Compton Edge Calculator

Inputs

Incident photon energy

Use your source energy, like 662 keV from Cs-137.

Scattering angle (θ)

deg

Compton edge uses θ = 180° backscatter.

Electron rest energy (mc²)

Default 511 keV. Keep units consistent and physical.

Output unit

Controls units for all computed energies.

Results appear above this form after submission.

Compton scattering relates the scattered photon energy E′ to the incident energy E and scattering angle θ:

E′ = E / (1 + (E/mc²)(1 − cosθ))

Here mc² is the electron rest energy.

The recoil electron kinetic energy is:

T_e = E − E′

The Compton edge is the maximum recoil energy, occurring at θ = 180° (backscatter):

E′_edge = E / (1 + 2E/mc²)

T_edge = E − E′_edge = (2E²)/(mc² + 2E)

Enter the incident photon energy and choose its unit.
Set the scattering angle θ. Use 180° for the Compton edge.
Keep mc² at 511 keV unless using a custom constant.
Select an output unit, then click Calculate.
Use the download buttons to export CSV or PDF.

Typical Compton edges for common gamma energies (mc² = 511 keV, θ = 180°).

Source energy (keV)	Backscatter photon (keV)	Compton edge (keV)
511	170.33	340.67
662	184.33	477.67
1173	208.57	964.43
1332	214.87	1117.13

Values are rounded for readability. Use the calculator for exact results.

1. Meaning of the Compton edge

The Compton edge is the maximum kinetic energy a recoil electron can receive from a single Compton scatter. In gamma spectra it sits at the upper end of the Compton continuum when the scattered photon escapes. Its value is a physics limit set by the incident energy E and the electron rest energy mc^2.

2. Why 180 degrees sets the maximum

Energy transfer increases with scattering angle. The maximum occurs for backscatter at theta = 180 degrees, where (1 - cos(theta)) reaches 2. At this limit the scattered photon energy is E_edge = E / (1 + 2E/mc^2), and the recoil electron reaches its maximum single-scatter value.

3. Inputs and unit handling

This calculator accepts E in eV, keV, MeV, or GeV and converts internally to keV. The default mc^2 value is 511 keV for electrons, which is appropriate for standard Compton scattering in matter. Non-default constants can be explored for sensitivity checks, but physical interpretation should remain consistent.

4. Connection to real detector spectra

The Compton continuum comes from partial energy deposition followed by photon escape. The photopeak corresponds to full absorption, while the edge corresponds to the largest single-scatter deposit. Finite energy resolution, multiple scatters, and geometry smear the ideal step into a broadened shoulder, so edge fitting is often model-based.

5. Useful reference values

Common benchmarks help validate a spectrum. For a 662 keV gamma (Cs-137), the Compton edge is about 477.67 keV and the backscatter photon is about 184.33 keV. For Co-60, 1173 keV gives an edge near 964.43 keV and 1332 keV gives an edge near 1117.13 keV. These values are widely used as quick cross-checks.

6. Material and resolution considerations

The edge position is fixed by kinematics, but its visibility depends on detector performance. A typical NaI(Tl) scintillator may show about 7% FWHM resolution at 662 keV, which strongly rounds the edge. High-purity germanium systems can be around 0.2% at similar energies, making continuum features sharper and calibration more repeatable.

7. Sensitivity and uncertainty

Calibration uncertainty shifts the apparent edge, especially if the spectrum is nonlinear near the continuum. Angle matters for general scattering calculations, but the Compton edge assumes 180 degrees. Multiple scattering can produce events above the single-scatter edge, so choose a consistent analysis window and method.

8. Common applications

Compton edge estimates support detector calibration, continuum interpretation, and cross-checks for Monte Carlo simulations. They are useful in Compton suppression studies, shielding evaluations, and lab exercises on scattering kinematics. Exporting CSV or PDF results helps document runs, analysis settings, and reporting requirements.

1) What is the difference between the Compton edge and the photopeak?

The photopeak is full photon energy deposition. The Compton edge is the maximum energy deposited by a single Compton scatter when the scattered photon escapes, so it lies below the photopeak for the same incident energy.

2) Why is the Compton edge always below the incident energy?

In Compton scattering, part of the energy remains with the scattered photon. Even for 180 degree backscatter, the photon energy is not zero, so the recoil electron cannot take the full incident energy.

3) Does changing the scattering angle change the edge?

Angle changes the scattered photon energy and recoil energy. The Compton edge specifically refers to the maximum recoil at 180 degrees. For other angles, use the calculator output for that theta to study the kinematics.

4) Should I ever change mc^2 from 511 keV?

For standard electron Compton scattering, keep mc^2 = 511 keV. Changing it is mainly for sensitivity checks or demonstrations. If you modify it, interpret results carefully because the calculation may no longer represent real electron scattering.

5) Can I input energies in MeV and output in keV?

Yes. Select the incident-energy unit you have (for example, MeV) and then choose the output unit you want. The calculator converts units consistently for the scattered photon energy, recoil energy, and Compton edge.

6) Why is my measured edge not sharp?

Real spectra include detector resolution, multiple scattering, and geometry effects, which smear the ideal edge into a shoulder. Background and pileup can further distort the continuum. Use a consistent fitting method rather than relying on one channel.

7) What is the Compton edge for a 1 MeV gamma ray?

For E = 1 MeV (1000 keV) and mc^2 = 511 keV, the single-scatter Compton edge is about 796.50 keV and the backscatter photon energy is about 203.50 keV. Use the calculator for exact values and conversions.