Skin depth (δ) is the distance below a conductor's surface where the current density has fallen to 1/e (about 37%) of its surface value. At higher frequencies, current concentrates in a thinner surface layer, increasing effective resistance.

What formula is used?

δ = √(ρ / (π × f × μ₀ × μᵣ)), where ρ is resistivity (Ω·m), f is frequency (Hz), μ₀ = 4π × 10⁻⁷ H/m is the permeability of free space, and μᵣ is the relative permeability of the material.

What is the relative permeability for copper?

Copper, aluminum, gold, and most non-magnetic metals have a relative permeability very close to 1. Only ferromagnetic materials like iron or nickel have significantly higher values.

Why does skin depth decrease at higher frequencies?

Higher-frequency currents induce opposing eddy currents deeper in the conductor, which push the net current toward the surface. The skin depth is inversely proportional to the square root of frequency.

What are typical skin depths for copper at common frequencies?

At 60 Hz: ~8.5 mm; at 1 MHz: ~66 µm; at 1 GHz: ~2.1 µm. At microwave frequencies the skin depth is only a few micrometers, so thin plating is sufficient for RF conductors.

Skin Depth Calculator

Calculate how deeply an AC electromagnetic field penetrates a conductor based on frequency, resistivity, and permeability.

Conductor Parameters

Frequency

Current value: 1 MHz

Resistivity (Ω·m)

Copper ≈ 1.72×10⁻⁸ Ω·m

Relative Permeability (μᵣ)

1 for non-magnetic metals; ~200 for soft iron

Common Materials

Results

Enter values and click Calculate

Summary

The skin depth calculator computes how deeply an alternating electromagnetic field penetrates a conducting material. It uses the standard formula δ = √(ρ / (π·f·μ₀·μᵣ)), where resistivity, frequency, and magnetic permeability determine the result. This is essential for RF engineering, PCB design, transformer core analysis, and any application where AC resistance differs significantly from DC resistance.

How it works

Enter the signal frequency in Hz (or use the unit selector for kHz/MHz/GHz).
Enter the electrical resistivity of the conductor in ohm-meters.
Enter the relative magnetic permeability (1 for most non-magnetic metals).
The tool applies the formula δ = √(ρ / (π·f·μ₀·μᵣ)) and displays the skin depth in meters, millimeters, and micrometers.
Use the preset buttons to quickly load common conductor values.

Use cases

Design PCB traces and RF shielding at specific frequencies.
Determine effective conductor thickness for high-frequency cables.
Evaluate eddy current losses in transformer cores.
Select conductor materials for antenna and waveguide construction.
Verify the skin effect impact on resistance at power-line frequencies.
Compare penetration depth across copper, aluminum, and steel.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu