Magnetic Permeability Calculator

Magnetic permeability (μ) describes how easily a material can be magnetised by an applied magnetic field. It is defined as the ratio of magnetic flux density (B) to magnetic field strength (H): μ = B / H. Higher permeability means a material conducts magnetic flux more readily. The SI unit is henries per metre (H/m).

Absolute permeability (μ) is the actual measured permeability of a material in H/m. Relative permeability (μᵣ) is a dimensionless ratio comparing the material's permeability to the permeability of free space (μ₀ ≈ 1.2566 × 10⁻⁶ H/m): μᵣ = μ / μ₀. Relative permeability is more commonly used in engineering because it gives an intuitive sense of how much better a material conducts magnetic flux than a vacuum.

Magnetic susceptibility (χₘ) measures how strongly a material responds to an applied magnetic field. It is directly linked to relative permeability by the formula χₘ = μᵣ − 1. Diamagnetic materials have small negative susceptibility, paramagnetic materials have small positive susceptibility, and ferromagnetic materials have very large positive susceptibility (often hundreds to thousands).

Relative permeability depends on atomic structure and the alignment of magnetic domains within a material. Ferromagnetic materials like iron and silicon steel have μᵣ values in the thousands because their magnetic domains align strongly with applied fields. Paramagnetic materials (like aluminium) have μᵣ just above 1, while diamagnetic materials (like copper) have μᵣ slightly below 1 due to opposing induced fields.

Temperature has a significant effect on ferromagnetic permeability. As temperature increases, thermal agitation disrupts domain alignment, reducing permeability. Above the Curie temperature, ferromagnetic materials lose their ferromagnetism entirely and behave like paramagnetic materials. For most engineering applications, it is important to account for operating temperature when selecting core materials.

A superconductor is a material that, when cooled below its critical temperature, expels all magnetic flux from its interior (the Meissner effect). This results in a relative permeability of μᵣ = 0 and a magnetic susceptibility of χₘ = −1, making superconductors perfect diamagnets. This property enables levitation above a magnetic source and is exploited in technologies like maglev trains and MRI machines.

Air gaps are intentionally introduced in transformer and inductor cores to prevent magnetic saturation and to store energy. An air gap reduces the effective permeability of the core, which linearises the B-H relationship and increases the saturation current threshold. This makes the component more stable and predictable under varying load conditions, especially in power electronics.

High-permeability materials are used in magnetic shielding to redirect magnetic flux away from sensitive components. Materials such as mu-metal (μᵣ up to ~100,000) provide effective shielding at low frequencies by offering a low-reluctance path for magnetic field lines. The shielding effectiveness increases with the permeability of the shield material and its thickness relative to the magnetic field frequency.