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. Thickness or HVL inputs can be entered in cm, mm, or inches using the adjacent unit selector; calculated HVL, TVL, and thickness results are displayed in cm.

Can I use this result to design a radiation barrier?

No. The result is an ideal narrow-beam estimate. Real barrier design must account for spectrum, workload, occupancy, geometry, scatter, leakage, buildup, material density, and applicable regulations. Use a qualified medical or health physicist.

Half-Value Layer Calculator

Enter a linear attenuation coefficient, a known HVL, or two intensity readings and filter thickness to estimate ideal narrow-beam HVL, TVL, and transmission.

Material & Radiation Input

Input mode

Attenuation coefficient (μ) Known HVL Beam measurement

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 (%)

Important: Ideal narrow-beam, homogeneous-material model only. It excludes scatter, buildup, leakage, beam hardening, spectrum and geometry effects. Do not use it alone for shielding design, compliance, or exposure decisions.

Common HVL values (approx.)

Material	Energy	HVL (cm)
Lead	100 keV	0.0110
Lead	1 MeV	0.860
Concrete	100 keV	1.734
Concrete	1 MeV	4.640
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

The Half-Value Layer (HVL) is the thickness of a specified material that reduces a narrow photon beam to 50% of its initial intensity. The Tenth-Value Layer (TVL) reduces it to 10%. Both depend on material, density, photon energy, beam spectrum, and measurement geometry. This calculator applies the ideal exponential model and is not a barrier-design or compliance tool.

How it works

Enter the linear attenuation coefficient (μ), a known HVL, or initial/transmitted readings with test-filter thickness.
The tool computes HVL = ln(2) / μ and TVL = ln(10) / μ.
Enter a shield thickness to calculate the transmitted dose fraction using I/I₀ = e^(−μx).
Alternatively, enter a desired transmission fraction to find the required shield thickness.
Review the narrow-beam limitations before using the estimate in any safety-related context.

Use cases

Explore how an ideal monoenergetic narrow beam attenuates through a homogeneous material.
Convert a known linear attenuation coefficient into HVL and TVL.
Estimate an effective coefficient from two same-unit beam readings.
Calculate number of HVLs needed to achieve a target dose reduction.
Convert between attenuation coefficient and HVL/TVL values.
Create an educational attenuation schedule by number of HVLs.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu