How this calculator works
Alternating fields and current decay into a good conductor. Skin depth is the distance over which their amplitudes fall to 1/e of the surface value. The classical approximation assumes conduction current dominates displacement current, linear real permeability, local conductivity and a conductor thick relative to penetration depth. Metal presets use approximate 20 °C resistivity and relative permeability 1. Enter measured values for nickel, ferromagnets or other operating temperatures. It does not model anomalous skin effect, superconductors, or a complete cylindrical-wire current profile.
Formula
delta = sqrt(2 rho/(omega mu)) = sqrt(rho/(pi f mu0 mur)); omega = 2 pi f. Current amplitude J(x) = J(0) exp(-x/delta).
Worked example
A material with rho = 0.000394784175991 ohm m and relative permeability 1 has skin depth about 0.1 m at 10 kHz. At 40 kHz, the depth halves to 0.05 m.
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Frequently asked questions
Does most current stop exactly at one skin depth?
No. Amplitude decays continuously and is 36.8% of its surface value at one depth.
What happens when frequency is quadrupled?
Skin depth halves when the material properties stay constant.
Can I use DC?
The ideal skin depth tends to infinity at zero frequency. This finite calculation requires a positive frequency.