Compton Scattering Angle Energy Calculator

Calculator

Calculation mode Scattered energy from angle Angle from energies Compare angle & energy inputs

Select how you want to solve the Compton relation.

Incident photon energy (E)

eVkeVMeVGeVJ

Typical lab gamma energies are in keV or MeV.

Angle unit Degrees (deg) Radians (rad)

Angle inputs and angle outputs use this choice.

Scattering angle (θ)

Valid range: 0–180 deg or 0–π rad.

Scattered photon energy (E′)

eVkeVMeVGeVJ

Used for solving angle or comparing inputs.

Output energy unit eVkeVMeVJ

Energies in the results table follow this choice.

Decimal places 2345678910

Higher precision helps compare experimental datasets.

Calculate

Formula Used

This calculator uses the Compton scattering energy relationship for photons scattering from free electrons. With incident photon energy E and scattering angle θ, the scattered photon energy is:

E′ = E / [ 1 + (E / (m_ec²)) (1 − cosθ) ]

If you instead know E and E′, the angle follows from:

cosθ = 1 − (m_ec²) (1/E′ − 1/E)

The wavelength shift is computed using Δλ = λ′ − λ = λ_C(1 − cosθ), where λ_C is the electron Compton wavelength.

How to Use This Calculator

1. Pick a calculation mode that matches your known variables.
2. Enter the incident photon energy and select its unit.
3. If needed, enter the scattering angle or the scattered energy.
4. Choose output unit and decimal precision for reporting.
5. Press Calculate to view results above this form.
6. Use CSV or PDF export for lab notes and reports.

Example Data Table

Example values use an incident energy of 662 keV (common gamma source).

Compton Scattering Angle–Energy Article

1) What Compton scattering tells you

Compton scattering describes how an X‑ray or gamma photon transfers energy to an electron and leaves at a new angle. The measurable link between scattering angle and outgoing photon energy makes it a practical tool for spectroscopy, imaging, and radiation shielding studies. It models interactions with free or weakly bound electrons at these energies.

2) Key constants used in the calculation

The calculation relies on the electron rest energy m_ec² = 511 keV. A related quantity is the Compton wavelength λ_C ≈ 2.426×10⁻¹² m, which controls the wavelength shift at a given angle.

3) Angle to scattered‑energy relationship

For an incident energy E and scattering angle θ, the scattered energy is E′ = E / (1 + (E/511)(1 − cosθ)) when energies are in keV. Larger angles increase (1 − cosθ), so E′ decreases. Example: for E = 662 keV at 90°, E′ is about 289 keV.

4) Electron kinetic energy and spectrum features

Energy conservation gives the recoil‑electron kinetic energy as T = E − E′. This value is often what a detector responds to when a photon scatters and then deposits energy. For a 662 keV photon, near‑backscatter events can yield T close to 478 keV.

5) Useful limits: forward and backscatter

At θ = 0°, cosθ = 1, so E′ ≈ E and the transfer is minimal. At θ = 180°, the photon is backscattered and the energy drop is largest. For E = 662 keV, the backscatter energy is about 184 keV.

6) Choosing units and interpreting outputs

This calculator supports common energy units and reports E′, T, and the wavelength shift. The wavelength shift is small for high‑energy photons, so using Ångström output helps keep values readable. Keep the same output unit and decimals when comparing multiple detector runs.

7) Measurement geometry and typical angles

Many lab setups place detectors at angles like 30°, 60°, 90°, and 120°. Small angles keep E′ close to E, while larger angles emphasize energy transfer and improve peak separation.

8) Uncertainty and reporting

Angle uncertainty propagates through cosθ, so degree‑level errors matter most near 90° and above. Report results with consistent precision, and export CSV or PDF to preserve units and assumptions accurately.

FAQs

1) What is the input energy range?

Any positive photon energy works, but the model is most used for X‑rays and gamma rays. Typical labs use tens of keV to a few MeV, depending on source and detector response.

2) Why does scattered energy drop with angle?

Higher angles increase momentum transfer to the electron. The term (1 − cosθ) grows as θ increases, raising the denominator in the equation and reducing E′.

3) What does electron kinetic energy represent?

T = E − E′ is the energy given to the recoil electron in a single scatter. It is closely related to the energy deposited in a detector when the photon is later absorbed.

4) Can this find the angle from measured E′?

Yes. Select the mode that solves for θ using the incident energy and the scattered energy. The calculator inverts the Compton formula to return an angle in degrees or radians.

5) What happens at 0° and 180°?

At 0° there is almost no energy change, so E′ ≈ E. At 180° the energy loss is maximal, producing a characteristic backscatter energy used in radiation measurements.

6) Why include wavelength shift?

The wavelength shift provides a complementary view that is independent of the original wavelength scale. It is useful when comparing datasets from different photon energies or when working in diffraction‑style units.

7) How should I report results in a lab write‑up?

State the incident energy, angle or measured scattered energy, chosen units, and computed outputs. Include uncertainty sources like angle alignment and detector resolution, then attach the exported CSV or PDF for traceability.