# Skin effect

The skin effect is the tendency of alternating electric current to distribute itself non-uniformly in a conductor, with current density largest at the surface and decreasing with depth, so that at high frequencies a thin outer layer carries essentially all the current.<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup> [Direct current](https://www.edgepedia.org/direct-current), by contrast, flows uniformly over the conductor's cross-section. The effect grows with frequency and raises the effective AC resistance of a conductor above its DC resistance.<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup>

| Key fact | Detail |
|---|---|
| Definition | AC current crowds toward the conductor surface; current density is greatest at the surface and decreases at greater depths<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup> |
| Skin depth | Depth at which current density falls to 1/e (about 37%) of its surface value; δ = √(2/ωμσ)<sup>[2](https://link.springer.com/chapter/10.1007/978-3-031-14186-7_10)</sup><sup> • </sup><sup>[3](https://www.allaboutcircuits.com/technical-articles/learn-about-the-physics-behind-the-skin-effect-phenomenon/)</sup> |
| Current fraction | 63% of the current flows within one skin depth of the surface, 98% within 4δ<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup> |
| Copper values | Skin depth 8.47 mm at 60 Hz, 0.66 mm at 10 kHz, 66 µm at 1 MHz, 6.6 µm at 100 MHz<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup> |
| Resistance growth | AC resistance increases proportionally to the square root of frequency once the skin depth is small compared with the conductor size<sup>[4](https://www.ti.com/lit/ml/slyp172/slyp172.pdf)</sup> |
| Power frequency impact | At 50 Hz the AC resistance of a transmission line conductor may be 5–10% higher than its DC resistance<sup>[5](https://electrical-engineering-portal.com/respr/Electrical-power-systems-analysis-for-electrical-engineers-students-and-researchers.pdf)</sup> |
| Transient case | A fast DC current pulse also produces a transient skin effect: current first flows at the surface and diffuses inward over time<sup>[6](https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/joe.2018.8132)</sup> |

## Mechanism

The effect arises from the interaction of the conductor's own magnetic field with the current it carries. A longitudinal element near the center of a round conductor is linked by more magnetic flux than an element near the rim, so the counter-emf induced in the center is larger and the net driving emf there is reduced; current density consequently falls toward the center.<sup>[7](https://electrical-engineering-portal.com/sizing-of-power-cables-for-circuit-breaker-controlled-feeders-part-3)</sup> In the frequency-domain view, the fields inside the conductor obey a magnetic diffusion equation, and the sinusoidal steady-state solution is a diffusion wave that decays exponentially with depth while also advancing in phase.<sup>[8](https://web.mit.edu/6.013_book/www/chapter10/10.7.html)</sup>

The current density at depth y below the surface follows

\[ J_z(y) = J_0\, e^{-y/\delta}\, e^{-jy/\delta} \]

where J₀ is the surface current density. The first exponential gives the amplitude decay; the second gives a phase lag of one radian at one skin depth, and the current direction at particular depths can even reverse relative to the surface.<sup>[3](https://www.allaboutcircuits.com/technical-articles/learn-about-the-physics-behind-the-skin-effect-phenomenon/)</sup>

## Skin depth

The skin depth δ is defined as the depth at which the current density has fallen to 1/e, about 37%, of its value at the conductor surface.<sup>[2](https://link.springer.com/chapter/10.1007/978-3-031-14186-7_10)</sup> For a good conductor it is given by

\[ \delta = \sqrt{\frac{2}{\omega \mu \sigma}} \]

where ω = 2πf is the angular frequency, μ is the magnetic permeability, and σ is the conductivity.<sup>[3](https://www.allaboutcircuits.com/technical-articles/learn-about-the-physics-behind-the-skin-effect-phenomenon/)</sup> Equivalently, δ = √(ρ/(π·μ·f)) in terms of resistivity ρ.<sup>[9](https://getitdigital.uni-wuppertal.de/en/index.php?modul=6%2F08_skinEffekt.html&site=module)</sup> Because skin depth δ varies inversely with the square root of frequency, an order-of-magnitude change in frequency or conductivity changes δ only by a factor of about 3.<sup>[10](https://ocw.mit.edu/courses/res-6-001-electromagnetic-fields-and-energy-spring-2008/c2c9f1b3799709c8dcc448356b30a382_10.pdf)</sup><sup> • </sup><sup>[20](https://ntrs.nasa.gov/api/citations/19780021410/downloads/19780021410.pdf)</sup>

