Shield Thickness for a Target Dose Rate Calculator

The thickness that takes a dose rate down to the figure you name — in millimetres, in half-value layers, in lead codes and in concrete courses, with the published broad-beam thickness printed beside the narrow-beam one because the narrow-beam one is always smaller.

Last updated 7 Oct 2026

This is narrow-beam attenuation through uniform material: the physics, not a shielding design. Real geometry scatters, and the scattered photons a narrow-beam calculation ignores can add tens of per cent to the dose behind a thick shield — that is what a build-up factor is for, and where a page omits one it says so on the page. A shield arrived at from a figure here has not been designed: shielding is specified by a qualified expert against the regulation that applies, and then verified by measurement.

Shield thickness for a target dose rate

Two rates and a material → the thickness, both ways

Shielding materialEight materials, every coefficient from NIST’s X-Ray Mass Attenuation Coefficients tables — a work of the United States Government, which is why these numbers can be printed here at all rather than cited from a copyrighted standard. Lead first because it is the default, and the reason it is the default is its atomic number rather than its density: photoelectric absorption scales roughly as Z to the fourth or fifth power, so at 100 keV a gram of lead absorbs 32 times as much as a gram of concrete. At 1.25 MeV, where Compton scattering runs the show and depends on electrons per gram alone, a gram of lead is seven per cent WORSE than a gram of water, and only its density saves it.

Photon energySix sources, and two of the six are conventions rather than lines. Technetium-99m, iodine-131, fluorine-18 and caesium-137 each have one photon that decides the shielding, and the preset is that photon. Cobalt-60 has two lines and iridium-192 has nine, so their presets are single-energy stand-ins: the conventional 1.25 MeV for cobalt-60 is 0.2 per cent from the yield-weighted mean of its two lines and is an exact point on the NIST grid, which makes it the better input of the two; the conventional 380 keV for iridium-192 sits between its yield-weighted mean of 371.6 keV and its energy-weighted mean of 397.8. No single energy reproduces a nine-line spectrum through a thick shield, because the soft lines are stripped out first and what is left is harder than what went in.

…or the energy itselfIn MeV. Locked while a source is selected above; choose the last option and this becomes the input. The NIST grid runs from 1 keV to 20 MeV and this page returns nothing outside it rather than an extrapolation, which is deliberate: the coefficient curve is not a polynomial and there is nothing honest to extend it with.

DensityNIST’s coefficient is per GRAM, so a density has to come from somewhere else before it becomes a per-centimetre attenuation, and that density is not NIST’s measurement of your material. Ordinary structural concrete is anywhere from 2.2 to 2.4 g/cm3 and much more when it is loaded with barytes or magnetite; rolled lead sheet is close to theoretical but lead glass and leaded acrylic are nowhere near it. A density wrong by five per cent makes every thickness on this page wrong by five per cent, in whichever direction you cannot see.

DensityIn g/cm3. Locked while the conventional value is in use. The values used are NIST’s own table entries: lead 11.35, tungsten 19.30, iron 7.874, aluminium 2.699, concrete 2.300, water 1.000, ICRU-44 soft tissue 1.060 and dry air 0.0012048. If you are working to a concrete mix design or a supplier’s certificate, use their figure instead of this one.

Where the unshielded rate comes fromThe thickness depends only on the RATIO of the two rates, so whatever quantity they are in cancels exactly as long as both ends are the same quantity — a meter reading divided by another meter reading on the same instrument works perfectly. The activity route cannot have that luxury: an air kerma rate constant gives microgray per hour of AIR KERMA, and ambient dose equivalent H*(10) is a different quantity: ICRU Report 47 puts the conversion at about 1.20 Sv/Gy at caesium-137’s 662 keV, and it is energy-dependent. So set your target in the same quantity as the rate, or accept a bias of roughly that size in the optimistic direction.

Unshielded rateIn whatever unit you like — microsieverts per hour, microgray per hour, millisieverts per hour, counts on a meter — provided the target below is in the SAME unit. Only the ratio enters the arithmetic. Locked while the activity route is selected.

Activity, for the activity routeIn GBq. Used only when the activity route is selected above. The published air kerma rate constants behind it are ranges rather than single numbers — caesium-137 is 77 to 93 microgray per square metre per GBq per hour — because compilations differ by 10 to 20 per cent on which lines and what low-energy cut-off they include. Both ends are printed, and so is the thickness of lead that spread is worth.

Distance from the sourceIn metres, and to the point you are protecting rather than to the shield. A point source and an inverse square law: the rate falls as the square of the distance, so doubling the distance quarters it, which is usually the cheapest shielding there is. The approximation fails close in, where the source has extent — inside about three source diameters, treat the answer as indicative.

