Skin Depth Calculator

Skin depth refers to the phenomenon where alternating current (AC) tends to flow mostly at the outer surface of a conductor, rather than uniformly throughout its cross-section. This effective concentration of current near the surface is known as the skin effect. The standard formula used to compute skin depth (δ) is:

δ = √[ ρ / (π × f × μ_r × μ_0) ]

Where ρ is the electrical resistivity of the material in ohm-meters, f is the frequency in hertz, μ_r is the relative magnetic permeability of the material, and μ_0 is the permeability of free space (4π × 10^-7 H/m).

Let us calculate the skin depth for a copper wire carrying a high-frequency radio signal at f = 1,000,000 Hz (1 MHz). For copper, the electrical resistivity (ρ) is approximately 1.68 × 10^-8 ohm-meters, and the relative permeability (μ_r) is roughly 1.0 (non-magnetic).

Step 1: Identify the constants and inputs. f = 1,000,000, ρ = 1.68 × 10^-8, μ_r = 1, and μ_0 = 4π × 10^-7.

Step 2: Multiply the denominator terms: π × 1,000,000 × 1 × (4π × 10^-7) ≈ 3.9478.

Step 3: Divide resistivity by the denominator: (1.68 × 10^-8) / 3.9478 ≈ 4.255 × 10^-9.

Step 4: Take the square root to find skin depth: δ = √(4.255 × 10^-9) ≈ 6.52 × 10^-5 meters, or about 0.065 mm (65 micrometers).

When designing high-frequency transformers or transmission lines, always select a skin depth value calculated specifically for your operating frequency. Remember that ferromagnetic materials have a high relative permeability, which drastically reduces skin depth and concentrates currents into even thinner surface layers. To minimize AC resistance and thermal buildup, consider using stranded wire, Litz wire, or silver-plated conductors in high-frequency applications.