For copper a convenient shortcut is δ ≈ 66/√f mm with f in Hz.<sup>[11](https://unseel.com/engineering/skin-effect)</sup> Representative values for copper are:<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup>

| Frequency | Skin depth in copper |
|---|---|
| 60 Hz | 8.47 mm |
| 10 kHz | 0.66 mm |
| 100 kHz | 0.21 mm |
| 1 MHz | 66 µm |
| 10 MHz | 21 µm |
| 100 MHz | 6.6 µm |

Material matters as much as frequency. Copper and aluminum are essentially non-magnetic (relative permeability near 1), while a ferromagnetic material with μ_r ≈ 1000 collapses the skin depth dramatically; aluminum's skin depth is √2 times that of copper at the same frequency.<sup>[11](https://unseel.com/engineering/skin-effect)</sup><sup> • </sup><sup>[12](https://electrical-engineering-portal.com/losses-power-transmission-system)</sup> A US military handbook gives copper skin depths of 0.34 inch (8.63 mm) at 60 Hz but only 0.00026 inch (0.066 mm) at 1 MHz.<sup>[13](https://www.wbdg.org/FFC/NAVFAC/DMMHNAV/hdbk419a_vol1.pdf)</sup>

## Consequences for resistance

Because current occupies only the outer layer, the effective cross-section shrinks as frequency rises, and the AC resistance increases.<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup> When the skin depth is small compared with the conductor radius, the AC resistance rises in proportion to the square root of frequency.<sup>[4](https://www.ti.com/lit/ml/slyp172/slyp172.pdf)</sup> If the skin depth exceeds the wire radius, the AC resistance is essentially the DC resistance determined by the full cross-section.<sup>[14](https://www.nessengr.com/techdata/skin/skindepth.html)</sup>

The penalty is not confined to radio frequencies. At 50 Hz, transmission line conductors may show AC resistance 5–10% above DC.<sup>[5](https://electrical-engineering-portal.com/respr/Electrical-power-systems-analysis-for-electrical-engineers-students-and-researchers.pdf)</sup> For large distribution conductors carrying 2000 A, the resistance increase can reach 10–20%, and a [Schneider Electric](https://www.edgepedia.org/schneider-electric) guide estimates that a 10% extra loss in a 1000 mm² conductor carrying 2000 A costs, over a 20-year installation life, about the price of the copper it contains.<sup>[15](https://electrical-engineering-portal.com/download-center/books-and-guides/schneider-electric/losses-skin-proximity-effects)</sup>

## Related effects and mitigation

**Proximity effect.** Current distribution is also distorted by nearby current-carrying conductors. The alternating flux from an adjacent conductor induces eddy currents that further crowd the current; in a microstrip line over a [ground plane](https://www.edgepedia.org/ground-plane), the bottom surface of the trace carries more current than the top, and in two parallel wires carrying opposite currents the current crowds on the facing surfaces.<sup>[16](https://www.allaboutcircuits.com/technical-articles/understanding-the-skin-effect-cylindrical-and-rectangular-conductors-eddy-currents-and-current-crowding/)</sup> Cable AC resistance is commonly expressed as an AC/DC ratio combining skin and proximity factors.<sup>[7](https://electrical-engineering-portal.com/sizing-of-power-cables-for-circuit-breaker-controlled-feeders-part-3)</sup>

**Conductor design.** Above roughly 100 MHz, solid conductors waste metal, so multiconductor straps or tubing are used to exploit the larger surface area.<sup>[1](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)</sup> For windings, [Litz wire](https://www.edgepedia.org/litz-wire), made of many thin insulated strands, reduces skin effect losses; the skin effect is negligible in a round wire when the skin depth exceeds the wire radius.<sup>[17](https://www.allaboutcircuits.com/technical-articles/basic-inductor-design-constraints/)</sup> In transmission lines, the fact that current flows near the surface allows aluminum conductors to be reinforced with a braided steel core without lowering current-carrying capacity.<sup>[12](https://electrical-engineering-portal.com/losses-power-transmission-system)</sup>

**Transient skin effect.** The effect is not limited to sinusoidal excitation. When a fast DC current pulse is applied to a conductor, the current density initially appears only at the surface and diffuses inward; in a 20 mm × 10 mm copper bus bar carrying a 10 A step pulse, 2D finite-element simulation shows full penetration and uniform current density only after about 2 ms.<sup>[6](https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/joe.2018.8132)</sup> During this transient the conductor impedance varies with time, with likely consequences of increased resistance and joule heating, modified inductance, and a transient voltage that changes the apparent dynamic response of the circuit; switched-mode power electronics, power system transients, and pulsed DC applications are the situations most exposed.<sup>[6](https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/joe.2018.8132)</sup>

