Compton Wavelength Calculator — λ_C = h / (mc)
The Compton wavelength λ_C = h/(mc) is the characteristic quantum length scale of a particle. Select a particle to instantly see its Compton wavelength in pm, fm, and metres, the reduced Compton wavelength ƛ_C = λ_C/(2π), and the rest mass energy in MeV.
Particle
λ_C = h / (m c) — decreases as particle mass increases
- 1
Denominator m × c
9.1094e-31 × 2.9979e+8 = 2.7309e-22 kg·m/s - 2
Compton wavelength in metres
6.6261e-34 ÷ 2.7309e-22 = 2.426310e-12 mλ_C = h / (m c) - 3
Convert to picometres (× 10¹²)
2.426310e-12 × 10¹² = 2.42631
How does this calculator work?
The Compton wavelength λ_C = h/(mc) is the length at which a photon's energy equals the particle's rest mass energy mc². For an electron: ≈ 2.426 pm. Heavier particles (proton, neutron) have much shorter Compton wavelengths (≈ 1.32 fm). The reduced form ƛ_C = λ_C/(2π) appears in relativistic wave equations.
Formula
How this is calculated
The Compton wavelength of a particle of mass m is λ_C = h/(mc), where h is Planck's constant and c is the speed of light. It represents the wavelength of a photon whose energy equals the rest mass energy of the particle (mc²). Equivalently, at length scales below λ_C, quantum field effects become important and particle–antiparticle pair creation becomes energetically possible — so λ_C marks the boundary where single-particle quantum mechanics breaks down and quantum field theory is required.
The reduced Compton wavelength ƛ_C = ħ/(mc) = λ_C/(2π) (where ħ = h/2π is the reduced Planck constant) appears more naturally in relativistic quantum field equations. For the electron, ƛ_C ≈ 386 fm; this is the length scale entering the Dirac equation and the Klein–Gordon equation.
The Compton wavelength is distinct from the de Broglie wavelength (which depends on kinetic energy/momentum) and from the classical electron radius r_e = α × ƛ_C ≈ 2.82 fm (where α ≈ 1/137 is the fine-structure constant). These three lengths are related: r_e = α × ƛ_C = α² × a_0 (Bohr radius).
Frequently asked questions
The electron Compton wavelength is λ_C = h/(m_e c) ≈ 2.42631 pm (2.42631 × 10⁻¹² m). The reduced Compton wavelength is ƛ_C = ħ/(m_e c) ≈ 386.16 fm. These values are exact given the 2019 SI redefinition that fixed h and c.
A photon with wavelength equal to λ_C has energy mc² — the rest mass energy of the particle. Below this length scale, quantum field effects (pair production) are significant. It also appears directly in Compton scattering: the wavelength shift Δλ = λ_C × (1 − cos θ) for scattering off a free electron.
The de Broglie wavelength λ = h/p depends on the particle's momentum p (and therefore on its kinetic energy and speed) — it decreases as the particle speeds up. The Compton wavelength depends only on the particle's rest mass and is a fixed property of that particle species, independent of energy or velocity.
Also known as
TG we-Calculate Editorial Team. (2026). Compton Wavelength Calculator — λ_C = h / (mc) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/compton-wavelength-calculator
TG we-Calculate Editorial Team. "Compton Wavelength Calculator — λ_C = h / (mc)." TG we-Calculate. 2026. https://we-calculate.com/calculator/compton-wavelength-calculator.
TG we-Calculate Editorial Team, "Compton Wavelength Calculator — λ_C = h / (mc)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/compton-wavelength-calculator
@misc{wecalculate_compton_wavelength_calculator, title = {Compton Wavelength Calculator — λ_C = h / (mc)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/compton-wavelength-calculator}}, year = {2026}, note = {TG we-Calculate} }
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