Magnetic Permeability Calculator — B = μrμ₀H

Formula

How this is calculated

Magnetic permeability measures how easily a material supports the formation of a magnetic field within it. The absolute permeability μ = μr · μ₀ (units: H/m or T·m/A) is the product of the permeability of free space μ₀ = 4π × 10⁻⁷ H/m and the dimensionless relative permeability μr, which describes how much more (or less) permeable the material is compared to vacuum. The flux density B inside the material is then B = μ · H = μr · μ₀ · H, where H (in A/m) is the applied magnetic field intensity (related to the driving current). The magnetic susceptibility χm = μr − 1 describes the magnetisation response directly.

Materials are classified by their μr: diamagnetic materials (μr slightly < 1, χm < 0) — such as copper (μr ≈ 0.99999) and bismuth — weakly oppose applied fields. Paramagnetic materials (μr slightly > 1, χm > 0) — such as aluminium (μr ≈ 1.000021) — weakly enhance the field. Ferromagnetic materials (μr >> 1) — such as soft iron (μr ≈ 1000–5000) or permalloy (μr up to 100 000) — dramatically amplify B. The XY plot compares the B-H relationship for the entered μr against free space (μr = 1), illustrating the amplification factor.

Note that ferromagnetic materials exhibit non-linear B-H curves (hysteresis) and saturation at high H values. This calculator uses the linear μr approximation valid at low to moderate field levels, below magnetic saturation. For soft iron this typically holds below about H = 1000 A/m; beyond that μr drops. The μr value you enter should be the incremental or small-signal permeability appropriate to your operating point.