Skin Depth Calculator — Electromagnetic Penetration in Conductors

Formula

How this is calculated

When alternating current flows in a conductor, the changing magnetic field induces eddy currents that oppose the applied current in the interior — the skin effect. The resulting current density is highest at the surface and falls exponentially with depth, characterised by the skin depth δ = √(ρ / (π f μ₀ μᵣ)), where ρ is electrical resistivity (Ω·m), f is frequency (Hz), μ₀ = 4π × 10⁻⁷ H/m is the permeability of free space, and μᵣ is the relative magnetic permeability of the material.

For non-magnetic metals like copper, aluminium and gold, μᵣ ≈ 1 and only resistivity and frequency matter. Ferromagnetic materials such as iron and nickel have μᵣ in the hundreds to thousands, dramatically reducing the skin depth — at 1 MHz, iron has a skin depth of roughly 1.6 μm compared to copper's 66 μm. Increasing frequency always reduces δ because δ ∝ 1/√f. The formula assumes a planar conductor much thicker than δ (plane-wave approximation), linear isotropic behaviour and a frequency-independent μᵣ — simplifications that hold well for most RF engineering but break down for ferromagnetics near saturation or above their Curie temperature.

Skin depth has direct engineering consequences: at high frequencies nearly all AC current flows in a thin shell near the conductor surface, raising effective resistance and driving the use of hollow conductors, silver plating, Litz wire and thin-film metallisation in RF coils, waveguides and PCB traces.