# Half-Value Layer

The thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). The HVL is expressed in units of distance (mm or cm). Like the attenuation coefficient, it is photon energy dependant. Increasing the penetrating energy of a stream of photons will result in an increase in a material's HVL.

The HVL is inversely proportional to the attenuation coefficient. If an incident energy of 1 and a transmitted energy is 0.5 is plugged into the equation introduced on the preceding page, it can be seen that the HVL multiplied by μ must equal 0.693.

$I=I_{0}e^{-\mu x}$

$0.5=1.0e^{-\mu x}$

If x is the HVL then μ times HVL must equal 0.693 (since the number 0.693 is the exponent value that gives a value of 0.5).

Therefore, the HVL and μ are related as follows:

$HVL=\frac{0.693}{\mu}$

The HVL is often used in radiography simply because it is easier to remember values and perform simple calculations. In a shielding calculation, such as illustrated to the right, it can be seen that if the thickness of one HVL is known, it is possible to quickly determine how much material is needed to reduce the intensity to less than 1%.

Approximate HVL for Various Materials when Radiation is from a Gamma Source

 Half-Value Layer, mm (inch) Source Concrete Steel Lead Tungsten Uranium Iridium-192 44.5 (1.75) 12.7 (0.5) 4.8 (0.19) 3.3 (0.13) 2.8 (0.11) Cobalt-60 60.5 (2.38) 21.6 (0.85) 12.5 (0.49) 7.9 (0.31) 6.9 (0.27)

Approximate Half-Value Layer for Various Materials when Radiation is from an X-ray Source

 Half-Value Layer, mm (inch) Peak Voltage (kVp) Lead Concrete 50 0.06 (0.002) 4.32 (0.170) 100 0.27 (0.010) 15.10 (0.595) 150 0.30 (0.012) 22.32 (0.879) 200 0.52 (0.021) 25.0 (0.984) 250 0.88 (0.035) 28.0 (1.102) 300 1.47 (0.055) 31.21 (1.229) 400 2.5 (0.098) 33.0 (1.299) 1000 7.9 (0.311) 44.45 (1.75)

Note: The values presented on this page are intended for educational purposes. Other sources of information should be consulted when designing shielding for radiation sources.