Target rate — the same unit as the rate aboveWhatever design constraint you are working to. This page does not know and does not check what that should be: a target here is an input, not a limit, and nothing on this page is a statement that any rate is permitted.

47.506mmExample

Lead against caesium-137, reducing 1,000 µSv/h to 2.5 µSv/h — a factor of 400

Three lines of algebra, and the term that is missing from them

x = ln(R₀/R) / μ · n_HVL = log₂(R₀/R) · R₀ = Γ·A / d² · x_broad ≈ log₂(R₀/R)·HVL_published

R₀/R: the reduction factor, and the only thing the thickness depends on. Both rates cancel their units, so a meter reading divided by another meter reading on the same instrument is a perfectly good input — provided they ARE the same quantity. Mixing an air kerma rate with an ambient dose equivalent target biases the answer, by about 20 per cent at caesium-137 and by an energy-dependent amount elsewhere
log₂(R₀/R): the number of half-value layers, which is the material-independent form of the requirement. A factor of 400 is 8.64 half-value layers whatever you build the shield out of; the material only decides how many millimetres that is
Γ: the air kerma rate constant, in µGy·m²/(GBq·h). Published as a RANGE rather than a number — caesium-137 is 77 to 93 — because compilations differ on which lines they include and where they cut off at the low-energy end. Both ends are printed above, and so is the thickness of lead the spread is worth, which is under three millimetres for every nuclide here
d: the distance, in metres, to the point being protected. An inverse square law, so doubling it quarters the rate — worth 0.60 of a decade, or two half-value layers of any material, for nothing. It is the first thing to try and the last thing people think of
x_broad: the thickness a published broad-beam half-value layer implies for the same reduction factor, and the number to design against where it exists. It is larger than ln(R₀/R)/µ by the same 11 to 33 per cent that separates a published half-value layer from ln2/µ
B: the build-up factor, absent from the equation and present in reality. The dose behind a shield is B·R₀e^(−µx) with B above 1 and growing with depth. Recovering the reduction you wanted costs ln(B)/µ of extra material, which is log₂(B) half-value layers: B = 4 costs two extra layers, NOT four times the thickness

Worked example

Lead against caesium-137, reducing 1,000 µSv/h to 2.5 µSv/h — a factor of 400
THE REQUIREMENT, AS A FACTOR. 1,000 down to 2.5 is a reduction factor of 400. Nothing about the material has entered yet, and nothing about the units: if both rates came off the same instrument the units cancel and the factor is all that survives. In half-value layers that is log₂400 = 8.644, and in decades log₁₀400 = 2.602
THE COEFFICIENT. Lead at 661.7 keV, log-log interpolated from the NIST grid and multiplied by 11.35 g/cm³, gives μ = 1.261213 per cm. Its half-value layer is 5.4959 mm and its tenth-value layer is 18.2569 mm
THE NARROW-BEAM THICKNESS. x = ln(400)/μ = 5.9915/1.2612 = 47.506 mm. Check it the other way: 8.644 half-value layers × 5.4959 mm = 47.506 mm, the same number. That slab weighs 539 kg on every square metre
AND NOW THE NUMBER TO ACTUALLY DESIGN WITH. The published broad-beam half-value layer for lead at caesium-137 is 6.5 mm, not the 5.50 mm the coefficient gives. Multiply the same 8.644 half-value layers by 6.5 and the requirement becomes 56.2 mm — 8.7 mm more lead, 1.183 times as much, and 99 kg/m² more weight. The gap is build-up, and it is the whole reason this page prints both
WHAT HAPPENS IF YOU BUILD THE NARROW-BEAM ANSWER. Suppose the published 6.5 mm layer is the honest one. Then 47.5 mm of lead is only 7.309 half-value layers, not 8.644, and the rate behind it is 6.31 µSv/h rather than 2.5 — 2.5 times the target. A sixth too little lead is not a sixth too much dose; the exponential makes it worse than that
WHAT GETS ORDERED. 47.5 mm of lead is past the end of the BS EN 12588 sheet codes altogether — Code 8, the thickest in the standard, is 3.55 mm, so this is 27 layers of Code 4 or, more sensibly, lead plate or 1 two-inch lead brick deep. In concrete at 2.3 g/cm³ the same factor of 400 is 33.1 cm narrow-beam, which is three 100 mm courses and then some
WHAT THE ACTIVITY ROUTE WOULD HAVE GIVEN. 100 GBq of caesium-137 at one metre, with the published air kerma rate constant of 77 to 93 µGy·m²/(GBq·h), is 7,700 to 9,300 µGy/h — a 21 per cent spread, which is worth 1.50 mm of lead. Small beside the 8.7 mm the build-up correction costs, which is the right way round to learn it: the published constants are not the weak link in this calculation and the beam geometry is
WHAT THIS IS NOT. It is not a shield design and nothing here says any rate is permitted. The target rate is whatever you typed. A design needs a build-up factor for the actual geometry or a Monte Carlo calculation, an allowance for radiation coming round the shield rather than through it — the door, the duct, the ceiling — and a survey with an instrument at the end

