Skin Depth & High-Frequency AC Resistance Calculator

The skin effect is the tendency of alternating electric current (AC) to distribute non-uniformly within a conductor such that current density is greatest near the surface.

Skin depth (δ) is defined as the depth below the conductor surface where current density drops to 1/e (approximately 36.8%) of its surface value.

Alternating currents create internal circulating magnetic flux that induces counter-electromotive force eddy currents in the center, opposing current flow in the core and pushing it outward.

Because current flows through only a thin outer annular shell of thickness δ, the effective cross-sectional area shrinks and resistance increases proportionally to √f.

When wire radius is much greater than skin depth (r >> δ), AC resistance increases by the factor r / (2·δ).

Surface resistivity Rs (Ω/square) dictates waveguide and RF resonator dissipation factors.

• Frequency: Skin depth drops inversely with the square root of frequency (√f).
• Magnetic permeability: Ferromagnetic conductors (iron, nickel) have high μ, resulting in extremely shallow skin depths and huge AC losses.

• Designing inductors, transformers, and switch-mode power supplies.
• Evaluating transmission line attenuation and antenna conductor losses.

• Assumes isolated round conductor without proximity effects from adjacent conductors.