Calculate skin depth, required frequency, or shield thickness from frequency, material conductivity, permeability, and attenuation goal.

Penetration Depth Calculator

Skin Depth
Required Frequency
Shield Thickness

Calculate standard skin depth δ = 1 / √(π f μ σ). Choose a material or enter custom values.

Notes: 100% IACS = 58 MS/m at 20°C. μ = μ0 μr with μ0 = 4π×10⁻⁷ H/m. Results are idealized plane-wave estimates; real probes and alloys vary.

Penetration Depth Formula

The following formula is used to calculate penetration depth (skin depth) in a conductor.

d = (1) / (√(π f μ σ))
  • Where d is the penetration depth (skin depth) (m) (multiply by 1000 to convert to mm)
  • f is the test frequency (Hz)
  • μ is the magnetic permeability of the material (H/m), where μ = μ0 μr and μ0 = 4π×10⁻⁷ H/m
  • σ is the electrical conductivity (S/m) (if using %IACS: σ = (%IACS/100) × 58×10⁶ S/m at 20°C)

To calculate the penetration depth, take the reciprocal of the square root of π multiplied by the frequency, magnetic permeability, and electrical conductivity.

What is Penetration Depth?

Definition:

Penetration depth (also called skin depth) is the characteristic distance an AC electromagnetic field and the associated induced current penetrate into a conductor. At a depth of one skin depth, the field/current amplitude has dropped to 1/e (about 37%) of its value at the surface.

How to calculate Penetration Depth?

Example Problem:

The following example outlines the steps and information needed to calculate a Penetration Depth.

First, determine the test frequency. In this example, the test frequency is 50 Hz.

Next, determine the magnetic permeability. For a non-magnetic conductor, use μr ≈ 1, so μ = μ0 μr = 4π×10⁻⁷ H/m.

Next, determine the electrical conductivity. In this example, assume 100% IACS, so σ = 58×10⁶ S/m (58 MS/m at 20°C).

Finally, calculate the Penetration Depth using the formula above;

d = 1 / √(π f μ σ)

d = 1 / √(π·50·(4π×10⁻⁷)·(58×10⁶))

d ≈ 0.00935 m = 9.35 mm