Narrow-beam thickness for a required reduction factor, at caesium-137

Read the second column first. A reduction factor turns into a number of half-value layers through log₂, and that number is the same whatever material you then choose — the material only sets how many millimetres a half-value layer is. So the design question is always “how many half-value layers”, and the materials comparison is a separate question answered by the four middle columns. Every figure here is NARROW BEAM and is therefore the smallest thickness that could possibly do the job; a published broad-beam table would add 11 to 33 per cent. The last column is the one that decides real projects: a factor of a thousand at caesium-137 is 55 mm of lead and 620 kg on every square metre, which is a structural-engineering conversation. The same factor in concrete is 38 cm, which is 880 kg per square metre — so the concrete is 40 per cent heavier and seven times thicker, and lead is bought for the space it saves rather than the weight. This is NARROW-BEAM attenuation: one uniform slab, a parallel beam, and every scattered photon assumed lost. A real shield scatters photons back into the beam, and the published half-value layers in shielding tables are 11 to 33 per cent LARGER than ln2/μ for exactly that reason. A narrow-beam answer therefore UNDER-states the shield a real room needs, which is the unsafe direction, and closing that gap is what a build-up factor is for. The mass attenuation coefficient is per gram, so a density has to come from somewhere else to turn it into a per-centimetre attenuation, and the density used is not NIST’s. Ordinary structural concrete runs anywhere from 2.2 to 2.4 g/cm3 and much higher when loaded with barytes or magnetite; lead sheet is close to theoretical but lead glass and leaded acrylic are not. A density wrong by five per cent makes every thickness on this page wrong by five per cent.
Reduction factor	Half-value layers	Decades	Lead (mm)	Concrete	Iron	Tungsten	Lead areal density (kg/m²)
1 in 2 (a half)	1.000	0.301	5.5	38.3	12.0	3.6	62
1 in 10 (a tenth)	3.322	1.000	18.3	12.7 cm	39.8	12.1	207
1 in 20 (a twentieth)	4.322	1.301	23.8	16.5 cm	51.8	15.7	270
1 in 100 (a hundredth)	6.644	2.000	36.5	25.4 cm	79.6	24.2	414
1 in 400 (the worked example)	8.644	2.602	47.5	33.1 cm	10.4 cm	31.5	539
1 in 1,000 (a thousandth)	9.966	3.000	54.8	38.1 cm	11.9 cm	36.3	622
1 in 10,000	13.288	4.000	73.0	50.8 cm	15.9 cm	48.4	829
1 in 100,000	16.610	5.000	91.3	63.5 cm	19.9 cm	60.5	1,036
1 in 1,000,000 (a millionth)	19.932	6.000	11.0 cm	76.2 cm	23.9 cm	72.6	1,243
1 in 100,000,000	26.575	8.000	14.6 cm	101.7 cm	31.8 cm	96.8	1,658

What a build-up factor costs in millimetres, and the arithmetic people get wrong

A build-up factor multiplies the DOSE behind a given thickness. It does not multiply the thickness, and the difference is the whole table. To recover the reduction you wanted you add ln(B)/μ of material, which is ln(B)/ln2 = log₂(B) HALF-VALUE LAYERS — so B = 2 costs one extra layer, B = 4 costs two, and B = 10 costs 3.32. The error matters in both directions. Reading B = 4 as “four times the thickness” over-specifies a shield by a factor of two or three and costs real money; ignoring B altogether under-specifies it by the amounts in the third and fourth columns and is the dangerous direction. Steiner and colleagues measured B = 4.0 for a wide beam through 20 cm of concrete at 511 keV; that is 7.1 cm more concrete — a third again, not four times 20 cm. Note also what a build-up factor belongs to: a material, an energy AND a geometry. The Health Protection Agency’s Monte Carlo work for a plane-parallel source “effectively infinite in extent” gives lead at 511 keV a half-value thickness of about 5 mm against ln2/μ of 3.90, a ratio of 1.28 — larger than any of the shielding-table ratios, because an infinite plane source is a harsher geometry than a collimated room. This is NARROW-BEAM attenuation: one uniform slab, a parallel beam, and every scattered photon assumed lost. A real shield scatters photons back into the beam, and the published half-value layers in shielding tables are 11 to 33 per cent LARGER than ln2/μ for exactly that reason. A narrow-beam answer therefore UNDER-states the shield a real room needs, which is the unsafe direction, and closing that gap is what a build-up factor is for.
Build-up factor B	Extra thickness, in half-value layers	…in lead at Cs-137 (mm)	…in concrete at Cs-137 (cm)	A common misreading
1.1	0.138	0.76	0.53	—
1.5	0.585	3.21	2.24	“half again as thick” — it is 0.585 of a half-value layer, about 3.2 mm of lead
2	1.000	5.50	3.83	“twice as thick” — it is exactly ONE extra half-value layer
4	2.000	10.99	7.65	“four times as thick” — it is exactly TWO extra half-value layers
10	3.322	18.26	12.71	“ten times as thick” — it is 3.322 extra half-value layers, one tenth-value layer

