Skin Depth Calculator

The Skin Depth Calculator computes the skin depth (δ) of a conductor at a specified frequency — the critical parameter that governs how alternating current distributes within the conductor cross-section. At DC, current flows uniformly throughout the conductor. As frequency increases, electromagnetic induction causes current to concentrate progressively closer to the conductor surface, leaving the interior virtually unused. This phenomenon, called the skin effect, is one of the most important considerations in the design of power cables, RF transmission lines, transformer windings, bus bars, and high-frequency electronic interconnects.

The skin depth is defined as the distance from the surface at which the current density falls to 1/e ≈ 36.8% of its surface value. The formula is: δ = √(ρ / (π × f × μ)), where ρ is the conductor's resistivity (Ω·m), f is the frequency (Hz), and μ is the absolute permeability (μ = μ₀ × μᵣ = 4π × 10⁻⁷ × μᵣ H/m). This elegant formula reveals the three factors controlling skin depth: material resistivity, frequency, and magnetic permeability.

For copper at 50 Hz power frequency, δ ≈ 9.3 mm. A standard power cable has a conductor diameter much larger than this — meaning current does not penetrate to the centre. For this reason, large power conductors (above about 300 mm²) are manufactured as stranded or Milliken constructions to minimise effective AC resistance by using multiple smaller sub-conductors that individually fit within one skin depth. At 1 MHz, copper skin depth drops to about 66 μm; at 1 GHz it is only 2.1 μm, confining current to a surface layer thinner than a sheet of paper.

Magnetic permeability profoundly amplifies the skin effect. Steel, with μᵣ ≈ 100–1000, has a skin depth at 50 Hz of only 0.5–1.7 mm compared to 9.3 mm for copper. This is why steel conduit effectively shields the magnetic field of a single-phase circuit: the return current redistributes to the conduit surface, cancelling external fields. It is also why stranded cables with steel-core (ACSR) require careful treatment — the steel core carries little AC current.

In transformer and inductor design, the skin effect forces winding designers to use Litz wire (many insulated sub-conductors woven to equalise current distribution) at audio and radio frequencies. A single 1 mm diameter copper wire at 100 kHz has an effective resistance approximately 3× its DC resistance due to the skin effect. Litz wire keeps each strand within one skin depth, restoring the DC resistance value.

PCB designers must account for skin depth when routing high-frequency traces. The effective current-carrying cross-section shrinks with frequency, increasing trace resistance and insertion loss. Trace plating choices (copper, gold, silver) affect skin depth because each material has a different resistivity. At 10 GHz, the skin depth in copper is only 0.66 μm — thinner than many plating layers.

Eddy current losses in transformer cores, motor laminations, and magnetic shielding are directly related to skin depth in the magnetic material. Core laminations are designed to be thinner than the skin depth at the operating frequency to prevent significant eddy current loops — typically 0.1–0.5 mm for 50/60 Hz power transformers, and far thinner (or powdered core composites) for switching power supplies operating at 20 kHz and above.

This calculator provides skin depth in both millimetres and micrometres for cross-reference with conductor dimensions. The AC/DC resistance ratio and effective area factor give a first-order estimate of how much the skin effect increases the effective resistance of a conductor whose radius is comparable to or larger than δ.