0.0005
H/m
397.887358
396.887358
39,788.736
%
0.5
mT per A/m
0.0005
H/m
397.887358
396.887358
39,788.736
%
0.5
mT per A/m
The Magnetic Permeability Calculator determines the absolute permeability, relative permeability, and magnetic susceptibility of a material from measurements of the magnetic flux density B and the magnetic field intensity H. These quantities characterize how easily a material can be magnetized and are essential for designing transformers, inductors, magnetic shielding, and electromagnetic devices.
Permeability is the magnetic analog of electrical permittivity — it quantifies the degree to which a material supports the formation of a magnetic field within itself. Materials range from diamagnetic (slightly opposing applied fields) to ferromagnetic (strongly amplifying fields by factors of thousands).
The absolute permeability $$\mu$$ relates the magnetic flux density $$B$$ (in tesla) to the magnetic field intensity $$H$$ (in amperes per meter):
$$\mu = \frac{B}{H}$$
The relative permeability $$\mu_r$$ expresses how many times more permeable the material is compared to free space:
$$\mu_r = \frac{\mu}{\mu_0}$$
where $$\mu_0 = 4\pi \times 10^{-7}$$ H/m is the permeability of free space (vacuum permeability).
The magnetic susceptibility $$\chi_m$$ measures the material's response to the applied field:
$$\chi_m = \mu_r - 1$$
For diamagnetic materials, $$\chi_m$$ is small and negative ($$\mu_r < 1$$). For paramagnetic materials, $$\chi_m$$ is small and positive. For ferromagnetic materials like iron, nickel, and cobalt, $$\mu_r$$ can range from hundreds to hundreds of thousands, indicating extremely strong magnetic response. Note that in ferromagnetic materials, permeability is nonlinear and depends on the operating point on the B-H curve.
The calculator also classifies the material type based on the computed $$\mu_r$$ value to help identify whether the sample is diamagnetic, paramagnetic, or ferromagnetic.
Absolute Permeability (μ) in H/m tells you the material's intrinsic ability to support magnetic flux. Relative Permeability (μᵣ) is dimensionless and compares the material to vacuum — values near 1 indicate non-magnetic materials, while values of 1000+ indicate strong ferromagnets. Magnetic Susceptibility (χ) near zero means the material barely responds to external fields. The Material Classification provides a quick identification: diamagnetic (copper, bismuth), paramagnetic (aluminum, platinum), or ferromagnetic (iron, nickel, ferrites).
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Results
Soft iron with B = 0.5 T at H = 100 A/m gives μᵣ ≈ 3979, confirming strong ferromagnetic behavior typical for transformer cores.
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Results
Aluminum is weakly paramagnetic with μᵣ just above 1, meaning it barely enhances the applied field.
The permeability of free space (vacuum permeability) is $$\mu_0 = 4\pi \times 10^{-7}$$ H/m ≈ 1.2566 × 10⁻⁶ H/m. This is a fundamental physical constant used as the reference for relative permeability calculations.
B (magnetic flux density, in tesla) measures the total magnetic field including the material's response. H (magnetic field intensity, in A/m) measures the externally applied magnetizing force. They are related by $$B = \mu H$$.
Ferromagnetic materials contain magnetic domains that align with the applied field. As H increases, more domains align until saturation is reached. This means μ varies with H, producing the characteristic S-shaped B-H hysteresis curve.
Absolute permeability is always positive. However, magnetic susceptibility $$\chi_m$$ can be negative for diamagnetic materials (where $$\mu_r < 1$$), indicating the material slightly opposes the applied field.
Mu-metal and permalloy (nickel-iron alloys) can have relative permeabilities exceeding 100,000. Supermalloy reaches up to 1,000,000. These materials are used for magnetic shielding in sensitive instruments.
A toroidal core wound with a known number of turns is used. Measuring the current (to find H from $$H = NI/l$$) and the induced flux (to find B from a search coil or fluxmeter) gives the B-H data needed to compute $$\mu = B/H$$.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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