What a sheet of lead actually does: BS EN 12588 codes at two energies

Rolled lead sheet is sold by CODE, not by millimetre, and the six codes are the whole range: 1.32, 1.80, 2.24, 2.65, 3.15 and 3.55 mm, with a ±5 per cent tolerance. Three suppliers publish the same six thicknesses and the same six weights, which is why the numbers are printed here — BS EN 12588 itself is a copyrighted standard and is not reproduced. The fourth column is a check worth doing: every published weight reproduces to the last printed digit from thickness × 11.34 g/cm³, and NOT from NIST’s 11.35, so the trade’s table is internally consistent and is computed at a density 0.09 per cent below the one this page attenuates with. The last four columns are the point. At technetium-99m, where lead’s half-value layer is 0.258 mm, even Code 3 is 5.1 half-value layers and transmits under 3 per cent — sheet lead is a real shield. At caesium-137 the thickest code in the standard, Code 8, is 0.65 of a half-value layer and transmits 64 per cent. Sheet lead codes are a diagnostic-energy system; at gamma-source energies the units are lead plate and lead brick, and IonActive’s guidance says so directly: “where significantly thick lead is required (e.g. 10’s – 100’s mm), lead bricks are often the better option”. The mass attenuation coefficient is per gram, so a density has to come from somewhere else to turn it into a per-centimetre attenuation, and the density used is not NIST’s. Ordinary structural concrete runs anywhere from 2.2 to 2.4 g/cm3 and much higher when loaded with barytes or magnetite; lead sheet is close to theoretical but lead glass and leaded acrylic are not. A density wrong by five per cent makes every thickness on this page wrong by five per cent.
Code	Nominal thickness (mm)	Published weight (kg/m²)	Weight from thickness × 11.34	HVLs at Tc-99m	Transmission at Tc-99m (%)	HVLs at Cs-137	Transmission at Cs-137 (%)
Code 3	1.32	14.97	14.969	5.126	2.86	0.240	84.66
Code 4	1.80	20.41	20.412	6.989	0.79	0.328	79.69
Code 5	2.24	25.40	25.402	8.698	0.24	0.408	75.39
Code 6	2.65	30.05	30.051	10.290	0.08	0.482	71.59
Code 7	3.15	35.72	35.721	12.232	0.02	0.573	67.21
Code 8	3.55	40.26	40.257	13.785	0.01	0.646	63.91

Air kerma rate constants, as ranges, and what the range is worth in lead

These are the constants behind the activity route, and they are printed as RANGES because that is how the literature leaves them: compilations differ by 10 to 20 per cent depending on which lines they sum and where they cut off at the low-energy end. The seventh column is the useful one, and it is reassuring: across every nuclide here the whole published spread is worth under three millimetres of lead, which is smaller than the build-up correction and far smaller than the uncertainty in a real room’s geometry. So the range is not the weak link. The last column names what each published figure contains, and technetium-99m is the one to read: a gamma-only sum over its single 140.5 keV line gives 14.2 against a published 19 to 23, because the 18 to 21 keV technetium K X-rays make up the rest. For an electron-capture nuclide the X-rays can BE the dose, which is why the published constants are used here as the primary figure and the line sum is not. This sums the PRINCIPAL GAMMA lines only. It omits the many weak lines and, more importantly, the characteristic X-rays that follow electron capture and internal conversion. For a clean gamma emitter that makes the sum a few per cent low; for an electron-capture nuclide it can be most of the answer — iodine-125 emits its 35.5 keV gamma in only 6.7 per cent of decays while its tellurium K X-rays come out at around 140 per cent, so a gamma-only sum understates its air kerma rate by a factor of several. This is a first-pass calculation on an idealised geometry — a point source, a uniform slab, no self-absorption in the source, no container, no floor and no walls. Real sources have extent and encapsulation, and real rooms scatter. A closed-form answer cannot see any of that.
Nuclide	Energy used here	Published range (µGy·m²/GBq/h)	Midpoint	Spread (%)	Rate from 100 GBq at 1 m (µGy/h)	Thickness of lead the spread is worth (mm)	What the published figure includes
Tc-99m	140.511 keV	19–23	21.0	21.1	2,100	0.07	the 18-21 keV Tc K X-rays add about a third
I-131	364.489 keV	50–66	58.0	32.0	5,800	0.88	gamma dominated by the 364 keV
Ir-192	380 keV	108–130	119.0	20.4	11,900	0.64	nine significant lines; derivation agrees to 7%
F-18	511 keV	130–156	143.0	20.0	14,300	1.03	two 511 keV annihilation photons per decay
Cs-137	661.657 keV	77–93	85.0	20.8	8,500	1.50	single 662 keV line; derivation agrees to 3%
Co-60	1.25 MeV	300–351	325.5	17.0	32,550	2.35	gamma dominated; derivation agrees to 2%

