Example data table
These values are illustrative examples for learning and interface testing, not a reference dataset.
| Particle | Energy (MeV) | Material (MeV·cm²/g) | Reference (MeV·cm²/g) | SPR |
|---|---|---|---|---|
| Proton | 150 | 4.20 | 4.80 | 0.875 |
| Proton | 200 | 3.95 | 4.30 | 0.919 |
| Alpha | 50 | 7.10 | 6.85 | 1.036 |
| Electron | 10 | 1.85 | 2.05 | 0.902 |
| Carbon ion | 300 | 11.2 | 10.6 | 1.057 |
Formula used
The stopping power ratio (SPR) compares the mass stopping power of a material to a reference medium at the same particle type and energy:
If you only know linear stopping power S = dE/dx and density ρ, the calculator converts to mass stopping power:
SPR is dimensionless when both mass stopping powers use consistent units.
How to use this calculator
- Select an input mode: mass stopping powers, or linear stopping plus density.
- Enter the particle type and kinetic energy used for your data.
- Provide the material and reference stopping values in your chosen units.
- Optionally add uncertainties to estimate a 1σ uncertainty for SPR.
- Press Calculate. Use the export buttons to download CSV or PDF.
Stopping power ratio in practical dosimetry
1) What the ratio represents
Stopping power ratio (SPR) compares the mass stopping power of a material to a reference medium for the same particle and kinetic energy. It is calculated as (S/ρ)material ÷ (S/ρ)reference. From the example table, 4.20 MeV·cm²/g divided by 4.80 MeV·cm²/g gives SPR = 0.875, so the material loses about 12.5% less energy per gram than the reference at that point.
2) Typical values and energy ranges
Magnitudes depend on particle type and energy. Proton datasets often cover about 70–250 MeV, while many electron datasets sit around 1–20 MeV. In condensed materials, mass stopping powers are often a few MeV·cm²/g and rise as particles slow, so energy must be stated alongside SPR.
3) Selecting a reference medium
Water is widely used as a reference because it is a convenient tissue surrogate and a common reporting standard. Air is often used for gas-filled detector work. If you change the reference medium, the ratio changes even when the material data are unchanged, so keep the reference consistent across comparisons.
4) Mass inputs versus linear inputs
If you already have mass stopping power (S/ρ), enter it directly. If you only have linear stopping power S (dE/dx) and density ρ, use (S/ρ) = S/ρ. Example: S = 9.60 MeV/cm and ρ = 1.00 g/cm³ yields 9.60 MeV·cm²/g. For keV/mm, multiply by 0.01 to get MeV/cm before dividing by density.
5) Unit checks that prevent mistakes
The calculator normalizes inputs to MeV·cm²/g so SPR stays dimensionless. A useful identity is that keV·cm²/mg is numerically equal to MeV·cm²/g. In contrast, MeV·cm²/kg is 1000 times smaller than MeV·cm²/g, so a missed conversion can shift SPR by a factor of 1000. Small unit mistakes can dominate the ratio more than physics effects.
6) Interpreting results
An SPR near 1.00 indicates the material is close to the reference in stopping behavior at that energy. Values below 1.00 imply less energy loss per unit mass, while values above 1.00 imply more. Because stopping varies with energy, avoid mixing values taken at different energies in one comparison.
7) Reporting and uncertainty
For traceable results, record particle, energy, labels, and the source of stopping data. If uncertainties are available, the calculator applies √((σA/A)²+(σB/B)²). Example: 1.5% on the material and 1.0% on the reference combine to about 1.8%; for SPR = 0.875, that is roughly ±0.016 (1σ). Use CSV and PDF exports for documentation.
Frequently asked questions
1) What does SPR tell me?
It tells how energy loss per unit mass in your material compares with a reference at the same particle and energy. SPR is dimensionless and is commonly reported alongside the energy value.
2) Which input mode should I use?
Use mass stopping mode if you already have (S/ρ) values. Use linear mode when you only know dE/dx and density, and let the calculator convert them into mass stopping power internally.
3) Why must energy match for both media?
Stopping power changes with particle energy. Mixing values taken at different energies can create an incorrect ratio that reflects the mismatch, not a true material difference.
4) Can I enter keV·cm²/mg directly?
Yes. keV·cm²/mg is numerically equal to MeV·cm²/g, so the ratio stays consistent. Select the matching unit option so the report clearly documents your inputs.
5) How should I handle density in linear mode?
Enter density in g/cm³ and linear stopping in MeV/cm or keV/mm. The calculator converts to MeV/cm if needed, then divides by density to obtain (S/ρ) in MeV·cm²/g.
6) How is uncertainty computed?
If you enable uncertainty propagation, the calculator combines relative uncertainties using √((σA/A)²+(σB/B)²) and multiplies by SPR to produce an absolute 1σ estimate.
7) Are the example values a reference dataset?
No. The example table is for learning and interface testing. For real work, use peer-reviewed tabulations, measurements, or validated simulations and keep the particle type and energy consistent.