What is the half-value layer (HVL)?

The HVL is the thickness of a given material needed to reduce the radiation intensity to half (50%) of its initial value. It depends on the photon energy and the material's atomic number and density.

How is HVL related to the attenuation coefficient?

HVL = ln(2) / μ, where μ is the linear attenuation coefficient of the material in cm⁻¹. A higher μ means stronger attenuation and therefore a thinner HVL.

What is the tenth-value layer (TVL)?

The TVL is the thickness that reduces intensity to 10% of the initial value. TVL = ln(10) / μ ≈ 3.322 × HVL. It is often used in practical shielding design because a single TVL gives a 10× dose reduction.

Does this account for scatter and buildup?

No. This calculator uses the narrow-beam (good geometry) exponential attenuation model. In real installations, scatter and buildup factors increase the required thickness. Consult NCRP or IAEA guidelines for broad-beam design.

Where can I find attenuation coefficient data?

NIST XCOM database (physics.nist.gov/PhysRefData/Xcom) provides mass attenuation coefficients for all elements and compounds. Multiply by material density to get the linear attenuation coefficient μ.

What units does this calculator use?

μ is entered in cm⁻¹ and thickness in cm. HVL and TVL are displayed in cm. You can convert to mm or inches using the built-in unit toggle.

What is the half-value layer of Co-60?

For Cobalt-60 gamma rays (average ~1.25 MeV), typical HVL values are about 1.2 cm of lead, 6.3 cm of concrete, and 11 cm of water. Enter μ ≈ 0.578 cm⁻¹ (lead, 1.25 MeV) to compute it directly.

Half-Value Layer Calculator

Name: Half-Value Layer Calculator
Availability: InStock
Author: Nham Vu

Enter a linear attenuation coefficient or known HVL to compute HVL, TVL, and transmitted dose fraction through any shield thickness.

Material & Radiation Input

Input mode

Attenuation coefficient (μ) Known HVL

Linear attenuation coefficient (μ)

cm⁻¹

Find μ in NIST XCOM for your material and energy.

Shield thickness & transmission

Enter either thickness OR desired transmission — the other is computed.

Shield thickness (x)

Desired transmission (%)

Common HVL values (approx.)

Material	Energy	HVL (cm)
Lead	100 keV	0.105
Lead	1 MeV	7.94
Concrete	100 keV	4.15
Concrete	1 MeV	9.80
Water	100 keV	4.06
Water	1 MeV	9.81

Click a row to load its μ value.

Enter parameters and click Calculate

Shielding Parameters

μ (cm⁻¹)

—

HVL

—

TVL

—

TVL/HVL

3.322

constant

Attenuation vs. Thickness

HVLs	Thickness (cm)	Transmission (%)	Attenuation (%)

Formulas used

HVL = ln(2) / μ ≈ 0.6931 / μ

TVL = ln(10) / μ ≈ 2.3026 / μ

I/I₀ = e^(−μx)

x = −ln(T) / μ (for target T)

Narrow-beam (good geometry) model — no buildup factor.

Summary