How this instrument works
Permeability measures how much a material amplifies a magnetic field compared with the field a bare coil would produce on its own. The absolute value, μ = B ⁄ H, is not derived from a deeper law — it is the direct definition of the material's response, the magnetic parallel to how resistance R = V ⁄ I defines a resistor's response to voltage. A high μ means the material's internal atomic dipoles line up readily and add their own field on top of the one supplied.
Relative permeability, μr = μ ⁄ μ₀, restates that response against vacuum, where μ₀ = 4π × 10⁻⁷ H/m (about 1.2566 × 10⁻⁶ H/m) is the constant for empty space. Air and most non-magnetic stuff sit at μr ≈ 1; plain carbon steel runs from a few hundred to a couple thousand; nickel-iron alloys used for shielding cans and transformer laminations can reach into the tens of thousands. The figure tells a core designer, in one glance, how many turns of wire they can save.
The one thing this ratio does not capture is that ferromagnetic response is not a fixed constant the way density or resistivity is. Plot B against H for real steel and the curve bends: the slope climbs steeply at low field, peaks, then falls back toward 1 as the sample saturates and simply cannot align any more internal dipoles. The figure this instrument returns is the chord value at one operating point — feed it a higher H and the same sample gives a different answer.
- Enter the flux density into "Magnetic flux density, T" — the B field actually measured inside the material, in teslas.
- Enter the driving field into "Magnetizing field strength, A/m" — the H field set by coil turns, current, and geometry.
- Read "Absolute permeability, H/m" for μ = B ⁄ H, the response in physical units.
- Read "Relative permeability (vs. vacuum)" for μr = μ ⁄ μ₀, the dimensionless comparison against empty space.
- Keep H above zero — a zero magnetizing field leaves nothing to divide by, so the instrument flags it.
Worked example — silicon steel core at 1.2 T
A transformer-grade silicon steel lamination is driven to a flux density of 1.2 T by a coil producing a magnetizing field of 1,000 A/m — realistic operating figures for a 50/60 Hz power transformer core. Dividing gives the absolute figure directly: μ = 1.2 T ⁄ 1000 A/m = 0.0012 H/m.
Dividing that by μ₀ = 1.2566370614 × 10⁻⁶ H/m converts it to the more familiar relative figure: μr = 0.0012 ⁄ 0.0000012566 ≈ 954.93. The steel is concentrating flux almost a thousand times more effectively than an air-core coil would at the same 1,000 A/m — exactly why transformer and motor cores are built from iron alloys rather than left as air.
Questions
What is the difference between absolute and relative permeability?
Absolute μ = B ⁄ H carries units, henries per metre, and states the response in physical terms. Relative μr = μ ⁄ μ₀ strips the units away by comparing that response to vacuum, so μr = 1 means no magnetic effect at all and μr = 2000 means the sample concentrates flux two thousand times more than empty space at that operating point.
Why is relative permeability above 1 for iron and steel but essentially 1 for wood or aluminium?
Iron, nickel, and cobalt are ferromagnetic — their unpaired electron spins lock into aligned domains that add their own field on top of the applied one, pushing μr into the hundreds or thousands. Wood, aluminium, and most other materials are paramagnetic or diamagnetic, with no such domain structure, so their internal contribution is negligible and μr sits within a fraction of a percent of 1.
Is permeability really a fixed property of a material?
Not for ferromagnetic samples. This instrument returns the chord value at whatever single B and H pair you enter, but a real B-H curve is nonlinear: the ratio rises from a low starting point, peaks at moderate field strengths, then falls toward 1 as the sample saturates. The same steel can report a different figure at a different operating point, and even depends on its magnetic history through hysteresis.
What does a relative permeability of 1 mean?
It means the material has no magnetic effect of its own — the flux density it produces under a given field is exactly what vacuum would produce, μ = μ₀. Air, most plastics, wood, and copper all sit within a hair of μr = 1, which is why coils wound on non-magnetic formers behave, magnetically, almost identically to a plain air-core coil.
Why does the calculator require the magnetizing field strength to be greater than zero?
Because μ = B ⁄ H divides by H directly, and a zero magnetizing field makes that division undefined no matter what flux density is entered. Physically, zero H means no coil current and no driving field at all, so there is nothing for the sample to respond to and no ratio to compute.
How does magnetic flux density differ from magnetizing field strength?
H is the field supplied — set by coil turns, current, and geometry, independent of what core material sits inside the coil. B is what the sample actually produces in response, including its own internal magnetization on top of H. The ratio between the two, μ = B ⁄ H, is precisely the measure of how much the sample adds.