Skin Depth Calculator

At high frequency, AC current crowds toward a conductor's surface — the skin effect.

How the Math Works

The skin depth formula δ = √(ρ ÷ (π·f·μ)) calculates how deeply alternating current penetrates a conductive material. Delta (δ) represents the depth where current density falls to about 37% of its surface value. Resistivity (ρ) measures how strongly a material opposes current flow, while frequency (f) determines how rapidly the current changes direction. Permeability (μ) describes how easily a material supports magnetic field formation. Higher frequencies or more resistive materials result in shallower skin depths, meaning current concentrates near the surface.

Practical Applications

Engineers use skin depth calculations when designing transformers, motors, and transmission lines. For high-frequency applications like radio transmitters or switching power supplies, choosing appropriate conductor materials and thicknesses prevents energy loss and heating. When shielding electronic devices, knowing the skin depth helps determine how much metal is needed to block electromagnetic interference effectively. Audio equipment designers consider skin depth when selecting materials for speaker voice coils and magnetic circuits to optimize performance.

Day-to-Day Use

Skin depth effects impact many devices you use daily. Your smartphone's wireless charging pad relies on proper conductor design to transfer power efficiently through electromagnetic fields. The radio in your car depends on understanding how radio waves penetrate metal and plastic components. Fluorescent lighting ballasts and modern LED drivers use high-frequency switching that's optimized using skin depth principles. Even your Wi-Fi router's antenna design considers how current flows within the conductive elements to maximize signal transmission and reception.

Worked example

Copper at 1 MHz → about 65 µm.

FAQ