Calculate electromagnetic skin depth, inverse frequency, or absorption-only thickness for a target remaining field amplitude. The good-conductor approximation requires σ ≫ 2πfε and homogeneous material with appropriate real permeability and conductivity. Presets are approximate room-temperature values; purity, alloy and temperature matter.

Good-conductor approximation (σ ≫ 2πfε), using real, frequency-appropriate permeability and conductivity. Presets are approximate room-temperature values.

Round-wire comparison

Optional. Blank omits the radius / skin-depth ratio.

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 skin depth, take the reciprocal of the square root of πfμσ. Inverse frequency is f = 1/(πμσδ²). For remaining field amplitude p%, absorption-only thickness is t = −δ ln(p/100), with 0 < p < 100. This describes amplitude relative to the material surface, excludes interfaces, reflection, apertures, seams and enclosure geometry, and does not establish total shielding effectiveness. Power decays as exp(−2t/δ). The optional wire-radius ratio is a comparison, not a full cylindrical AC-resistance model. See MIT’s Electromagnetics and Applications, section 9.2.4.

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