Half-Value Layer Calculator

About this calculator

The half-value layer (HVL) is the thickness of a given material — lead, concrete, aluminum, tissue — needed to reduce the intensity of a beam of X-rays or gamma rays to exactly half its original value. It is derived directly from the material’s linear attenuation coefficient (μ), which describes how quickly a beam is absorbed and scattered per unit thickness under the exponential attenuation law I = I₀e^(−μx). Setting the transmitted fraction to one half and solving for x gives HVL = ln(2) / μ, a single number that lets physicists reason about shielding without working through the exponential each time.

A related figure, the tenth-value layer (TVL = ln(10) / μ), gives the thickness needed to cut intensity to one-tenth, and the two are simply proportional: TVL ≈ 3.32 × HVL. Radiologic physicists and radiation safety officers use HVL and TVL to specify shielding barriers around X-ray rooms and gamma sources, and HVL is also a standard beam-quality metric in diagnostic imaging quality assurance — a low HVL for a given kVp setting can flag inadequate beam filtration. This calculator converts a linear attenuation coefficient into both values directly.