X Ray Attenuation Calculator
Use direct linear attenuation data or derive it from mass attenuation and density. Choose the solve mode that fits your shielding task.
For realistic shielding design, use attenuation data matched to beam energy and material composition. Broad beam buildup should come from validated reference data.
Example Data Table
These sample rows show how the exponential model behaves for different barrier cases.
| Case | Incident I₀ | μ (cm⁻¹) | Thickness (cm) | Buildup B | Transmitted I | Attenuation % |
|---|---|---|---|---|---|---|
| Sample Plate A | 100.00 | 0.450 | 1.20 | 1.00 | 58.275 | 41.73% |
| Sample Barrier B | 100.00 | 0.750 | 2.50 | 1.10 | 16.869 | 83.13% |
| Sample Sheet C | 50.00 | 1.200 | 0.80 | 1.00 | 19.145 | 61.71% |
Formula Used
Transmitted intensity equals the incident intensity multiplied by the buildup factor and the exponential attenuation term.
Linear attenuation equals mass attenuation times density. This converts material property data into path-based attenuation in cm⁻¹.
Required thickness is found by rearranging the attenuation equation for the barrier depth.
Half-value layer and tenth-value layer show how much thickness reduces the beam to 50 percent and 10 percent.
How to Use This Calculator
- Select the solve mode based on what you need: transmitted intensity, thickness, linear coefficient, or mass coefficient.
- Enter the incident beam intensity and, when needed, the target transmitted intensity.
- Choose the attenuation input method. Use a direct linear coefficient or combine mass attenuation with density.
- Set thickness and thickness units. If you are solving thickness, the calculator returns the required depth in your selected unit.
- Choose narrow beam for simple Beer–Lambert attenuation or broad beam if you already have an appropriate buildup factor.
- Click Calculate Attenuation to show the result summary above the form, then export the results as CSV or PDF if needed.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates transmitted X ray intensity, required barrier thickness, attenuation coefficients, HVL, TVL, optical depth, and dose reduction factors.
2. When should I use mass attenuation instead of linear attenuation?
Use mass attenuation when your reference data is reported in cm²/g. Multiply it by density to obtain the linear coefficient used in path attenuation.
3. Why does beam energy matter?
Attenuation changes with photon energy. Always pair the material coefficient with the same beam energy range used in your shielding problem.
4. What is the difference between narrow and broad beam geometry?
Narrow beam assumes scattered photons are excluded. Broad beam includes scatter effects, often modeled with a buildup factor greater than one.
5. What does HVL tell me?
HVL is the thickness that halves the beam intensity. It is useful for quick comparisons between candidate shielding materials.
6. Can I use this tool for medical or regulatory design?
Use it for screening, education, and early engineering studies. Final medical or regulatory designs need validated data, geometry checks, and expert review.
7. Why can attenuation percent look lower than expected with buildup?
A buildup factor adds scattered radiation back into the detected beam. That raises transmitted intensity compared with the pure exponential term alone.
8. What unit should I use for thickness?
Use any supported thickness unit. The calculator internally converts to centimeters, applies the equations, and returns results in your chosen unit.