How Thick Should a Mu-Metal Shield Be?

Thick enough that the flux density inside the alloy stays under about 7,000 gauss, and no thicker than 3a/2μ - where a is the shield's inner radius and μ is the permeability at the flux density it ends up carrying.

Those are the two ends of the answer. They come from different documents, published decades apart, and neither one is a datasheet.

The 7,000 gauss ceiling lives in a design kit's instruction pamphlet. The 3a/2μ ceiling lives in a NASA technical report from 1970. Neither appears on the material datasheet you'd normally design from.

Read the diagram as a warning about both ends. A thin foil in a large enclosure saturates, and a heavy gauge in a small one is money spent on stiffness you may not need.

What Flux Density Will Your Shield Actually See?

The method starts by working out how much flux the wall has to carry. It's one equation, and every term in it is either measured or chosen.

B = 2.5 × d × H₀ ÷ 2t - d is the shield diameter or diagonal in inches, H₀ is the ambient field in gauss, t is the wall thickness in inches, and 2.5 is a conversion constant that carries the answer into cgs gauss.

The kit's worked example uses a 5 gauss ambient field and a 4.5 inch enclosure. At 0.010 in of wall, that gives B = 2,812.5 gauss.

You then take that number to the material's B-H curve and read the permeability at that point - 275,000 in the example, not the 350,000 peak the alloy is usually sold on.

Attenuation follows as A = μt ÷ d. In the example: (275,000 × 0.010) ÷ 4.5 = 611, so a 5 gauss field arrives on the inside at about 0.008 gauss.

Now change one number. The thickness is the variable you actually buy, so here's the same enclosure at every gauge the kit supplies.

0.004 in is the standard shielding foil gauge, and in this geometry it lands 31 gauss over the ceiling. The equation isn't saying the foil is poor. It's saying a 4.5 inch enclosure at 5 gauss is more than that gauge can carry.

Halve the enclosure to 2.25 in and the same foil drops to 3,516 gauss, comfortably inside. Thickness, enclosure size and field strength move together, and you get to choose two of them.

Is There a Point Where More Thickness Stops Helping?

Yes, and it arrives much earlier than most buyers expect. The NASA report states the rule as t ≤ 3a/2μ, with a as the shield's inner radius.

Run it with the report's own figures - a 0.5 metre radius and an initial permeability of 20,000 - and the maximum useful wall works out to 0.0375 mm. That is thinner than any foil on the market.

"When this point is reached," the report says, "it is magnetically worthless to increase the thickness further."

The same report then recommends 0.020 to 0.060 in for a self-supporting shield, which is more than ten times that figure. It explains the gap in six words: "usually a much thicker material is used for mechanical reasons."

So there are two different thicknesses in play. The one that decides whether the shield works is set by flux density. The one you actually order is set by whether the part can hold its own shape.

The report also gives the bottom end, from a worked shield that was already sitting close to its limit.

"One half the thickness of material or twice the diameter would have pushed us just over the hump into saturation. If we had a flux density of around 7000 gauss we would have had both a drastically reduced permeability and shielding factor."

Two documents, half a century apart, naming the same wall at 7,000 gauss.

Which Wall Thicknesses Are Actually Made?

Foil runs from 0.002 to 0.010 in (0.051 to 0.254 mm), and sheet runs from 0.014 to 0.062 in (0.356 to 1.58 mm). Both ranges come from a shielding alloy catalog, and the split isn't arbitrary.

The sample kit hands you a ladder that crosses both: foil at 0.004, 0.006 and 0.010 in, sheet at 0.020, 0.040 and 0.060 in, plus a medium-permeability foil and a high-saturation silicon iron sheet.

Notice what that ladder is for. You aren't meant to guess which row applies to your design. You're meant to build the thing and measure it.

When Should You Add a Layer Instead of Millimetres?

Once you're past the magnetic ceiling, the answer isn't a heavier sheet. It's a second shell.

The NASA report is direct about it: beyond 3a/2μ, "to achieve greater shielding it is necessary to use multiple concentric shields. Each shield then attenuating the residual field remaining from the previous one."

The modern design kit gives the same instruction for strong fields, with an arrangement attached: a medium-permeability layer outside and a high-permeability layer inside, separated by at least half an inch. The outer layer takes the field down to something the inner one can still carry.

There's a third lever that costs no metal at all. One alloy catalog states the gain from heat treatment bluntly: annealing "approximately doubles the attenuation in db or squares the attenuation ratio."

Squaring is the bigger number. A shield that cuts the field 100 times before the anneal is specified at something like 10,000 times after it. Wall thickness moves attenuation linearly. The anneal moves it quadratically, for the price of a furnace run.

What Do the Published Formulas Leave Out?

More than the worked examples suggest, and the sources are refreshingly direct about it. The equations size a cylinder in a laboratory field. Everything outside that is on you.

The material's own data comes with a condition attached as well. The catalog note under the magnetic table says it plainly: the data "is for sheet material measured in a D.C. field."

There is one published AC curve, and it's worth knowing exactly what it covers. A shielding alloy brochure carries a shield thickness vs attenuation ratio chart at 60 Hz.

Its conditions are stated on the chart: a cylindrical shield 3 in in diameter by 7.5 in, annealed at 1,121 °C for four hours, with a separate curve for 1, 2 and 4 oersteds.

