How do you calculate shielding thickness for a target dose rate?

Divide the unshielded dose rate by the target to get the reduction factor, take log₁₀ of it to get the number of tenth-value layers, and multiply by the material's TVL. Example: Cs-137 at 1,000 µSv/h reduced to 1 µSv/h is 1000×, which is 3 TVLs × 2.1 cm = 6.3 cm of lead.

How much lead do I need to shield Co-60 or Cs-137?

Using OSHA broad-beam values, each 10× reduction needs about 4.0 cm of lead for Co-60 and 2.1 cm for Cs-137. So 100× needs about 8 cm (Co-60) or 4.2 cm (Cs-137) and 1000× about 12 cm or 6.3 cm.

What is a buildup factor and why does it matter?

Photons scattered inside the shield still reach the detector, so the real dose behind a thick shield is higher than the narrow-beam formula e^(−μx) predicts. The buildup factor B (often 2–10 or more for thick shields) multiplies the transmitted dose. Ignoring it makes a shield too thin; the practical TVLs used here already include it.

Why is the narrow-beam result thinner?

Narrow-beam (good geometry) attenuation assumes every scattered photon is removed. Around a real source that is not true, so the effective HVL and TVL are larger. For Cs-137 in lead, the narrow-beam TVL is about 1.83 cm versus the practical 2.1 cm.

How much concrete equals 1 cm of lead?

It depends on energy. For Cs-137 the practical TVLs give about 7.5 cm of concrete per cm of lead (15.7 ÷ 2.1); for Co-60 about 5.2 cm (20.8 ÷ 4.0). At low energy lead is far more effective because of the photoelectric effect.

Can I use this for X-ray rooms, linacs or neutrons?

Only for rough estimates. Diagnostic X-ray and linac barriers are designed with NCRP Report 147 and 151 methods (workload, use and occupancy factors, transmission curves for polyenergetic beams). Neutrons need hydrogenous shields and different physics. Have a qualified expert confirm any real shield.

What is the difference between this and the half-value layer calculator?

This page starts from your dose-rate goal and gives a thickness, including practical broad-beam values and a material comparison. The half-value layer calculator gives the narrow-beam HVL, TVL and μ of a material at any energy from NIST data.

Radiation Shielding Thickness Calculator

Pick a source (Cs-137, Co-60, Ir-192, Tc-99m, F-18 or an energy) and a material, enter the unshielded and target dose rate or a reduction factor, and get the shield thickness with buildup accounted for, plus a lead / steel / concrete / water comparison.

Shield thickness = number of tenth-value layers × TVL, where the number of TVLs is log₁₀(unshielded dose rate ÷ target dose rate).

Shielding Parameters

Radiation source / photon energy

Shielding material

Method

Target given as

Unshielded dose rate (I₀)

Target dose rate (I)

µSv/h

Same unit as I₀ and lower than it. Get I₀ for a source with the activity-to-dose calculator.

HVL / TVL used (selected source & material)

HVL

—

TVL

—

Shielding Results

Enter parameters and click Calculate to see the required shielding thickness.

Required Shielding Thickness

—

inches

—

HVLs / TVLs

—

Dose Reduction

—

I₀ / I factor

Attenuation

—

% blocked

Dose transmitted through shield —

Formula used

—

Same reduction in other materials

Material	Practical	Narrow beam

Dose rate behind a thickness you have (mm)

—

Note: Estimates for point-like gamma sources only. Real shields also depend on geometry, gaps, streaming, scatter around the shield and distance. Facility and container shielding must be reviewed by a qualified health or medical physicist under NCRP, IAEA and local rules. For the narrow-beam HVL, TVL and μ of a material at any energy, see the half-value layer calculator.

Shield thickness for 10×, 100× and 1000× dose-rate reduction (cm)

Practical rows use published broad-beam TVLs (include buildup). Narrow-beam rows use NIST μ/ρ with no buildup and are shown for comparison only.

