Skin effect

The depth at which the current has fallen to 1/e = 0.37 of its value at the surface. A signal travelling along a conductor flows more readily near the surface and less readily deeper in. The higher the frequency, the more pronounced the effect. Impulse and ESD noise is high in frequency, so the skin effect keeps it on the surface of conductors and boards.

Signal frequency

SI prefixes accepted (4k7 / 1M / 10m / 220). Upper-case M = mega, lower-case m = milli

Depth at 1/e of surface current

—mm

History

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Formula

Skin depth in copper: δ = 66 / √f [mm]
(f: frequency [Hz])
Example: 1 GHz → δ ≈ 2.1 µm

Design notes

Alternating current crowds towards the surface of a conductor as frequency rises. The effective cross-section shrinks, resistance goes up and so does loss.

Skin depth in copper:
• 60 Hz (mains): ≈ 8.5 mm
• 1 MHz: ≈ 0.066 mm
• 100 MHz: ≈ 6.6 µm
• 1 GHz: ≈ 2.1 µm

ESD and surge currents ride the surface of conductors and boards for the same reason, which is something shielding design can turn to its advantage.

When you need this

For estimating conductor loss at high frequency, and for understanding why thicker copper stops helping above a certain point. It looks like a power topic but it drives high-speed signal attenuation and switching-converter inductor design.

What skin depth is

Alternating current does not fill a conductor uniformly. The higher the frequency, the more it crowds towards the surface, leaving the interior carrying almost nothing. Skin depth δ is where the current density has fallen to 1/e (about 37%) of the surface value.

In practice you can treat it as only a layer δ deep being used. Once the conductor is more than about twice δ thick, adding thickness barely reduces AC resistance.

Skin depth in copper

Copper at 20°C, ρ = 1.72×10⁻⁸ Ω·m. Compare against 35µm for 1oz foil.
Frequency	Skin depth	Versus 1oz (35µm)
100 kHz	about 209 µm	The full thickness is in use
1 MHz	about 66 µm	Still uses the full thickness
3.5 MHz	about 35 µm	Equal to the foil thickness
10 MHz	about 21 µm	Only 60% of the thickness
100 MHz	about 6.6 µm	20% of the thickness
1 GHz	about 2.1 µm	6% of the thickness

For 1oz copper the crossover is around 3.5MHz. Above that, moving to 2oz barely changes AC resistance. Make the trace wider instead — skin effect scales with perimeter.

Where it shows up

High-speed differential loss. At a few GHz, copper surface roughness (Rz) adds to skin effect. Rough foil lengthens the current path and raises loss. Above 10Gbps, specify low-profile foil (VLP / HVLP).
Switching converter inductors. Against a few hundred kilohertz of ripple, bundled fine strands (Litz wire) achieve lower AC resistance than one thick conductor.
AC content on power traces. DC uses the whole cross-section, but ripple and switching noise use only the surface. Estimating heating from DC resistance alone understates it.
Return current in ground planes. High-frequency return current concentrates directly under the signal trace and, because of skin effect, uses only the surface of the plane — so plane thickness contributes almost nothing at high frequency.

Frequently asked questions

Does thicker copper reduce high-frequency loss?

Barely. Anything deeper than the skin depth is not used. 1oz (35µm) matches skin depth at 3.5MHz, so above that, extra thickness is wasted. Widen the trace or choose a lower-loss-tangent laminate instead.

Does temperature affect skin depth?

Yes. Resistivity rises with temperature, so skin depth increases. Copper is about 31% more resistive at 100°C, making skin depth about √1.31 ≈ 1.14 times deeper. In practice the frequency dependence (inverse square root) matters far more.

How much does copper roughness cost?

It becomes significant above a few GHz. Standard foil has Rz around 5µm, larger than the 2.1µm skin depth at 1GHz. Current follows the profile, lengthening the path and raising loss by as much as 1.5 times. Low-profile foil is under 2µm.

Is it different for aluminium or gold?

It scales with resistivity and permeability. Aluminium is more resistive, so its skin depth is about 1.3 times deeper. This calculator is fixed to copper. Note that iron and nickel have far higher permeability and hence very shallow skin depth, which is why surface plating material matters at high frequency.

Standards and references

IPC-2141A — Conductor loss and skin effect at high frequency.
IPC-4562 — Copper foil specification, including profile (roughness) classes.

Last updated: 2026-08-29