Skin Depth Calculator

The skin effect — AC current concentrating near the conductor surface instead of distributing uniformly — was observed experimentally by Horace Lamb in 1883 and explained theoretically by Oliver Heaviside in 1885. Heaviside derived the exponential current-density decay that gives δ = √(2/ωμσ), still the foundational formula in use today. At the time, it was a puzzle: why did high-frequency telegraph signals behave differently than DC in the same wire?

The practical impact emerged with the growth of radio in the 1910s–20s. Vacuum-tube transmitters at MHz frequencies developed unexpected heating in their output coils because skin effect had concentrated current into a tiny surface layer that couldn\'t handle the total power. Silver-plated and Litz-wire conductors were developed in response: silver plating gave the surface layer the highest possible conductivity, while Litz wire (many individually insulated thin strands braided together) forced current to distribute across all strands by making each thinner than δ.

Modern applications include: PCB trace design at GHz frequencies (where δ < 2 µm means even thick traces conduct only in a thin skin), SMPS transformer windings (Litz wire or foil at 100+ kHz), superconducting RF cavities (the "skin" is replaced by the superconducting penetration depth), and MRI gradient coils (Litz construction handles fast-switched currents without eddy-current losses).

Enter frequency (Hz, kHz, MHz, GHz) and pick a conductor material. The tool computes skin depth δ in micrometers, compares it to 1 oz. copper PCB cladding (35 µm) to tell you whether your traces are in the "all of it conducts" regime or the "only surface conducts" regime, and plots the exponential current-density profile.

For ferromagnetic materials like iron, the relative permeability µ_r can reach 1000+, which shrinks δ by √µ_r — magnetic materials have much shallower skin depth than copper at the same frequency. That\'s why transformer laminations are thin even at 60 Hz: to stay below 3δ and keep core losses manageable. Everything runs client-side.