Engineering CalculatorsSkin Depth Calculator
The classical AC skin depth of a conductor — the depth beneath the surface at which current density has fallen to 1/e (~37%) of its surface value — from a material's resistivity and relative permeability at a given frequency, direct-entered or derived from motor speed and pole pairs.
New to Skin Effect? Read the guide: Skin Depth & Skin Effect: Why AC Current Crowds the Surface — a plain-language explainer of the standard behind this calculator.
Skin effect is the tendency of AC current to concentrate near a conductor's surface as frequency rises, driven by the conductor's own changing magnetic field inducing eddy currents that oppose current flow in its centre. Skin depth δ is the depth at which current density has fallen to 1/e (about 37%) of its value at the surface — it is a property of the material and frequency alone (via resistivity ρ and relative permeability µr), not of the conductor's size or shape. δ = √(ρ/(π·f·µ₀·µr)), with µ₀ = 4π×10⁻⁷ H/m the permeability of free space. Non-magnetic conductors (copper, aluminium, silver, gold, brass, austenitic stainless) have µr = 1; ferromagnetic materials (steel, nickel) have µr > 1, which sharply reduces skin depth — but µr for these materials is not a fixed constant: it depends on field strength, saturates well below the values often quoted for DC, and is itself somewhat frequency-dependent, so any result for a magnetic material here should be treated as illustrative only. The effective-conduction-area figure (shown when a conductor diameter is entered) is a simplified geometric approximation — the true current-density profile falls off smoothly rather than as a step function, and real AC/DC resistance ratios for a given conductor geometry require a full Bessel-function solution. For an exact busbar or cable AC resistance ratio, use this site's Busbar Calculator or Cable/Wire Sizing tool, both of which apply the IEC 60287-1-1 empirical kₛ correction for a real conductor cross-section. This tool supports engineering estimation — verify against manufacturer/material data for critical designs.
Validated: checked against the widely-published reference skin-depth values for copper — 8.5 mm at 60 Hz, 9.3 mm at 50 Hz, 0.66 mm at 10 kHz, and 66 µm at 1 MHz (the classic ~1/√10-per-decade progression found in most AC power/RF references) — this calculator returns 8.52 mm, 9.33 mm, 0.660 mm, and 0.0660 mm respectively for those exact frequencies.