Only the ratio matters, every decade costs the same thickness, and the narrow-beam answer is the smaller one

This page answers the question people actually arrive with, and that is exactly why its caveat has to be louder than record one’s. A half-value layer is a property of a material and nobody orders one. A thickness is a number of millimetres, a lead code, a count of sheets, a concrete course — and somebody can take it to a supplier. The thickness this page computes is NARROW BEAM, which means it is the smallest thickness that could possibly do the job, and every published broad-beam figure for these materials and energies is 11 to 33 per cent larger. So wherever there is a published half-value layer to compare against, the page computes the requirement BOTH ways and prints the difference in millimetres and in kilograms per square metre. Design against the larger number, and treat even that as a starting point rather than an answer.

Only the ratio matters, and that is worth understanding before anything else. x = ln(R₀/R)/μ. The two rates appear only as a quotient, so their units cancel completely: a meter reading of 840 divided by a meter reading of 2.1 on the same instrument is a perfectly good input and needs no calibration at all. The requirement then converts to half-value layers through log₂, which is the MATERIAL-INDEPENDENT form of it — a factor of 400 is 8.64 half-value layers whether you build the shield from lead, concrete or water, and the material only decides how many millimetres a layer is. The one place the cancellation fails is the activity route, because an air kerma rate constant delivers microgray per hour of air kerma while a target is usually written in microsieverts of ambient dose equivalent, and the ratio between those quantities is not 1 — about 1.20 Sv/Gy at caesium-137’s 662 keV, and energy-dependent. Keep both ends in the same quantity and the problem disappears.

Every factor of ten costs the same thickness, and that is the whole economics. The thickness is linear in the number of decades, with a slope of exactly one tenth-value layer per decade, forever. There is no threshold and no diminishing return in the thickness — the return diminishes in what the thickness buys. The last tenth-value layer of a shield costs the same as the first and removes a ten-thousandth as much radiation. The practical consequences are unglamorous and reliable. Doubling the distance from a point source is a factor of four, which is 0.60 of a decade or two half-value layers, and it is free. Halving the time spent there is a factor of two, which is one half-value layer, and it is also free. A shield is the expensive protection and it is the third thing to reach for, not the first.

A build-up factor is not a multiplier on the thickness, and the slip goes wrong in both directions. B multiplies the dose behind a given thickness. To recover the reduction you wanted you add ln(B)/μ of material, which is log₂(B) half-value layers: B = 2 costs exactly one extra layer, B = 4 costs two, B = 10 costs 3.32. Reading B = 4 as “four times as thick” over-specifies a shield by a factor of two or three and wastes real money; leaving B out altogether under-specifies it by a fifth or so, and that is the direction that gets someone a dose. Steiner and colleagues measured B = 4.0 for a wide beam through 20 cm of concrete at 511 keV: the correction is 7.1 cm of extra concrete, a third again, not eighty centimetres. And a build-up factor belongs to a geometry as much as to a material — the Health Protection Agency’s Monte Carlo result for a plane-parallel source of effectively infinite extent puts lead’s half-value thickness at 511 keV at about 5 mm against ln2/μ of 3.90, which is a bigger correction than any shielding table’s, because an infinite plane source is a harsher geometry than a collimated room.

What gets ordered is not a number of millimetres. Rolled lead sheet comes in six codes, 1.32 to 3.55 mm, with a five per cent tolerance, and the thickest of them is two thirds of a half-value layer at caesium-137 — sheet lead is a diagnostic-energy system, and at gamma-source energies the units are plate and brick. Concrete is laid in courses and formed in whole hundreds of millimetres. So the page prints the code at or above the answer, the number of sheets or bricks or courses, and the areal density, because the mass is often the binding constraint before the thickness is: a factor of a thousand at caesium-137 is 55 mm of lead and 620 kg on every square metre, which is a structural conversation before it is a radiation one. The same factor in concrete is 38 cm and 880 kg per square metre — 40 per cent heavier and seven times thicker, which is the honest statement of what lead buys: space, not weight.

