Calculator
Enter energy and material. Add optional layers to subtract water-equivalent thickness. Results appear above this form after submission.
Example Data Table
Sample outputs in water using the empirical areal range fit.
| Energy (MeV) | Range in water (cm) | Estimated Bragg peak (cm) |
|---|---|---|
| 50 | 2.2367 | 2.1696 |
| 100 | 7.6282 | 7.3994 |
| 150 | 15.6352 | 15.1662 |
Formula Used
This tool estimates the continuous slowing down approximation (CSDA) range using a power-law fit in g/cm² and converts it to a physical thickness with the selected density.
Note: These models are engineering approximations for quick planning. For high-accuracy work, use tabulated stopping power data (ICRU/NIST) and full transport methods.
How to Use This Calculator
- Enter the incident proton energy in MeV.
- Select the target material that the beam will traverse.
- Pick a range model: reference fit, scaled, or user-defined.
- Optional: add layers (air gaps, windows, plastics) with thickness in cm.
- Optional: set incidence angle and energy spread for projections and uncertainty.
- Press Compute Range to show results under the header.
- Use the export buttons to download CSV or a PDF report.
Technical Notes on Proton Range Estimation
1) What “range” means in practice
The calculator reports a CSDA-style penetration depth: the distance where the beam’s mean energy is exhausted. In experiments and therapy planning, the more operational metric is the practical range (often near the distal 80–90% dose point), which typically lies close to the computed projected depth.
2) Energy bands and typical depths
Clinical proton beams span 70–250 MeV. Using power-law fits, that corresponds to water ranges from a few centimeters up to about three decimeters. The example table (50, 100, 150 MeV) highlights the non-linear scaling that makes energy changes impactful at high energy.
3) Why the calculator uses areal range
Range is first estimated as areal density (g/cm²). This is convenient because it separates energy loss physics from geometry: converting to a thickness only requires the chosen material density. For water, 1 g/cm² equals 1 cm by definition, which keeps sanity checks straightforward.
4) Material effects via density and Z/A
When you select Bragg–Kleeman scaling, the calculator adjusts the water fit using an effective Z/A term. This captures major material trends. Dense media reduce physical thickness for the same areal range, so a proton that travels 15 cm in water travels less in plastics or metals at the same energy.
5) Layered paths and water-equivalent thickness
Real beamlines often include air gaps, windows, and phantom inserts. The layer module converts each layer to water-equivalent thickness (WET) using an estimated relative stopping power (RSP) and subtracts it before converting to the target’s physical thickness. This is useful for quick “what-if” checks of added slabs or setup changes.
6) Angle of incidence and projected depth
If the beam enters at an angle, the path length through the medium is longer than the normal depth. The calculator reports both: the along-path range and the projected depth normal to the surface via cos(θ). This helps interpret depth in slabs or imaging geometries where normal depth is the reference axis.
7) Uncertainty from energy spread and straggling
The range uncertainty σ is estimated by propagating an energy spread through the range–energy slope and adding a small straggling term. For narrow beams, even a 1% energy spread can shift the distal region by millimeters, while larger spreads broaden the falloff more noticeably. Treat σ as a planning guide, not a guarantee.
8) Interpreting outputs and exporting results
Use the depth–dose table to understand where the distal peak sits relative to the computed range; the peak is shown near the end of the track. Export CSV for spreadsheets and QA logs, and export PDF to attach a compact summary to lab notes. For definitive work, validate against tabulated stopping powers and measured depth–dose curves.
FAQs
1) Which range model should I choose?
Use the empirical areal fit for quick water-like estimates, Bragg–Kleeman scaling for approximate material differences, and the user power law when you have a fit from your own reference data or literature.
2) What is WET and why does it matter?
Water-equivalent thickness converts a layer into an equivalent depth in water based on stopping behavior. Subtracting WET accounts for beamline components and setup layers that consume range before the target medium begins.
3) Does this replace NIST/ICRU stopping power tables?
No. It is an engineering approximation for planning, education, and rapid sensitivity checks. For high-accuracy calculations, use tabulated stopping powers and validated range–energy data for the exact material and beam conditions.
4) Why do I see both “path length” and “projected depth”?
Path length is the distance traveled along the beam direction. Projected depth is the normal-to-surface depth, computed with cos(θ). Use projected depth when comparing to depth markers defined along a normal axis.
5) How should I interpret the Bragg peak depth shown?
The displayed peak is a simple placement near the distal end (about 97% of the projected range). Real peak position and falloff depend on energy spread, scattering, and material heterogeneity, so verify with measured curves.
6) What energy spread values are reasonable?
Well-collimated monoenergetic beams can be below 1%, while clinical beams may be broader depending on modulation and delivery. If unsure, start with 0.5–1% for lab beams or a few percent for broader beams.
7) Why is the dose table “normalized”?
It is a qualitative depth profile for visualization. Values are scaled so the maximum equals 1, which helps compare shapes across energies. It is not a substitute for absolute dosimetry or a full transport simulation.