Compton Scattering Calculator
The wavelength shift that proved photons carry momentum.
Work out Compton Scattering. The wavelength shift that proved photons carry momentum. Names the assumption that breaks it.
0.0709 nm is the molybdenum K-alpha X-ray line Compton used.
Wavelength shift
2.4263 pm
Scattered at 0.07333 nm · 3.31% of the energy lost
Δλ = (h/mc)(1 − cos θ). A photon bouncing off an electron comes away with a LONGER wavelength, having handed over some energy and momentum. That is impossible on a wave picture — a wave scattering off a charge should re-radiate at the same frequency — and it is the result that made photon momentum undeniable in 1923. The shift depends only on the angle, never on the incoming wavelength. It is always about 2.4 pm at 90°, which is a rounding error for visible light at 500,000 pm and an obvious effect for X-rays at 70.
How the Compton Scattering Calculator works
Enter an incoming wavelength and scattering angle for the Compton shift and the scattered wavelength. The shift depends only on angle, never on the incoming wavelength — which is why it is invisible for light and obvious for X-rays.
Also known as: compton shift calculator · compton wavelength calculator · compton effect formula · photon scattering calculator
Frequently asked questions
What is the Compton effect?
A photon scattering off a free electron loses energy and comes away at a longer wavelength. Δλ = (h/mc)(1 − cos θ).
Why did it matter historically?
Because a wave scattering off a charge should keep its frequency, and it does not. The 1923 result made photon momentum undeniable and settled the particle side of wave-particle duality.
What is the Compton wavelength?
h/mc for the electron, about 2.426 pm. It is the maximum shift at 90° and twice that for a full backscatter.
Why does this not happen with visible light?
It does, but the shift is always about 2.4 pm regardless of wavelength. Against a 500,000 pm visible photon that is unmeasurable; against a 70 pm X-ray it is a third of the wavelength.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/compton-scattering-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Compton Scattering Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/compton-scattering-calculator" style="color:#64748b">Compton Scattering Calculator</a> from The Calc Library</p>The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.
Related calculators
Photoelectric Effect Calculator
KEmax = hf − φ, and the threshold that broke classical physics.
OpenPhoton Energy Calculator
Energy, wavelength and frequency, from whichever you know.
Opende Broglie Wavelength Calculator
Matter wavelength for an electron, proton or anything else.
Open