Skin Depth Calculator

Skin depth (symbol δ) is the distance from the conductor surface where alternating current (AC) density drops to 1/e (about 37%) of its surface value. At high frequencies, current tends to flow only in a thin layer near the surface, and this phenomenon is called the skin effect.

The formula is the square root of ρ divided by π times f times μ₀ times μᵣ, where ρ is electrical resistivity in ohm-meters, f is frequency in hertz, μ₀ = 4π × 10⁻⁷ H/m, and μᵣ is the material's relative permeability. This formula applies to good conductors at frequencies where displacement current is negligible.

At 20°C, copper skin depth is about 9.23 mm at 50 Hz and 8.42 mm at 60 Hz. That is why skin effect is practically negligible in home wiring — cable diameters are much smaller than the skin depth.

About 65.2 micrometers at 20°C. At radio frequencies, current flows only in a hair-thin layer at the conductor surface, so AC resistance becomes much larger than DC resistance.

Metal resistivity rises with temperature following ρ(T) = ρ₂₀ × [1 + α(T − 20)], with α the temperature coefficient (copper 0.00393/°C). Since skin depth is proportional to the square root of resistivity, skin depth grows when the conductor is hot — e.g.

Because their magnetic permeability is large (μᵣ in the hundreds to thousands), while skin depth is inversely proportional to √μᵣ. For example at 60 Hz, iron skin depth is about 0.64 mm, more than 13 times thinner than copper's 8.42 mm. Note that iron's μᵣ is nonlinear, so

Use the inverse formula: f = ρ / (π × μ₀ × μᵣ × δ²). Enter the target δ in this calculator's second tab. For example, for a 0.1 mm target in copper at 20°C, the maximum frequency is about 426 kHz.

Rac/Rdc is the ratio of AC to DC resistance in solid round wire. If wire diameter is much smaller than skin depth, the ratio approaches 1 and skin effect is negligible. If the diameter is comparable to or larger than skin depth, AC resistance rises. This calculator

No. This calculator only models skin effect in an isolated single conductor. In transformers, inductors, or tightly wound coils, proximity effect — the influence of neighboring conductors' magnetic fields — adds AC losses beyond the Rac/Rdc figures shown here.

The rule of thumb is that skin effect starts to matter when wire diameter exceeds about half the skin depth, and becomes dominant when the diameter is several times the skin depth. At 50/60 Hz this only happens in very thick busbars or power cables, while at kilohertz frequencies

At megahertz to gigahertz frequencies, skin depth is only a few micrometers — thinner than the typical 35 μm (1 oz) PCB copper layer. This means RF current flows only on the trace surface, raising effective resistance, and adding copper thickness beyond about 3× skin depth

For non-magnetic metals like copper, aluminum, silver, and gold, the formula is accurate within a few percent. For iron and steel, relative permeability depends strongly on magnetic field strength, frequency, and the material's magnetization history. The μᵣ values of 1000 for iron and 200 for steel here are assumed