Skin depth calculator, with AC resistance.
Skin depth for common conductors at any frequency and temperature, and how much it raises the resistance of your wire.
Skin depth calculator
- Skin depth δ
- 206.3 µm
- R_ac / R_dc of the round wire
- 1.466
- Largest strand for R_ac ≈ R_dc (d ≈ 2δ)
- 412.6 µm
- Resistivity at this temperature
- 1.68e-8 Ω·m
Isolated straight round wire; proximity effect from nearby turns raises AC resistance further.
What is skin depth?
Skin depth is the distance below a conductor’s surface at which an alternating current density has fallen to 1/e, about 37 %, of its value at the surface. It is δ = √(ρ / (π f μ0 μr)), so it shrinks with the square root of frequency: copper at 20 °C has a skin depth of about 9.2 mm at 50 Hz, 0.21 mm at 100 kHz and 0.065 mm at 1 MHz. Once a wire is much thicker than two skin depths, the current crowds into a thin outer layer and the AC resistance rises above the DC value, which is why high-frequency magnetics use Litz wire or foil. This calculator gives δ for common conductors at any frequency and temperature, plus the exact AC-to-DC resistance ratio of an isolated round wire from the Bessel-function solution.
Worked example
Copper at 20 °C (ρ = 1.68×10⁻⁸ Ω·m), and a 1 mm diameter round wire:
| 50 Hz | δ = 9.225 mm, 1 mm wire R_ac/R_dc = 1 |
|---|---|
| 1 kHz | δ = 2.063 mm, 1 mm wire R_ac/R_dc = 1 |
| 100 kHz | δ = 206.3 µm, 1 mm wire R_ac/R_dc = 1.47 |
| 1 MHz | δ = 65.23 µm, 1 mm wire R_ac/R_dc = 4.09 |
| 10 MHz | δ = 20.63 µm, 1 mm wire R_ac/R_dc = 12.4 |
Above about 100 kHz a 1 mm wire carries most of its current in a thin shell, so its AC resistance is several times its DC resistance.
When you need the full simulator
This calculator is free to use and answers one question at a time. The full AirInduct Sim simulator goes further:
- Winding AC resistance with proximity effect for multi-layer, foil and Litz windings in the Magnetics Designer.
- Eddy-current losses in plates, shields and workpieces in the 2D and 3D field solvers.
- Induction-heating power and temperature versus time in the Induction Heating & NDT module.
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Frequently asked questions
What wire size avoids skin effect?
A round wire whose diameter is no more than about twice the skin depth has an AC resistance within a few percent of its DC resistance. At 100 kHz in copper that is roughly 0.4 mm, which is why Litz strands for that range are usually 0.1 to 0.2 mm.
Does temperature change the skin depth?
Yes. Resistivity rises with temperature (about 0.39 % per °C for copper), and skin depth grows with the square root of resistivity, so a hot winding has a slightly larger skin depth but a higher resistance overall.
Is skin effect the same as proximity effect?
No. Skin effect is caused by a conductor’s own current. Proximity effect is current crowding caused by the field of neighbouring conductors, and in multi-layer windings it usually dominates. This calculator covers skin effect only; the Magnetics Designer includes both.