This page renders no verdict, and that is deliberate. The target rate is whatever you typed into the box. Nothing here checks it against a dose limit, compares it to a constraint, or says that any rate is permitted or any thickness adequate — because adequacy is a dose constraint, an occupancy factor, a workload, a regulator and a local rule, and none of those is an attenuation coefficient. What the page gives you is the physics and an honest statement of its own limits: one uniform slab, one photon energy, a parallel beam, no build-up, no leakage round the shield, no door and no duct. Use it to scope a problem, to price options, and to check somebody else’s arithmetic. A shield that someone will stand behind is designed by a radiation protection adviser or a medical physicist and is verified with an instrument.

Frequently asked questions

How thick does lead need to be to block caesium-137?

There is no thickness that blocks it — attenuation is exponential and never reaches zero — so the question has to be asked as a reduction factor. At caesium-137 one half-value layer of lead is 5.50 mm narrow-beam, so a factor of ten is 18.3 mm, a factor of a hundred 36.5 mm and a factor of a thousand 54.8 mm. Those are the smallest thicknesses that could possibly work: the published broad-beam half-value layer is 6.5 mm rather than 5.50, which puts a factor of a thousand at 64.8 mm. And 55 mm of lead is 620 kg on every square metre, which is usually the constraint that decides the project.

Does it matter whether my rates are in microsieverts or microgray?

Not at all, as long as BOTH are in the same one. The thickness depends only on the ratio R₀/R, so any consistent unit cancels — including raw counts on a meter, which makes a before-and-after measurement a legitimate input with no calibration needed. It matters a great deal if you mix them. An air kerma rate constant, which is what the activity route uses, gives microgray per hour of AIR KERMA; a target is usually written as ambient dose equivalent H*(10) in microsieverts; and those are different quantities. ICRU Report 47 Table A.2 gives the conversion as about 1.20 Sv/Gy at caesium-137’s 662 keV, and it varies with energy, so mixing them biases the ratio in the optimistic direction by roughly that factor and by a different one at another energy. The coefficients are in ICRP 74 and ICRU 47; this page does not reproduce them.

How much shielding does doubling the distance save?

Two half-value layers of any material, and it is free. Doubling the distance from a point source quarters the rate, a factor of four, which is log₂4 = 2 half-value layers or 0.60 of a decade. At caesium-137 that is 11 mm of lead or 7.7 cm of concrete you do not have to buy, support or install. The same arithmetic runs the other way and is the reason distance is the first thing to check: going from 2 m to 1 m costs you two half-value layers of shielding. Note the limit of the approximation — it is an inverse square law for a POINT source, and within about three source diameters a real source is not one.

Why does the page give two different thicknesses?

Because there are two honest answers and they are not the same number. The headline is ln(R₀/R)/μ, computed from the NIST coefficient, and it assumes a pencil beam through a uniform slab with every scattered photon lost for good. The second figure takes the same requirement in half-value layers and multiplies it by the PUBLISHED broad-beam half-value layer, which is 11 to 33 per cent larger because it includes build-up — scattered photons reaching the far face from directions the beam never pointed in. The second is the one to design against. The page also prints what would happen if you built the first: the rate behind it is higher than your target by a factor, and the factor is larger than the shortfall in thickness because the relationship is exponential.

What lead code do I need?

The page prints the BS EN 12588 code at or above the computed thickness, and quite often the answer is that no code will do it. The six codes are 1.32, 1.80, 2.24, 2.65, 3.15 and 3.55 mm, which at technetium-99m energies are 5 to 14 half-value layers and genuinely useful, and at caesium-137 are 0.24 to 0.65 of a half-value layer and essentially decorative. Because the codes are discrete you will usually install more lead than the calculation asked for, which is the right way to be wrong. Beyond Code 8 the practical materials are lead plate and lead brick — IonActive’s guidance says that where tens to hundreds of millimetres are needed, bricks are often the better option.

Can I add the thicknesses for two different materials?

Not the thicknesses, no, but the exponents add, which is almost as convenient. For a stack of layers the total transmission is the product of each layer’s own, so the quantity that adds is Σμₕxₕ — and because that is a sum, the order of the layers makes no difference to the total. A separate page on this site does the arithmetic for a three-layer stack and also works out which layer is doing the work, which is usually the useful question. One caution: the narrow-beam model is what makes the clean multiplication true, and in a real layered shield the interface between a low-Z and a high-Z layer matters — which is why a beta source is shielded with perspex first and lead second, and never the other way round.

Is 2.5 microsieverts an hour a safe target?

This page cannot answer that and does not try. The target rate is an input, not a limit: it is whatever design constraint you are working to, and nothing on this page checks it, compares it with a published limit, or states that any rate is permitted. Dose constraints come from regulation and from local policy, they depend on who is exposed and for how long — an occupancy factor of 1/20 for a corridor is worth 4.3 half-value layers of shielding you do not need — and they are the business of a radiation protection adviser or a medical physicist. What this page does is the attenuation arithmetic behind whatever target you choose.

