Half-Value Layer Calculator

How it is calculated

A narrow beam weakens exponentially, I = I₀ × e−μx. Setting I / I₀ = 1/2 and solving for the thickness x gives HVL = ln(2) / μ. The tenth-value layer, where the beam falls to 1/10, is TVL = ln(10) / μ. Here μ is the linear attenuation coefficient in cm⁻¹ (per centimetre), and both layers are returned in centimetres, rounded to four decimals. Because the formula depends only on μ, it takes no beam energy or material name: you must already know the μ for that material at that energy. μ must be above zero. A mass attenuation coefficient (cm²/g) is a different quantity and must first be multiplied by the material density in g/cm³ to give μ.

Common mistakes

• Entering the mass attenuation coefficient (cm²/g) as if it were μ. Multiply by density first, otherwise the thickness will be wrong by a factor equal to the density.
• Using a coefficient for the wrong beam energy. μ changes strongly with photon energy, so a value for one kVp or isotope does not apply to another.
• Mixing length units. The tool returns centimetres for μ in per centimetre; a μ taken from a table in per metre must be divided by 100 before entering.
• Expecting HVL to give the thickness for 90% or full absorption. A material never absorbs a beam completely: use TVL for one tenth, or multiply HVLs for other fractions.
• Applying the result to scatter-heavy or broad-beam geometry. The formula is for a narrow beam, and real shielding needs extra thickness.