Bethe-Bloch Energy Loss Calculator
Calculate the mean and most probable energy loss, straggling and estimated stopping thickness of a heavy charged particle in matter.
A Muon at 370 MeV/c crossing 300 µm of Silicon
| Most probable loss | 78.18 keV |
|---|---|
| Mean loss (Bethe × thickness) | 115.9 keV |
| ⟨dE/dx⟩ | 1.659 MeV cm²/g |
| FWHM of the Landau peak | 23.24 keV |
| κ | 4.777e-4 — Landau regime |
| Stops in (lower-energy-truncated estimate) | 61.68 cm (143.7 g/cm²) |
| Kinetic energy | 279.1 MeV |
| Maximum single-collision transfer | 12.11 MeV |
| Density effect | 0.4571 |
| β, γ, βγ | 0.9616; 3.642; 3.502 |
| pairs/µm — mean | 106.7 |
| pairs/µm — most probable | 71.99 |
| Pair-creation energy | 3.62 eV |
The range is integrated down to βγ = 0.05, so it is a lower-energy-truncated estimate. Shell and Barkas corrections are omitted, and are particularly relevant at low energies and in heavy materials.
Sources: PDG; NIST ESTAR; NIST PSTAR; Bertolini & Coche (w).
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Batch runs over a table of inputs, a PDF report with inputs, method and citations, CSV export and saved cases. Join the waiting list and we will write once, when it opens.
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Example: How much energy does a 100 MeV proton lose in 300 micrometres of silicon?
Proton CSDA ranges
The range is integrated down to βγ = 0.05, so it is a lower-energy-truncated estimate. Shell and Barkas corrections are omitted, and are particularly relevant at low energies and in heavy materials.
| Kinetic energy (MeV) | Water (g/cm²) | Silicon (g/cm²) | Lead (g/cm²) |
|---|---|---|---|
| 10 | 0.1185 | 0.1579 | 0.3164 |
| 50 | 2.219 | 2.828 | 4.889 |
| 100 | 7.708 | 9.7 | 16.14 |
| 200 | 25.95 | 32.34 | 52.31 |
| 500 | 117 | 144.6 | 227.2 |
Cite this
ScienceShot. Energy-loss calculator. https://scienceshot.com/energy-loss-calculator.
Sources: PDG; NIST ESTAR; NIST PSTAR.
Reviewed by a physicist with CERN and data-centre industry experience
ScienceShot calculation.
Cite this page
ScienceShot. (2026). Bethe-Bloch Energy Loss Calculator [Online calculator]. https://scienceshot.com/energy-loss-calculator
@misc{scienceshot-energy-loss-calculator-2026,
author = {{ScienceShot}},
title = {{Bethe-Bloch Energy Loss Calculator}},
year = {2026},
note = {Online calculator},
url = {https://scienceshot.com/energy-loss-calculator}
}