Compton Shift Calculator

How it is calculated

The shift depends only on the scattering angle, not on the incoming photon's wavelength: Δλ = λc × (1 − cos θ). Here θ is the angle in degrees between the incoming and scattered photon directions, and λc = h/(mₑc) = 2.42631023867×10⁻¹² m is the electron Compton wavelength. The tool converts the angle to radians, evaluates the cosine and reports the shift both in picometres (4 decimals) and in metres (scientific notation). It accepts angles from 0° to 180° only; anything outside that range returns no result. The shift is zero at 0° (no deflection) and largest at 180° (backscatter), where it equals 2λc.

Common mistakes

• Entering the angle in radians: the field expects degrees, so π/2 typed as 1.5708 is read as about 1.57°, giving a tiny shift.
• Confusing the scattering angle θ with the angle of the recoiling electron; the formula uses the photon's deflection angle.
• Expecting the shift to depend on the incident wavelength. It does not, which is why it is only noticeable for X-rays and gamma rays whose wavelength is comparable to a few picometres.
• Entering an angle above 180° (for example 270°) to mean a reflex angle; the tool returns nothing because the valid range is 0–180°.
• Treating the result as the new wavelength rather than the increase in wavelength.