Skin Depth Calculator: AC Current Penetration in Copper, Aluminium and Other Conductors
How deep AC current flows into a conductor.
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How this calculator works
Choose the conductor, or type its resistivity, and enter the permeability if it is magnetic.
Enter the frequency and the wire diameter.
The calculator gives the skin depth and the ratio of the AC resistance to the DC resistance.
Formulas used
- \delta = \sqrt{\frac{\rho}{\pi f \mu}}
- \mu = \mu_0\mu_r
- R_{ac}/R_{dc} \approx \frac{r^2}{2r\delta - \delta^2}
Worked example
With the default numbers in the calculator above:
- Skin depth: 0.065234 mm (65.234 micrometres)
- Resistance compared with the same wire on direct current: 7.923 times
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Frequency 50 Hz.
- Skin depth: 9.2255 mm (9225.5 micrometres)
- Resistance compared with the same wire on direct current: 1.0 (the current fills the wire)
Common questions
What is the skin effect?
At high frequency, AC current flows mainly near the surface of a conductor, so the resistance goes up.
What is the skin depth of copper at 50 Hz?
About 9.2 mm, so for normal wire sizes the skin effect is small at mains frequency.
What reduces the skin effect?
Using many thin insulated strands (Litz wire), or a hollow or flat conductor.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any electromagnetics text (the skin effect).
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