## Broader context

The same physics governs electromagnetic shielding and geophysical probing. In conducting media generally, the skin depth is the distance over which an electromagnetic wave's field strength decays to 1/e of its surface value; in copper at 1 GHz the skin depth is about 2 µm, roughly five orders of magnitude smaller than the 30 cm free-space wavelength.<sup>[18](https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-spring-2009/318e025511f2c95bb95b6322b30f9c06_MIT6_013S09_chap09.pdf)</sup> In geophysics, skin depth sets the trade-off between resolution and penetration: higher frequency gives finer resolution but shallower penetration.<sup>[19](https://www.epa.gov/environmental-geophysics/electromagnetic-signal-attenuation-skin-depth)</sup>

## References

1. [Skin Effect in AC Conduction, Georgia State University HyperPhysics](https://230nsc1.phy-astr.gsu.edu/hbase/electric/skineffect.html)
2. [Skin Effect, Springer Nature Link](https://link.springer.com/chapter/10.1007/978-3-031-14186-7_10)
3. [Demystifying the Skin Effect: Insights into AC Current Distribution, All About Circuits](https://www.allaboutcircuits.com/technical-articles/learn-about-the-physics-behind-the-skin-effect-phenomenon/)
4. [High Speed Analog Design and Application Seminar, Texas Instruments](https://www.ti.com/lit/ml/slyp172/slyp172.pdf)
5. [Electrical Power Systems Analysis for Electrical Engineers, Students and Researchers](https://electrical-engineering-portal.com/respr/Electrical-power-systems-analysis-for-electrical-engineers-students-and-researchers.pdf)
6. [Transient skin effect in power electronic applications, The Journal of Engineering (2019)](https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/joe.2018.8132)
7. [Sizing of power cables for circuit breaker controlled feeders (part 3), Electrical Engineering Portal](https://electrical-engineering-portal.com/sizing-of-power-cables-for-circuit-breaker-controlled-feeders-part-3)
8. [Skin Effect, MIT 6.013 Electromagnetic Fields and Energy, Sec. 10.7](https://web.mit.edu/6.013_book/www/chapter10/10.7.html)
9. [Skin effect module, GET it digital, University of Wuppertal](https://getitdigital.uni-wuppertal.de/en/index.php?modul=6%2F08_skinEffekt.html&site=module)
10. [Electromagnetic Fields and Energy, MIT OpenCourseWare](https://ocw.mit.edu/courses/res-6-001-electromagnetic-fields-and-energy-spring-2008/c2c9f1b3799709c8dcc448356b30a382_10.pdf)
11. [The Skin Effect — Formula, Skin Depth & Interactive Explainer, Unseel](https://unseel.com/engineering/skin-effect)
12. [Losses in the power transmission system, Electrical Engineering Portal](https://electrical-engineering-portal.com/losses-power-transmission-system)
13. [MIL-HDBK-419A, Grounding, Bonding, and Shielding, Volume 1](https://www.wbdg.org/FFC/NAVFAC/DMMHNAV/hdbk419a_vol1.pdf)
14. [Skin Depth and Skin Effect Formulas, Ness Engineering Technical Data](https://www.nessengr.com/techdata/skin/skindepth.html)
15. [Extra losses caused in high current conductors by skin and proximity effects, Schneider Electric guide](https://electrical-engineering-portal.com/download-center/books-and-guides/schneider-electric/losses-skin-proximity-effects)
16. [The Skin Effect in Cylindrical and Rectangular Conductors, All About Circuits](https://www.allaboutcircuits.com/technical-articles/understanding-the-skin-effect-cylindrical-and-rectangular-conductors-eddy-currents-and-current-crowding/)
17. [Basic Inductor Design, All About Circuits](https://www.allaboutcircuits.com/technical-articles/basic-inductor-design-constraints/)
18. [Electromagnetics and Applications, MIT 6.013, Chapter 9](https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-spring-2009/318e025511f2c95bb95b6322b30f9c06_MIT6_013S09_chap09.pdf)
19. [Electromagnetic Signal Attenuation (Skin Depth), US EPA](https://www.epa.gov/environmental-geophysics/electromagnetic-signal-attenuation-skin-depth)
20. [ntrs.nasa.gov](https://ntrs.nasa.gov/api/citations/19780021410/downloads/19780021410.pdf)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Electromagnetism › Electric and magnetic fields › Electromagnetic induction and time-varying fields › Eddy currents*

*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*

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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license