Skin Depth Calculator
Skin depth sets how much of a conductor actually carries high-frequency current. Pick a material or enter resistivity directly; the calculator also reports the sheet resistance of one skin depth and checks that the diffusion approximation still holds.
Choosing something to solve for makes Skin depth an editable target and computes the chosen input from it.
Formula
| delta | skin depth, the 1/e decay distance of current density (m) |
| rho | electrical resistivity at operating temperature (ohm m) |
| f | frequency (Hz) |
| mu0 | permeability of vacuum, 1.25663706 x 10^-6 H/m |
| mur | relative permeability, dimensionless |
| Rs | surface resistance, ohm per square |
What this model assumes, and where it stops
Assumptions
- A semi-infinite flat conductor with a plane wave arriving normal to the surface.
- Good conductor: conduction current dominates displacement current, sigma >> omega epsilon.
- Linear, isotropic, homogeneous material with a single scalar permeability.
- Steady-state sinusoidal excitation at one frequency.
Limitations
- Curvature is ignored. For a round wire whose radius is comparable to delta, the flat-surface result is optimistic; use the wire resistance calculator, which solves the cylindrical case exactly.
- Proximity effect is ignored entirely. In a multi-turn winding, current crowding from neighbouring conductors often exceeds the skin-effect loss.
- For ferromagnetic conductors mur is a strong function of field amplitude and stress; a single nominal value can be wrong by more than an order of magnitude, and delta scales as 1/sqrt(mur).
- The linear tempco of resistivity is not applied here - enter rho at the temperature you care about.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Conductors whose radius or thickness is within a factor of a few of delta, where the 1D decay picture breaks down.
- Any winding with more than one turn or layer, where proximity effect and circulating currents dominate.
- Edge and corner effects on rectangular busbars and PCB traces, where current concentrates at the corners.
- Ferromagnetic parts where local saturation changes mur, and therefore delta, from point to point.
- Fields near an air gap, where fringing flux drives eddy currents in nearby conductors.
Common questions
What is the skin depth of copper at 100 kHz?
About 206 um at 20 degC, using rho = 1.68e-8 ohm m. Skin depth scales as one over the square root of frequency, so copper is roughly 9.2 mm at 50 Hz, 206 um at 100 kHz and 65 um at 1 MHz.
Why is skin depth so much smaller in steel than in copper?
Steel is both more resistive and strongly magnetic. Skin depth scales as one over the square root of relative permeability, so a mild steel with mur around 1000 has a skin depth roughly 30 times smaller than a non-magnetic conductor of the same resistivity. That permeability is also field dependent, which is why a single number for steel is only ever indicative.
Does skin depth alone tell me the AC resistance of a wire?
No. Skin depth is derived for a flat semi-infinite conductor. For a round wire whose radius is comparable to the skin depth you need the cylindrical solution, and in any multi-turn winding proximity effect from neighbouring conductors usually exceeds the skin effect. Use the wire resistance and winding AC resistance calculators for those.
References
- Ramo, Whinnery & Van Duzer - Fields and Waves in Communication Electronics, 3rd ed., ch. 3
- Jackson - Classical Electrodynamics, 3rd ed., section 8.1