Half-Value Layer Calculator (Radiation Shielding)
How much X-ray or gamma radiation gets through a shield of a given thickness, and how thick it must be to cut it to a target, from the half-value layer.
Results
The dashed line marks the value you entered.
What this tool does
Each half-value layer halves the radiation, so ten of them cut it to about a thousandth; the tenth-value layer, 3.32 half-value layers, cuts it by ten. Half-value layers depend strongly on both the material and the radiation energy — take them from published tables for your source. This is the simple narrow-beam model: in a real, broad beam scattered radiation builds up behind thick shields and more gets through, so shielding design uses build-up factors and must be done by a qualified radiation protection expert.
Formula
I = I₀ × 2^(−x ÷ HVL) · μ = ln 2 ÷ HVL · TVL = HVL × log₂ 10
Variables
| Symbol | Meaning | Unit |
|---|---|---|
hv | Half-value layer of the material | mm |
x | Shield thickness | mm |
i0 | Level without the shield | — |
tg | Share you want to let through | % |
I | Level behind the shield | — |
TR | Share let through | % |
TV | Tenth-value layer | mm |
XT | Thickness for the target | mm |
MU | Attenuation coefficient | /mm |
Worked example
- Half-value layer of the material12 mm
- Shield thickness25 mm
- Level without the shield100
- Share you want to let through1 %
- Level behind the shield23.5969
- Share let through23.5969 %
- Tenth-value layer39.86 mm
- Thickness for the target79.73 mm
- Attenuation coefficient0.05776 /mm
Limitations
- Activity counts decays per second. It does not say how dangerous a source is: that depends on the type and energy of the radiation, distance, shielding and exposure time, and is a question for a radiation protection professional.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.