Compton Scattering Calculator
Wavelength shift, scattered photon energy and electron recoil energy for Compton scattering at any angle — with the Compton wavelength and the maximum (back-scatter) shift.
How it works
λ′ − λ = (h ÷ mₑc)(1 − cos θ) = 2.426 pm × (1 − cos θ); E′ = E ÷ [1 + (E/511 keV)(1 − cos θ)]
Compton showed in 1923 that X-rays scattering from electrons lose energy in exactly the way a particle collision predicts — proof that photons carry momentum. The shift depends only on the angle, never on the material or the initial wavelength, which is why it is tiny for visible light (2 pm against 500,000 pm) but dominant for gamma rays. The 180° back-scatter case sets the Compton edge seen in gamma spectra.
Worked example
A 100 keV photon scattered through 90°: Δλ = 2.426 pm, so λ goes from 12.4 pm to 14.8 pm and the photon drops to 83.6 keV, handing 16.4 keV to the electron.
Frequently asked questions
Why is there no shift at 0°?
A forward-scattered photon has not interacted in the momentum-transfer sense; the shift grows with 1 − cos θ.
What is the Compton edge?
The maximum electron energy (180° scatter) — the sharp drop in a scintillator spectrum below the photopeak.
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This calculator is for educational purposes. Double-check important results before acting on them.