Source, material	Basis	TVL	10×	100×	1000×
Cs-137, Lead	Practical (OSHA)	2.10	2.1	4.2	6.3
Cs-137, Lead	Narrow beam (NIST)	1.83	1.8	3.7	5.5
Cs-137, Steel	Practical (OSHA)	5.30	5.3	10.6	15.9
Cs-137, Steel	Narrow beam (NIST)	3.99	4.0	8.0	12.0
Cs-137, Concrete	Practical (OSHA)	15.70	15.7	31.4	47.1
Cs-137, Concrete	Narrow beam (NIST)	12.71	12.7	25.4	38.1
Cs-137, Water	Narrow beam (NIST)	26.88	26.9	53.8	80.6
Co-60, Lead	Practical (OSHA)	4.00	4.0	8.0	12.0
Co-60, Lead	Narrow beam (NIST)	3.45	3.5	6.9	10.4
Co-60, Steel	Practical (OSHA)	6.90	6.9	13.8	20.7
Co-60, Steel	Narrow beam (NIST)	5.48	5.5	11.0	16.4
Co-60, Concrete	Practical (OSHA)	20.80	20.8	41.6	62.4
Co-60, Concrete	Narrow beam (NIST)	17.24	17.2	34.5	51.7
Co-60, Water	Narrow beam (NIST)	36.42	36.4	72.8	109.2

Sources: OSHA shielding layer examples (Cs-137, Co-60 HVL/TVL); QSA Global Ir-192 (HVL: lead 5.1 mm, steel 13.0 mm, concrete 43.2 mm); NIST X-Ray Mass Attenuation Coefficients (SRD 126). Narrow-beam densities: lead 11.35, steel 7.85, concrete 2.30, water 1.00 g/cm³.

Quick answer

Shield thickness = number of tenth-value layers × TVL, where the number of TVLs is log₁₀(unshielded dose rate ÷ target dose rate). For Cs-137 a 1000× reduction (3 TVLs) needs about 6.3 cm of lead, 16 cm of steel or 47 cm of concrete; for Co-60 it needs about 12 cm of lead, 21 cm of steel or 62 cm of concrete (OSHA broad-beam TVLs, which include scattered radiation). Narrow-beam values from attenuation coefficients alone are thinner (about 5.5 cm of lead for Cs-137) because they ignore buildup.

Examples

Source	Reduction	Lead	Steel	Concrete
Cs-137 (662 keV)	10× (1 TVL)	2.1 cm	5.3 cm	15.7 cm
Cs-137 (662 keV)	1000× (3 TVL)	6.3 cm	15.9 cm	47.1 cm
Co-60 (1.17, 1.33 MeV)	10× (1 TVL)	4.0 cm	6.9 cm	20.8 cm
Co-60 (1.17, 1.33 MeV)	1000× (3 TVL)	12.0 cm	20.7 cm	62.4 cm
Ir-192	100× (6.6 HVL)	3.4 cm	8.6 cm	28.7 cm

Choose the source and material, then enter the dose rate before and after the shield.

Summary

This calculator answers "how thick does my shield need to be?" for gamma and X-ray photons. Enter the unshielded dose rate and the dose rate you want behind the shield (or a reduction factor or transmission), choose the source and the material, and it returns the thickness in mm, cm and inches. For Cs-137, Co-60 and Ir-192 it uses published practical (broad-beam) HVL and TVL values from OSHA and QSA Global, which include scattered photons (buildup) and are what you would use for a real shield. For other energies it uses NIST narrow-beam attenuation coefficients and lets you add a buildup factor. It also compares lead, steel, concrete and water for the same reduction and shows the dose rate behind any thickness you type. For the HVL and TVL of a material at a given energy, use the half-value layer calculator.

How it works

Choose the photon source or energy and the shielding material (lead, steel, ordinary concrete or water).
Enter the target as unshielded and target dose rates (same unit), a reduction factor (×) or a transmission (%). The reduction factor is DRF = I₀ ÷ I.
Practical method (Cs-137, Co-60, Ir-192, steel/lead/concrete): x = log₁₀(DRF) × TVL, or log₂(DRF) × HVL when only the HVL is published. These broad-beam values include buildup.
Narrow-beam method (any energy): μ = (μ/ρ) × ρ from NIST data, and x = ln(B × DRF) ÷ μ, where B is the buildup factor you enter (B = 1 means no scatter credit, which underestimates a real shield).
The tool also lists the thickness for every material and the dose rate behind a thickness you type: I = I₀ × 10^(−x/TVL), or I = I₀ × B × e^(−μx).

Use cases

Sizing a lead pig, castle or container for a Cs-137, Co-60 or Ir-192 source.
Estimating concrete wall thickness for a gamma irradiator, source store or radiography bay.
Checking how much steel shielding an industrial radiography camera or gauge needs.
Comparing lead, steel, concrete and water for the same dose-rate reduction.
Working out the dose rate behind an existing shield of known thickness.
Showing students why buildup makes real shields thicker than μ-only calculations.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu