 0.1c or electron energy is in the tens of keV and above. The percent error result shows how far the classical wavelength is from the corrected value.
Do photons have de Broglie wavelength?
Photons have wavelength and momentum related by λ = h/p, but they are massless. Use a photon energy or wavelength calculator rather than entering a rest mass here.
Why are matter waves negligible for everyday objects?
Large objects have large momentum, and wavelength is inversely proportional to momentum. That makes a baseball's matter wavelength many orders of magnitude smaller than atomic or nuclear dimensions.
