Radiation Shielding Calculator

Both are defined in terms of the same exponential attenuation, just for different reduction targets — HVL is the thickness for a 2x reduction, TVL for a 10x reduction. Since attenuation is exponential, TVL = HVL × log₂(10) ≈ HVL × 3.32, because it takes log₂(10) ≈ 3.32 doublings of reduction (i.e., HVLs) to reach a full order-of-magnitude (10x) reduction.

The pure exponential attenuation formula assumes every photon that interacts with the shield is either fully absorbed or removed from the beam, but in reality some photons scatter (Compton scattering) and lose only some energy and direction, then continue through the shield and still contribute to dose on the other side. The calculator's buildup factor (B ≈ 1 + 0.5 × number of HVLs) is a simplified linear approximation of this effect — real buildup factors are tabulated by specific photon energy, shield material, and thickness, so this is a rough correction rather than a precise one.

Required thickness depends on the material's HVL value (which you enter separately, since HVL varies by material and photon energy), while shield weight is that thickness times the material's bulk density. Lead's much smaller HVL for a given isotope means less thickness is needed, but its high density (11,340 kg/m³) can still produce a comparable or heavier shield per square meter than a thicker but far less dense material like concrete (2,300 kg/m³), depending on the specific HVL values involved.

HVL depends on how strongly a material attenuates gamma photons at a specific energy, and different isotopes emit gammas at different characteristic energies. Higher-energy gammas penetrate more easily and require a thicker HVL to halve their dose rate — for example, lead's HVL for Co-60 (1.2 cm, higher-energy gammas) is roughly double its HVL for Cs-137 (0.65 cm, lower-energy gammas), which is why this calculator asks you to enter the HVL value specific to your isotope and material combination rather than assuming one.