Particle Range Calculator

Calculator Inputs

Pick a model, enter energy, and convert mass range to thickness.

Particle type

Best near tens–hundreds of MeV depending on model

Medium

Liquid water ~1 g/cm³

Kinetic energy (MeV)

Use total particle energy, not per nucleon.

Model

Empirical fits are educational approximations.

Custom: a (g/cm²)

Used when model = custom: R = a·E^b.

Custom: b (exponent)

Typical exponents range 1.2–2.0.

Constant S (MeV·cm²/g)

Used when model = constant S: R = E/S.

Density override

g/cm³

Useful for mixtures, foams, or nonstandard conditions.

Use override?

If yes, calculator uses the override density.

Output thickness unit

Result is also shown in mm/cm/m.

Reset

Formula used

This tool estimates the mass range (areal range) in g/cm², then converts it to a linear thickness using density:

Mass range: R_m (g/cm²)
Thickness: x (cm) = R_m / ρ

Model options:

Empirical fit: built-in particle-specific approximations R_m ≈ k·E^p (or an electron CSDA fit).
Custom power law: R_m = a·E^b, where a and b are provided by you.
Constant mass stopping power: R_m = E / S, where S is in MeV·cm²/g.

How to use this calculator

Select the particle type and target medium.
Enter kinetic energy in MeV.
Pick a model: empirical, custom power law, or constant stopping power.
Optionally override density for special materials or conditions.
Click Calculate Range to view results above the form.
Use CSV/PDF buttons to export your latest calculation.

Example data table

Example estimates using the empirical fit and typical densities.

Particle	Medium	Energy (MeV)	Mass range (g/cm²)	Thickness (cm)
Alpha (He²⁺)	Air (STP)	5	0.055902	45.63404
Proton (H⁺)	Water	50	2.236658	2.236658
Proton (H⁺)	Aluminum	100	7.628211	2.825263
Electron (β⁻)	Water	5	3.002149	3.002149

Examples are for learning and quick comparisons, not certification-grade shielding design.

FAQs

1) What does “mass range” mean?

Mass range is thickness multiplied by density, reported in g/cm². It compares penetration across materials without mixing up geometry and density effects.

2) Why are results only approximate?

Real stopping power varies with energy and material composition. These models are simplified fits for quick estimates and learning, so precision can differ from detailed databases.

3) When should I use the constant stopping power model?

Use it when you have a known average mass stopping power value and want a fast estimate. It is most reasonable over small energy changes or narrow ranges.

4) Can I use this for radiation shielding certification?

No. For compliance or safety-critical design, use validated datasets, Monte Carlo tools, and professional review. This calculator is for educational and early-stage comparisons.

5) Why does density override matter?

Many materials are porous or mixed, so their effective density differs from textbook values. Overriding density lets you approximate foams, composites, or temperature-dependent gases.

6) Which unit should I choose?

Pick the unit that matches your use case. mm works for thin layers, cm for lab-scale slabs, and m for larger shields. The tool also shows all three for convenience.

7) What if I already have an R = a·E^b relation?

Select the custom power law model, enter your a and b, then calculate. The output will convert your mass range into thickness for the selected medium or your override density.

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