Why is the answer so sensitive to the density I use?

Because the required thickness is inversely proportional to it, exactly. The coefficient NIST publishes is per gram, so the thickness that attenuates is set by the AREAL density ρ·x in g/cm²; a density five per cent low gives a thickness five per cent high and the same mass of material either way. That is why the areal density is printed beside every thickness on this page — it is the robust number. It also explains the one trap in overriding the density: scaling is correct for a denser pour of the same concrete mix and wrong for barytes or magnetite concrete, where the heavy aggregate raises μ/ρ as well as ρ, by much more than the density change alone at low energies.

Related calculators

References

J. H. Hubbell and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients, NIST Standard Reference Database 126, physics.nist.gov/PhysRefData/XrayMassCoef/ (read 7 October 2026). Every coefficient on these pages comes from here: eight materials, 1 keV to 20 MeV, 369 tabulated rows. A work of the United States Government and therefore free of domestic copyright, which is the reason this vertical exists in the form it does — the alternative sources for the same numbers are copyrighted standards. Three things were checked against it before anything was written: every absorption edge sits at its published energy (lead K at 88.0045 keV, tungsten K at 69.525, iron K at 7.112); μ/ρ at 1 MeV reproduces the published spot value for all eight materials to the last printed digit; and μ_en/ρ is at or below μ/ρ in every one of the 369 rows, as it must be.
Ionizing Radiation — Shielding Layer Examples, Occupational Safety and Health Administration, osha.gov/ionizing-radiation/introduction/shielding-layer-examples (read 7 October 2026). A US Government work and reproduced here. Two rows, six materials-worth of numbers, all in centimetres: caesium-137 at 0.66 MeV, HVL 4.8 concrete / 1.6 steel / 0.7 lead and TVL 15.7 / 5.3 / 2.1; cobalt-60 at 1.17 and 1.33 MeV, HVL 6.6 / 2.1 / 1.2 and TVL 20.8 / 6.9 / 4.0. These are BROAD-BEAM figures and every one of them is larger than ln2/μ from the NIST coefficient. At caesium-137 the excess is 25 per cent for concrete, 33 for steel and 27 for lead; at cobalt-60 it is 27, 28 and 15. The ratio of TVL to HVL in the table is also worth reading: narrow-beam it would be exactly ln10/ln2 = 3.322 for every entry, and here it runs 3.27, 3.31, 3.00, 3.15, 3.29 and 3.33, which is the rounding of one-significant-figure entries rather than physics.
V. Steiner, A. Malki, T. Ben-Yehuda and M. Moinester, Concrete and Lead Shielding Requirements for PET Facilities, arXiv:2407.12991 (read 7 October 2026). The one source found that MEASURES the narrow-beam and wide-beam cases side by side on the same wall, which is what makes it worth citing above any table. Through 20 cm of Israeli B30 concrete (density 2.30 g/cm³) at 511 keV, the narrow-beam transmission was “T = (3.0±1.0)%, corresponding to a B = 1.4±0.5 buildup factor” and the wide-beam transmission “T = (8.8±1.8)%, corresponding to a buildup factor B = 4.0±0.8, consistent with Monte Carlo (MC) simulations B = 3.9±0.6”. It uses μ_m = 0.0833 cm²/g, μ = 0.196 cm⁻¹ and a mean free path of 5.10 cm, where NIST’s ordinary concrete interpolates to 0.08831 cm²/g — 6.0 per cent apart, which is two different concretes rather than an error. It also states that “a 3.3 cm lead wall results in <0.5% transmission”, which the NIST coefficient reproduces at 0.29 per cent.
J. Eakins, An MCNP-4C2 Determination of Gamma Source Shielding, HPA-RPD-030, Health Protection Agency, Centre for Radiation, Chemical and Environmental Hazards, Radiation Protection Division (September 2007; read 7 October 2026). Crown copyright, quoted briefly. It is a Monte Carlo calculation done explicitly for BROAD-beam geometry — its stated aim is transmission “corresponding to a source that is considered plane parallel and effectively infinite in extent” — which makes it the cleanest available statement of how much a narrow-beam answer under-states. For 511 keV photons it gives lead a half-value thickness and tenth-value thickness of “approximately 5 mm and 17 mm”, against ln2/μ = 3.90 mm and ln10/μ = 12.96 mm from the NIST coefficient: ratios of 1.28 and 1.31 — larger than any of the shielding-table ratios, which is the point. A build-up factor belongs to a GEOMETRY and not to a material, and an infinite plane source is a harsher geometry than the collimated room a shielding table has in mind. The report’s iron figures are read off a plotted curve rather than tabulated and are used here only for that qualitative statement: “approximately 21 mm and 55 mm” against ln2/μ = 10.57 and ln10/μ = 35.12 give ratios of 1.99 and 1.57, and a pair that inconsistent cannot both be right.
