Half-Value Layer & Lead Shielding Thickness Calculator

Model-based estimate. Use the stated geometry, composition and measurement assumptions; see the tool scope for limitations.

Input

Shield material, photon energy and geometry

Calculation mode

Shield material

Density, g/cm³

Gamma source

Photon energy, MeV

Spectrum of 1 lines (ENDF/B-VIII.0, ≥ 0.001 %); shown energy is the dose-weighted mean. Choose «Manual energy» to enter a single line. via Ba-137m in equilibrium.

Shield thickness, cm

Include build-up factor

Build-up accounts for scattered photons. Without it the dose behind thick shields is underestimated.

AssumptionsPoint isotropic source, single material, broad-beam geometry with exposure build-up.μ/ρ from NIST SRD-126; build-up factors from ANS-6.4.3 tabulated data (open literature).Presets use the major-line spectrum of the source (ENDF/B-VIII.0, lines ≥ 0.001 %), each line weighted by its air-kerma contribution y·E·(μ_en/ρ)_air and attenuated separately; manual mode is a single photon energy.Verify against radiation safety procedures; characteristic X-rays below 30 keV and bremsstrahlung are not included.

Result

Dose transmission

÷267.01

Transmitted fraction (I/I₀): 0.00374524
Attenuation factor (I₀/I): 267.005
Effective build-up (spectrum) B: 2.0519
Dose-weighted mean energy: 0.6617 MeV
Dominant line behind the shield: 0.6617 MeV
Without build-up (e^−μx): 0.00182526
Effective half-value layer (spectrum, with build-up): 0.70253 cm
Effective tenth-value layer (spectrum, with build-up): 2.1924 cm

Lines of the spectrum and their contribution

Energy, MeV	Yield	Dose share, unshielded	I/I₀	Dose share, behind shield
0.6617	85.1 %	100 %	0.003745	100 %

Attenuation vs thickness

Gamma Shielding Calculator

Attenuation formula and data sources

The calculator computes gamma dose-rate attenuation through a shield as I/I₀ = B·e^(−μx), where μ = (μ/ρ)·ρ is the linear attenuation coefficient, x is the shield thickness and B is the build-up factor. Mass attenuation coefficients μ/ρ are taken from NIST SRD-126, build-up factors from ANS-6.4.3 tabulated data.

Forward and inverse problem

It supports the forward problem (dose behind a shield of a given thickness) and the inverse problem (thickness for a required attenuation factor). Shield materials: lead, tungsten, steel/iron, concrete, aluminium, water. The build-up factor accounts for scattered photons — without it the dose behind a thick shield is underestimated several-fold, so it is enabled by default.

Output and model limits

The result includes the transmitted fraction and attenuation factor, the half-value (HVL) and tenth-value (TVL) layers. The model is a point isotropic source, a single material; source presets (Cs-137, Co-60, Ir-192, I-131, Se-75, Tc-99m, Am-241, Na-22) are computed over the major-line spectrum from ENDF/B-VIII.0 weighted by air-kerma contribution, while manual mode uses a single photon energy.

Frequently asked questions

How much lead is needed for Cs-137 or Ir-192?

Enter the required attenuation factor in the «Required thickness» mode: the calculator solves for the thickness including build-up. Through 5 cm of lead the Ir-192 dose rate drops roughly 3700-fold, Cs-137 even more because it has a single 662 keV line.

Why are source presets computed over a spectrum rather than one energy?

Behind a thick shield the most penetrating lines dominate, even weak ones: for I-131 the 637 and 723 keV lines with 7 % and 2 % yield govern transmission through 5 cm of lead. Presets take all lines with yield ≥ 0.001 % from ENDF/B-VIII.0 and weight them by dose contribution.

What is the build-up factor and when should it be off?

Build-up accounts for scattered photons that still reach the point behind the shield; without it the dose behind a thick shield is underestimated several-fold. Switch it off only for a narrow collimated beam, e.g. when working from narrow-beam HVL measurements.