Skin Depth Calculator
Electromagnetic skin depth in a conductor from frequency, conductivity and permeability — copper, aluminium, steel or custom — with the AC resistance rise of a round wire.
How it works
δ = √[1 ÷ (π·f·μ₀·μᵣ·σ)] = √[2ρ ÷ (ω·μ)]; R_ac ≈ R_dc · r² ÷ [r² − (r − δ)²] for δ < r
Alternating current induces eddy currents that cancel the flow in a conductor’s interior, so current crowds toward the surface within a layer of depth δ that shrinks with the square root of frequency. At 50 Hz copper’s skin depth is 9 mm and household wiring is unaffected; at 1 MHz it is 65 µm, so RF conductors are effectively hollow — which is why Litz wire, silver plating and hollow waveguides exist. Magnetic materials like steel have tiny skin depths because permeability multiplies the effect.
Worked example
Copper at 1 MHz: δ = 65 µm. A 1 mm wire therefore carries current in an annulus 0.065 mm thick and has 4.1× its DC resistance.
Frequently asked questions
At what frequency does skin effect matter for mains wiring?
A 2 mm copper wire equals its skin depth around 4.4 kHz; at 50 Hz the effect is under 1%.
Why does the AC resistance formula stop at δ = r?
When δ exceeds the radius the current fills the whole wire and R_ac ≈ R_dc; the annulus approximation only applies for δ < r.
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This calculator is for educational purposes. Double-check important results before acting on them.