Model scattered photons during shielding with simple inputs. See mean free paths and buildup quickly. Export tables, compare materials, and document your calculation steps.
Choose a material and enter thickness. For best accuracy, provide mu from trusted references. The built-in mu option is only a smooth estimate for quick exploration.
The number of mean free paths is: mu*t = mu × t, where mu is the linear attenuation coefficient and t is the shielding thickness.
A practical buildup estimate is modeled as: B = 1 + a(1 - e^(-b(mu*t)) ) + c(mu*t), where a, b, c are material-dependent fitting constants and a mild energy scaling is applied.
Transmission without buildup is T = e^(-mu*t). With buildup, T = B * e^(-mu*t), clamped to a maximum of 1.
| Material | Energy (MeV) | Thickness (cm) | mu (1/cm) | mu*t (mfp) | B (estimate) | Transmission (with buildup) |
|---|---|---|---|---|---|---|
| Concrete | 1.0 | 10 | 0.10 | 1.0 | ~1.77 | ~0.65 |
| Iron | 0.5 | 5 | 0.25 | 1.25 | ~2.32 | ~0.66 |
| Lead | 2.0 | 2 | 0.60 | 1.2 | ~2.82 | ~0.85 |
Example values are illustrative. Use trusted mu data for real designs.
Exponential attenuation describes the removal of primary photons, but real shields also create scattered photons that still reach the detector. The buildup factor (B) corrects this by scaling the uncollided transmission e^(-μt). In practical radiological work, ignoring buildup can underpredict exposure, especially when thickness produces multiple mean free paths.
Photon energy (MeV) controls interaction probabilities, while material composition controls scattering and absorption. Thickness sets the number of mean free paths: μt. For example, if μ = 0.10 1/cm and t = 10 cm, then μt = 1.0. This calculator accepts common thickness units and normalizes values internally to cm.
Mean free paths provide a compact way to compare situations. Values below about 0.5 often indicate modest attenuation and limited buildup. Values near 1–3 mean significant removal of the primary beam and increased importance of scatter. For very large μt, transmission becomes small, yet B can still increase the predicted transmitted fraction relative to the uncollided model.
Buildup factors are dimensionless and often start near 1.0 at small μt. Depending on energy and material, B can rise above 2 for moderate thickness and can be larger for deep penetration problems. High‑Z materials may reduce primary photons effectively, but their scatter behavior still depends on energy and geometry, so B does not automatically stay close to 1.
Suppose 1.0 MeV photons pass through 10 cm of concrete with μ = 0.10 1/cm. Uncollided transmission is e^(-1) ≈ 0.367. If an estimated buildup factor is B = 1.8, the corrected transmission becomes about 1.8 × 0.367 ≈ 0.661. That difference is substantial when translating transmission into dose or count rate.
For professional work, supply μ from trusted tabulations or measured data for your photon spectrum and material. The built‑in μ estimator is intentionally smooth and generalized to support “what‑if” exploration, not compliance calculations. If your shielding includes alloys, composites, or non‑standard densities, direct μ is strongly recommended.
Verify units first: μ must match the length unit used for thickness after conversion. Check that energy is consistent with the photon source (for gamma emitters or X‑ray beams). Review whether the geometry (broad beam vs narrow beam) aligns with your interpretation, since B is geometry dependent in formal methods.
When documenting results, record material, density assumptions, μ source, energy, and thickness, plus whether the scenario is a quick screening or a design basis. Use the CSV/PDF export to capture the computed μt, buildup factor, and transmissions. Treat this output as a planning estimate that should be validated for final decisions.
A buildup factor is a multiplier that accounts for scattered photons added to the uncollided beam after passing through shielding. It adjusts simple exponential attenuation to better reflect broad‑beam conditions.
More thickness increases interaction events. Even though the primary beam decreases, additional scatter can contribute to transmitted radiation. That contribution causes B to rise from near 1 toward larger values.
μt is the number of mean free paths through the shield. It is dimensionless and equals the attenuation coefficient multiplied by thickness. It helps compare different materials and thicknesses consistently.
No. Use direct μ from reliable references whenever accuracy matters. The estimator is a smooth approximation designed for fast screening and educational exploration, not strict engineering or regulatory reporting.
Physically, I/I0 should not exceed 1 for simple transmission reporting. This calculator clamps the “with buildup” transmission to 1, which is useful when B is applied outside its intended geometry assumptions.
Many practical checks involve roughly 0.06–2 MeV, depending on the source. Lower energies are more sensitive to material composition, while higher energies often need greater thickness for similar μt.
A large gap indicates scatter is likely important for your setup. Consider validating with reference buildup data, confirming geometry assumptions, and using spectrum‑appropriate μ values before making design decisions.
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.