Compton Wavelength Calculator

Background.

Every particle with mass carries a built-in length fixed by nothing but its mass and two constants of nature: λ_C = h/(mc). For the electron it is 2.426 × 10⁻¹² m, about 2.43 picometres, some 22 times smaller than the Bohr radius of a hydrogen atom.

The name comes from Arthur Compton's X-ray experiments of the early 1920s. When X-rays scatter off electrons, the scattered rays emerge with a longer wavelength, and the stretch depends only on the scattering angle: Δλ = λ_C(1 − cos θ). At 90° the shift is exactly one Compton wavelength; straight back, at 180°, it is two. That angle-only dependence was strong evidence that light arrives in quanta carrying momentum, colliding with electrons like billiard balls.

The length has a meaning of its own, too. A photon whose wavelength equals a particle's Compton wavelength carries an energy equal to that particle's rest energy mc², which is 511 keV for the electron. Squeeze a particle into a region much smaller than its Compton wavelength and the energies involved are enough to create particle–antiparticle pairs, so the picture of one well-defined particle breaks down. Roughly, it marks where quantum field theory has to take over from ordinary quantum mechanics.

Because mass sits in the denominator, heavier particles have shorter Compton wavelengths in exact proportion. A proton, about 1,836 times as massive as the electron, comes out at about 1.321 × 10⁻¹⁵ m, comparable to the proton's own size.

The page returns the unreduced form, h/(mc). Many theory texts use the reduced version, ħ/(mc), which is smaller by a factor of 2π. Planck's constant and the speed of light are both exact by definition in the SI, so the result is as precise as the mass you enter.

What is compton wavelength calculator?

The Compton wavelength of a particle is Planck's constant divided by the product of the particle's rest mass and the speed of light, λ_C = h/(mc). It is a length in metres that depends on nothing but the mass. It sets the size of the wavelength shift when a photon scatters off that particle, it equals the wavelength of a photon whose energy matches the particle's rest energy, and it marks roughly the scale below which the particle cannot be confined without creating new particles.

How to use this calculator.

1. 01Enter the particle's rest mass in kilograms. The default is the electron, 9.1093837139 × 10⁻³¹ kg, the CODATA 2022 recommended value.
2. 02If your mass is listed in MeV/c², multiply by 1.78266 × 10⁻³⁰ to get kilograms; if it is in unified atomic mass units, multiply by 1.66054 × 10⁻²⁷.
3. 03Read the result in metres. Divide by 10⁻¹² for picometres or by 10⁻¹⁵ for femtometres.
4. 04If your textbook or formula uses the reduced Compton wavelength ħ/(mc), divide the result by 2π.

The formula.

λ_C = h / (m c), where h = 6.62607015 × 10⁻³⁴ J s is the Planck constant, c = 299,792,458 m/s is the speed of light and m is the rest mass in kilograms. Both constants are exact by definition in the SI, so the only uncertainty in the answer comes from the mass. The product mc has the units of momentum, kg m/s, and h divided by a momentum is a length, the same structure as the de Broglie wavelength h/p. The result is inversely proportional to the mass: double the mass and the wavelength halves. It is the rest mass that goes in; the page does not use a speed-dependent mass, and it does not compute scattering angles or energies. The Compton shift at any angle θ follows directly from the result as λ_C(1 − cos θ).

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST, 2022 CODATA Recommended Values of the Fundamental Physical Constants.
2. [2]OpenStax, University Physics Volume 3, section 6.3, The Compton Effect.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.