Calculator Inputs
The page stays in a single-column flow. Inside the calculator, inputs use a responsive grid with three columns on large screens, two on medium, and one on mobile.
Plotly Graph
The graph shows estimated material range versus proton energy for the current density and stopping modifier.
Formula Used
This calculator uses an educational power-law range model. It first estimates proton areal range in a water-like reference medium and then scales that result for material density and your chosen stopping modifier.
Areal Range (g/cm²) ≈ 0.0022 × E1.77 Estimated Material Range (cm) ≈ Areal Range ÷ (ρ × k) Conservative Range (cm) = Estimated Material Range × (1 − Margin/100)- E = proton kinetic energy in MeV
- ρ = material density in g/cm³
- k = user-selected stopping modifier
- Margin = safety reduction for a conservative estimate
How to Use This Calculator
- Enter the proton beam energy in MeV.
- Select a preset material or choose custom values.
- Review or edit density and the stopping modifier.
- Add a safety margin if you want a conservative depth.
- Optionally enter a target thickness to test penetration.
- Choose the graph upper energy limit.
- Press the calculate button.
- Read the result card above the form, then export CSV or PDF if needed.
Example Data Table
These examples use the same empirical relation with a stopping modifier of 1.00.
| Energy (MeV) | Areal Range (g/cm²) | Water Range (cm) | Soft Tissue Range (cm) | PMMA Range (cm) |
|---|---|---|---|---|
| 60 | 3.0885 | 3.0885 | 2.9137 | 2.6174 |
| 100 | 7.6282 | 7.6282 | 7.1964 | 6.4646 |
| 150 | 15.6352 | 15.6352 | 14.7502 | 13.2502 |
| 200 | 26.0163 | 26.0163 | 24.5437 | 22.0477 |
| 250 | 38.6168 | 38.6168 | 36.4310 | 32.7261 |
Frequently Asked Questions
1) What does this calculator estimate?
It estimates proton penetration range from beam energy. The tool converts energy into an areal range and scales it using your material density and stopping modifier.
2) Is this suitable for clinical treatment planning?
No. This is an educational estimator. Clinical proton planning needs validated stopping power models, calibration data, uncertainty analysis, and dedicated medical planning systems.
3) Why does density matter so much?
Higher density means more mass is packed into each centimeter. That usually shortens geometric range because the proton loses energy through more material over the same distance.
4) What is the stopping modifier for?
The modifier lets you tune composition effects beyond simple density scaling. Keep it at 1.00 for a baseline estimate, or adjust it when you want stronger or weaker stopping behavior.
5) What is the conservative range?
It is the estimated range after reducing the nominal result by your safety margin. This is useful when you want a cautious depth rather than the full nominal penetration.
6) Why can similar densities still produce different real ranges?
Proton slowing depends on electron density, atomic composition, and nuclear effects, not density alone. Two materials with similar bulk density can still stop protons differently.
7) What do the CSV and PDF buttons export?
They export the current calculation summary so you can save, share, document, or compare runs without manually copying every result field.
8) What range definition is closest to this model?
It is closest to a smooth continuous-slowing-down style estimate. It does not explicitly model straggling, scattering tails, or detailed projected-range distributions.