Calculator inputs
Example data table
| Case | Particle | Material | Energy | Thickness | Mass stopping power | Linear stopping power | Estimated exit energy |
|---|---|---|---|---|---|---|---|
| 1 | Proton | Aluminum | 150 MeV | 0.50 cm | 4.2164 MeV·cm²/g | 11.3843 MeV/cm | 144.3079 MeV |
| 2 | Alpha Particle | Water | 20 MeV | 1.00 cm | 315.8840 MeV·cm²/g | 315.8840 MeV/cm | 0.0000 MeV |
| 3 | Carbon Ion | Silicon | 300 MeV | 0.20 cm | 597.7071 MeV·cm²/g | 1392.0598 MeV/cm | 21.5880 MeV |
Example rows illustrate the calculator workflow. They are engineering estimates from the same model implemented above.
Formula used
This calculator uses a heavy charged particle stopping power model based on the Bethe-style collision stopping power expression:
S/ρ = K × z² × (Z/A) × (1/β²) × [0.5 ln((2mec²β²γ²Tmax)/I²) − β² − δ/2 − C]
Here, S/ρ is mass stopping power, K is the stopping constant, z is projectile charge, Z/A is the target ratio, β and γ are relativistic factors, Tmax is the maximum transferable energy, I is mean excitation energy, δ is density correction, and C represents any additional correction term.
Linear stopping power is found from S = (S/ρ) × ρ. Estimated energy loss through the selected path is ΔE = S × teff, where the effective path length is angle-adjusted using teff = t / cos(θ).
This tool is intended for protons, alpha particles, and heavy ions. It is not a transport solver for photons, neutrons, or detailed electron interactions.
How to use this calculator
- Select a particle preset or choose a custom heavy ion.
- Enter the kinetic energy and choose the correct energy unit.
- Select a material preset, or enter custom density, Z/A, and mean excitation energy.
- Enter physical thickness, thickness unit, and beam incident angle.
- Adjust density correction and any additional correction term if you have better material data.
- Press the calculate button to show the result section above the form.
- Review stopping power, LET, estimated energy loss, exit energy, and approximate range.
- Download CSV for spreadsheets or PDF for reporting and documentation.
Frequently asked questions
1. What does stopping power mean?
Stopping power is the average energy lost by a particle per unit path length while it moves through matter. Higher values mean faster energy loss.
2. Which radiation types fit this calculator?
This model is best for protons, alpha particles, and heavy ions. It is not intended for photon shielding, neutron moderation, or detailed electron transport work.
3. Why does incident angle matter?
A larger angle increases the effective material path. More path length means greater energy loss, even when the physical slab thickness stays unchanged.
4. What is mass stopping power?
Mass stopping power normalizes energy loss by density. It lets you compare different materials more fairly before converting to linear stopping power.
5. Why can the particle stop completely?
If estimated energy loss exceeds the incident kinetic energy, the model reports zero exit energy. That means the selected path is sufficient to stop it.
6. Are the range values exact?
No. The displayed range is a first-order engineering estimate based on current stopping power. Accurate range work usually needs tabulated or iterative transport data.
7. What are density and additional corrections?
These inputs let you tune the logarithmic stopping term when you have better material data or need a closer engineering approximation for a known case.
8. When should I use custom material inputs?
Use custom inputs when your target is an alloy, composite, coating, process fluid, or engineered medium not represented by the included presets.