Lead shielding thickness — what are the lead codes?, IonActive Consulting radiation protection resource hub (read 7 October 2026). The source for the six BS EN 12588 rolled lead sheet codes and for the practical advice around them: Code 3 is 1.32 mm, Code 4 1.80, Code 5 2.24, Code 6 2.65, Code 7 3.15 and Code 8 3.55, with “a ± 5% tolerance”. Three statements are taken from it directly. Sheet lead codes “tend to be used for relatively low energy applications (i.e. up to about 150 kVp)”. “Where significantly thick lead is required (e.g. 10’s – 100’s mm), lead bricks are often the better option”. And “since lead codes relate to specific thickness dimensions there is often a compromise required, so you may need to use a lead code above what you actually require” — which is the reason the shield-thickness page prints the code at or above the answer rather than the nearest one. It also gives a useful anchor at the diagnostic end: “at 150 kV it is often reported that the TVT is 0.95 mm lead (so practically 1 mm lead)”.
Lead on Plasterboard / Lead on Plywood datasheet, Calder Lead (read 7 October 2026). The second independent source for the lead code table, and the one that prints the weights to two decimal places: 14.97, 20.41, 25.40, 30.05, 35.72 and 40.26 kg/m² for codes 3 to 8. Those six weights were re-derived here from thickness × density, and they reproduce to the last printed digit from 11.34 g/cm³ and NOT from NIST’s 11.35 — so the trade’s code table is internally consistent and is computed at a density 0.09 per cent below the one these pages attenuate with. The difference changes nothing and finding it confirmed that the thickness and weight columns are one table rather than two. The datasheet is also quoted for the sentence that matters more than any number on it: “the lead thickness required for shielding should be calculated by a fully qualified Radiation Protection Advisor”.
Rolled lead sheet codes — BS EN 12588, a UK lead sheet distributor’s technical page (read 7 October 2026). The third independent source for the same six thicknesses and weights, which is why they are printed here at all: BS EN 12588 is a copyrighted standard and is not reproduced, but three suppliers publishing the same six dimensions makes those dimensions a fact about what is on sale. It is cited for the statement that the standard “defines rolled sheet composition, mechanical properties and tight dimensional tolerances” rather than for any of its content.
ICRP Publication 74, Conversion Coefficients for use in Radiological Protection against External Radiation (1996), and ICRU Report 47. CITED BY NUMBER ONLY and nothing from either reproduced — both are copyrighted. They are referenced for one structural point the shield-thickness page depends on: air kerma and ambient dose equivalent H*(10) are DIFFERENT QUANTITIES, and the conversion between them for photons is not 1. One value is quoted here at second hand and is the only one this batch verified: the Health Physics Society’s “Ask the Experts” answer 8949 (read 7 October 2026) states that “the air kerma-to-ambient dose equivalent conversion factor given in Table A.2 of ICRU Report 47 is about 1.20 Sv Gy⁻¹ at a photon energy of 662 keV from ¹³⁷Cs”. So treating a microgray of air kerma as a microsievert under-states the dose quantity by about a fifth at caesium-137, and by an energy-dependent amount elsewhere which this batch did not attempt to pin down and which a reader should look up rather than interpolate. None of it affects a thickness computed from a RATIO of two rates in the same quantity, which is why that page insists on the same quantity at both ends and says so.
Answer to Question 8949, Health Physics Society “Ask the Experts” (read 7 October 2026). The source for the one air-kerma to ambient-dose-equivalent conversion figure used on these pages — about 1.20 Sv/Gy at caesium-137’s 662 keV, which it attributes to Table A.2 of ICRU Report 47 — and for the reminder that the ratio of effective dose to ambient dose equivalent is itself strongly energy-dependent, “from about 0.2 at 15 keV to about 1 at 10 MeV”. It is cited rather than ICRU 47 directly because ICRU 47 is copyrighted and was not read for this batch; the figure is therefore second-hand and is flagged as such on the page that uses it.
A. Pearce, NPL Report IR 6: Recommended Nuclear Decay Data, National Physical Laboratory. Cited, not reproduced — Crown copyright. Used here through `_nuclide_data.py` for the gamma line energies and emission probabilities behind the energy presets, and for the two numbers that show why a single-energy preset is a convention: iridium-192’s nine lines run from 205.8 to 612.5 keV and sum to 2.135 photons per decay, giving a yield-weighted mean of 371.6 keV and an energy-weighted mean of 397.8; cobalt-60’s two lines at 1173.2 and 1332.5 keV, at essentially one photon each, give a yield-weighted mean of 1252.9 keV against the conventional 1.25 MeV.