Two things stand out. The curves climb steeply at the low end and flatten well before the thickest stock - the diminishing return the 1970 report describes, showing up in measured data.

The second is the ordering. The 4 oersted curve sits above the 2 oersted curve, which sits above 1 oersted. A stronger field gives a higher attenuation ratio across the range.

That ordering isn't a contradiction. It's the same effect as the B-H curve. Permeability is low at tiny fields, rises toward its peak and then collapses. A 1 oersted measurement can sit on the low side of that curve rather than the peak.

Add it up and the formula gives you an order of magnitude and a direction, not a guaranteed number. That's why the method ships with a sample kit instead of a lookup table.

Which Thickness Should You Order?

Here's the sequence, in the order the numbers actually become available. The first two you measure. The rest fall out of the equations.

The short version: measure the field, fix the enclosure, and let the thickness fall out of the flux density limit. If it won't fit, change the enclosure or add a shell rather than reaching for a heavier gauge.

Why Buy Mu-Metal Shielding Foil from ICMASS?

Thickness sits at the front of every shielding quote we write, and it's the part buyers have the least information about. The equations above are the ones we run.

Send us three things - the field strength at the shield, the enclosure size, and the attenuation you need - and we'll come back with a wall thickness and, where it's needed, a layer stack.

We supply shielding foil in the standard gauges and cut it to size. Tell us the geometry and we'll tell you which gauge it actually needs, rather than the heaviest one that fits the budget.

Frequently Asked Questions About Mu-Metal Shield Thickness

Q1: How thick should a mu-metal shield be?

A: Thick enough that the flux density in the wall stays under about 7,000 gauss, and no thicker than 3a/2μ. Solve B = 2.5 × d × H₀ ÷ 2t for the thickness, then confirm the attenuation with A = μt ÷ d. Past the second limit, extra metal adds nothing magnetic.

Q2: How do I calculate the flux density inside a shielding wall?

A: B = 2.5 × d × H₀ ÷ 2t, with d in inches and H₀ in gauss. A 4.5 inch enclosure in a 5 gauss field carries 2,812 gauss at 0.010 in of wall, and 7,031 gauss at 0.004 in. The constant 2.5 carries the result into cgs gauss.

Q3: What happens if the shield is too thin?

A: It saturates, and a saturated shield behaves like air. Permeability falls toward 1, so the alloy has no carrying capacity left to divert flux with. One NASA worked example notes that halving the thickness would have pushed the shield "just over the hump into saturation" at around 7,000 gauss.

Q4: Is a thicker mu-metal shield always better?

A: No. Up to a point it helps, and past that point it does nothing magnetic at all. The limit is t = 3a/2μ. For a 0.5 metre radius at an initial permeability of 20,000 that works out to 0.0375 mm, which is why most shields end up specified by stiffness rather than by magnetic need.

Q5: What is the maximum useful thickness of mu-metal?

A: t = 3a/2μ, where a is the inner radius and μ is the permeability. A 1970 NASA report puts it plainly: past that point "it is magnetically worthless to increase the thickness further", and greater shielding then requires multiple concentric shells. Large shields hit this limit at fractions of a millimetre.

Q6: Why does the calculator say 0.04 mm when the fabricator wants 0.5 mm?

A: They're answering different questions. The magnetic limit says how much metal the flux needs. The mechanical limit says how much metal the shape needs. The NASA report recommends 0.020 to 0.060 in for self-supporting shields and notes that "usually a much thicker material is used for mechanical reasons".

Q7: Can I use two thinner layers instead of one thick one?

A: Yes, and for strong fields it's often the better arrangement. Concentric shields each attenuate the residual field left by the one outside them. A common arrangement puts a medium-permeability layer outside and a high-permeability layer inside, separated by at least half an inch.

Q8: Does the shielding formula work for AC fields?

A: Not directly. The published calculator states that it "computes DC magnetic fields only". The supporting material data carries the same restriction, being measured in a DC field. At AC, frequency and eddy currents change the answer, and the thickness that was correct for DC is no longer the design point.

Q9: How much attenuation does 0.004 in foil give?

A: It depends entirely on the enclosure size and the field. In the worked example - 4.5 in enclosure, 5 gauss - 0.004 in gives an attenuation ratio of roughly 611 at a permeability of 275,000. Halve the enclosure and the same foil carries half the flux density, which raises the permeability you can design against.

Q10: Does thickness change the permeability I should design with?

A: Yes, and the datasheets show it. One alloy maker reports a maximum permeability of 250,000 measured statically on 1.00 mm sheet and 150,000 at 50 Hz on 0.20 mm foil - the same alloy, a 40% difference driven by thickness and frequency together.

Q11: What field strength should I design for?

A: The one you measure at the shield's location, not the one at the source. Field strength falls with distance, so a reading taken at the magnet says little about the wall. Where the field can't be measured, bound it - then check that bounding case against the 7,000 gauss ceiling.

Q12: Does the shield have to be heat treated after forming?

A: Yes, if you need the magnetic properties the datasheet quotes. Annealing is described by one alloy catalog as approximately doubling the attenuation in dB, or squaring the attenuation ratio - a larger gain than any reasonable increase in wall thickness, and it has to happen on the finished part.