As an X-ray beam passes through matter, photons are progressively absorbed or scattered. This reduces the intensity of the transmitted beam. The attenuation of the beam follows the exponential attenuation law:

I = I₀​e^−μx

where I₀​ is the initial intensity, I is the transmitted intensity, μ is the linear attenuation coefficient of the filter material, and $x$ is the thickness of the absorbing material.

The half-value layer is defined as the thickness of material required to reduce the beam intensity to half of its initial value:

I = I₀ / 2

At this point the thickness of the tissue x = HVL. Substituting this into the attenuation equation gives:

I₀ / 2 = I₀​e^−μHVL

Solving for HVL yields:

HVL = ln2 / μ

This relationship shows that HVL depends on the attenuation coefficient of the material. Because the attenuation coefficient decreases as photon energy increases, higher-energy X-ray beams have larger HVLs.

In diagnostic radiology, HVL is typically measured using aluminium sheets placed in the X-ray beam. By progressively increasing the thickness of aluminium and measuring the transmitted intensity, the thickness required to reduce the beam intensity by half can be determined.

Because diagnostic X-ray beams contain photons with a range of energies, the HVL represents an average measure of beam penetration rather than a precise description of the energy spectrum.

Although HVL is a measure of material thickness (needed to reduce beam intensity by half) it is used as a proxy for beam quality (average energy of the beam).

Because HVL is used as a measure of beam quality, a common mistake is to say “HVL is the thickness required to reduce the beam energy by half.” This is wrong. It is the reduction in beam intensity (number of photons) by half.