Model simple depth–dose curve for charged particle beams. Switch mediums, energies, and smoothing controls easily. Get peak range, falloff, and printable results in seconds.
| Energy (MeV) | Estimated range (cm) | Approx peak depth (cm) | Use case note |
|---|---|---|---|
| 70 | ≈4.06 | ≈4.00 | Shallow targets and small phantoms |
| 100 | ≈7.63 | ≈7.51 | Head and neck depth checks |
| 150 | ≈15.64 | ≈15.41 | Mid-depth coverage in water |
| 200 | ≈26.02 | ≈25.63 | Deeper regions, thicker slabs |
| 250 | ≈38.62 | ≈38.04 | Near maximum clinical depth |
This tool estimates the particle CSDA range (distance to near-complete energy loss) using a power-law approximation:
A smooth Bragg curve is then generated as a sum of a baseline entrance term, a gradual rise term, and a Gaussian peak near the end of range. For the spread-out option (SOBP), multiple layers with shorter ranges are blended across a selected width.
Charged particles deposit modest dose at entry, then rise sharply near end of range. That maximum is the Bragg peak, and its depth tracks the initial energy. This tool reports peak depth from the modeled curve and normalizes peak dose to 100%.
In water-like tissue, common proton energies span about 70–250 MeV. With the same range law used here, 70 MeV reaches ~4.1 cm, 100 MeV ~7.6 cm, 150 MeV ~15.6 cm, 200 MeV ~26.0 cm, and 250 MeV ~38.6 cm. Use these as quick sanity checks
Range scales roughly with inverse density (R ∝ 1/ρ) in this simplified model. Moving from water (ρ≈1.00) to lung (ρ≈0.30) increases range by ~3.3×, while bone (ρ≈1.85) shortens range to ~0.54×. Presets help compare media quickly
The σ input (mm) widens or narrows the Gaussian peak term. Smaller σ yields a sharper peak and steeper distal edge, while larger σ mimics energy spread and range straggling for comparison studies. Step size controls sampling: 20 cm depth with 2 mm steps gives ~101 rows, while 1 mm gives ~201.
Dose is normalized so the maximum equals 100%. The entrance value depends on entrance %, σ, and amplitude settings. The peak-to-entrance ratio is a quick contrast indicator between entry and end-of-range dose. Higher amplitude usually increases this ratio.
Distal falloff is the distance from 80% to 20% on the post-peak side. Smaller numbers indicate a sharper cutoff. With a 2 mm step, the falloff is effectively quantized in ~2 mm increments, so smaller steps improve the readout resolution.
A spread-out peak is formed by summing multiple layers with shorter ranges. If you select width 4 cm and 9 layers, layer ranges span that 4 cm window from distal to proximal. Weights are normalized to sum to 100%, and the least-squares option aims to flatten dose across the window.
Exports include depth, normalized dose, and a cumulative relative integral. For QA-style checks, expect a smooth rise, a clear maximum near computed range, and a monotonic decrease beyond range. The cumulative column helps compare overall curve area between two runs, even when peak shapes differ.
It is the approximate depth where the particle has lost nearly all kinetic energy, assuming continuous slowing down. Real beams have spread, so measured range can differ slightly.
No. It is an educational approximation for trends and rough checks. Planning needs validated stopping-power tables, beamline measurements, and a clinically verified dose engine.
For heavier ions, energy is often expressed per nucleon. This tool uses a simple A/Z² scaling and treats the input as MeV per nucleon for a first-pass comparison.
Use 1–2 mm for smoother curves and better falloff resolution. Use 3–5 mm when you need faster runs and smaller exports. Very small steps create large tables.
It widens the modeled Bragg peak and softens the distal edge. Larger σ approximates added energy spread and straggling, while smaller σ produces a sharper, narrower peak.
The tool builds several layer curves, then solves a small linear system over plateau depths to find weights that make the summed dose close to flat. Weights are normalized and clipped nonnegative.
It is a trapezoidal integral of normalized dose versus depth, in relative units. It helps compare overall area under the curve between runs, but it is not an absolute physical dose.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.