What this calculator does
Alternating current does not spread evenly through a conductor. It crowds toward the surface, and the higher the frequency the thinner the conducting layer becomes. At mains frequency copper conducts through about 8.4 millimetres of its surface; at 1 MHz that has collapsed to 0.065 millimetres.
This is why high-frequency conductors are often silver-plated rather than solid silver, and why a thick solid bar is no better than a tube at radio frequencies. The centre simply carries no current.
The formula
Skin depth is the square root of resistivity divided by pi times frequency times the permeability. Since frequency sits under a square root, multiplying the frequency by a hundred only reduces the depth tenfold.
| Term | Meaning |
|---|---|
| Skin depth (δ) | The depth at which current density has fallen to about 37 per cent of the surface value. |
| Skin effect | The tendency of alternating current to concentrate near a conductor's surface. |
| Relative permeability (μr) | How strongly the material responds magnetically. Copper is 1; steel is in the hundreds. |
The inputs explained
| Field | What to enter |
|---|---|
| Resistivity (ρ) (Ω·m) | Resistivity in ohm metres. Copper is 1.68×10⁻⁸. |
| Frequency (f) (Hz) | The frequency of the alternating current, in hertz. |
| Relative permeability (μr) | Relative permeability. Use 1 for copper, aluminium and other non-magnetic conductors. |
When to use it
Choosing conductor geometry for RF
Beyond a few skin depths the extra metal does nothing, so tubes and plating work as well as solid bar.
Understanding why steel wire is lossy
Steel's high permeability shrinks the skin depth dramatically, concentrating current and raising AC resistance.
Specifying a shield thickness
A shield several skin depths thick attenuates the field effectively at the frequency of interest.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How deep does current flow in copper at each frequency?
Skin depth across five decades of frequency.
| Frequency | Skin depth (δ) | At 10× frequency |
|---|---|---|
| 60 Hz | 8.422 mm | 2.663 mm |
| 1 kHz | 2.063 mm | 0.6523 mm |
| 1 MHz | 0.0652 mm | 0.0206 mm |
Questions
Why does current avoid the centre of a conductor?
The changing current generates a magnetic field inside the conductor, which induces eddy currents that oppose flow in the middle and reinforce it at the surface. The net result pushes current outward.
Does current stop completely below the skin depth?
No, it decays exponentially rather than cutting off. At one skin depth it has fallen to about 37 per cent, and at three skin depths to about 5 per cent, so deeper metal contributes very little.
Why is steel worse than copper for AC?
Two reasons compound. Steel has higher resistivity and far higher permeability, and both shrink the skin depth, so the current is forced into a much thinner layer and the effective resistance rises sharply.
Why is silver plating enough for RF?
Because at high frequency essentially all the current flows within a few microns of the surface. A thin plating of a better conductor carries it, and the base metal underneath only provides structure.
For conductor resistance generally, see the resistor calculator. For how filters behave with frequency, see the low-pass filter calculator.