Model attenuation using exponential, HVL, or TVL. Enter mass coefficients, density, and thickness units easily. Get clear transmission, required shielding, and downloadable reports now.
The narrow-beam attenuation law models how gamma intensity decreases through a shield:
I = I₀ · e^(−μx)
If you have a mass attenuation coefficient, convert it to a linear coefficient:
μ = (μ/ρ) · ρ
Half-value and tenth-value layers are:
HVL = ln(2)/μ and TVL = ln(10)/μ
For a desired transmission ratio R = I/I₀, required thickness is:
x = −ln(R)/μ
Illustrative values for practicing inputs. Replace with your verified data.
| Material | μ (1/cm) | Thickness (cm) | Transmission (I/I₀) | Transmission (%) |
|---|---|---|---|---|
| Lead (example) | 1.200 | 1.0 | 0.3010 | 30.10% |
| Steel (example) | 0.450 | 2.0 | 0.4066 | 40.66% |
| Concrete (example) | 0.120 | 10.0 | 0.3010 | 30.10% |
| Water (example) | 0.070 | 15.0 | 0.3499 | 34.99% |
| Aluminum (example) | 0.180 | 3.0 | 0.5827 | 58.27% |
Gamma attenuation is the reduction of intensity as photons pass through matter. This calculator focuses on primary-beam loss, so the output is a clean transmission ratio, I/I₀. Ratios make comparisons easy across different measurement units.
The core model is I = I₀·e^(−μx). If μ = 0.15 1/cm and x = 10 cm, the ratio is e^(−1.5) = 0.223. That means about 22.3% of the original intensity remains, while 77.7% is removed from the narrow beam.
Many tables publish mass attenuation coefficient (μ/ρ) because it is less dependent on physical form. Convert it using μ = (μ/ρ)·ρ. Example: μ/ρ = 0.07 cm²/g and density ρ = 2.35 g/cm³ gives μ = 0.1645 1/cm, which you can use directly with thickness.
Half-value layer (HVL) and tenth-value layer (TVL) compress the exponential model into familiar steps. HVL = ln(2)/μ, TVL = ln(10)/μ. After n HVLs, the ratio is 0.5ⁿ (three HVLs → 12.5%). After n TVLs, the ratio is 0.1ⁿ (two TVLs → 1%).
This tool reports transmission as a ratio and optionally as dB: dB = −10·log10(R). If R = 0.01, transmission is 1% and attenuation is 20 dB. Percent values are simply R×100, which helps when comparing “before” and “after” survey readings.
When you choose a target ratio, the thickness comes from x = −ln(R)/μ. Example: μ = 0.20 1/cm and R = 0.05 gives x = −ln(0.05)/0.20 = 14.98 cm. The calculator performs unit conversions so you can enter mm, cm, or meters consistently.
Typical μ values vary widely with photon energy and material composition, so always use verified references. As a practical input sanity check, μ often falls between about 0.01 and 2.0 1/cm for common shields across many energies. Remember: 1/m converts to 1/cm by dividing by 100. For density, kg/m³ converts to g/cm³ by dividing by 1000. For mass coefficient, m²/kg converts to cm²/g by multiplying by 10.
Field measurements can differ because scatter adds “buildup” and geometries vary. Use these results as an estimate for planning, learning, and quick review, not as a sole safety basis. For real designs, follow local regulations and consult qualified radiation-safety professionals.
μ is the linear attenuation coefficient. It describes how quickly a narrow gamma beam decreases per unit thickness. Larger μ means stronger attenuation for the same shield thickness.
Different references report attenuation differently. The tool converts any one of these inputs into μ, then uses the same exponential model to compute transmission, HVL, TVL, or required thickness.
No. The ratio I/I₀ is unitless, so you can use cps, µSv/h, or any consistent unit. The transmitted value I will be reported in the same unit you selected for I₀.
Enter a number strictly between 0 and 1, such as 0.1, 0.01, or 0.001. Smaller values mean more reduction and will produce a larger required thickness for the same μ.
This model assumes a narrow, unscattered beam. In real setups, scattered photons can increase the detected intensity. Geometry, source energy spectrum, and buildup factors can shift the measured attenuation.
A ratio above 1 usually indicates incorrect inputs, such as negative thickness, wrong units, or an invalid coefficient. Recheck conversions and ensure μ and thickness are positive values.
The math form is similar, but coefficients and buildup behavior depend strongly on spectrum and filtration. For diagnostic or industrial X-ray work, use coefficients and standards that match the specific beam quality.
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.