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

Name: Skin Depth Calculator
Availability: InStock
Author: Nham Vu

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