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Skin Depth Percentage Calculator

Express skin depth as a percentage of trace thickness and get the AC/DC resistance ratio that follows, so you can tell whether a copper weight choice still matters at your frequency.

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Formula

δ=ρπfμ0,δt×100%,teff=2δ(1−e−t/2δ)\delta = \sqrt{\frac{\rho}{\pi f \mu_0}},\qquad \frac{\delta}{t}\times 100\%,\qquad t_{eff} = 2\delta\left(1 - e^{-t/2\delta}\right)

Reference: Standard skin-effect result; ρ₂₀(Cu) = 1.724×10⁻⁸ Ω·m, α = 0.00393/°C.

δ— Skin depth (μm)
t— Conductor thickness (μm)
ρ— Resistivity at temperature (Ω·m)
f— Frequency (MHz)
μ₀— Permeability of free space, 4π×10⁻⁷ H/m (H/m)

How It Works

Skin depth on its own is not an actionable number. Knowing that the skin depth in copper at 1 GHz is about 2 µm tells you nothing until you know whether the conductor is 17.5 µm thick or 105 µm thick. The useful quantity is the ratio.

Skin depth is the distance over which current density falls to 1/e of its surface value. It depends on resistivity and frequency and not at all on the geometry, and it scales as the inverse square root of frequency — quadruple the frequency and the skin depth halves.

A flat conductor such as a PCB trace conducts on both faces, so integrating the exponential current profile through the thickness gives an effective conducting depth of 2δ(1 − e^(−t/2δ)), capped at the real thickness. The AC to DC resistance ratio is then simply the thickness divided by that effective depth. At low frequency, where the skin depth exceeds the thickness, the ratio approaches 1 and the whole cross-section carries current. At high frequency it grows as the square root of frequency.

Expressed as a percentage, the number tells you directly whether a copper weight decision still matters. Above about 100% the conductor is fully used and adding copper reduces AC resistance proportionally. Below about a third, most of the copper is idle at that frequency and extra thickness buys almost nothing electrically — though it still helps thermally and at DC, so heavier copper is not wasted, it just stops helping the AC case.

Resistivity is corrected for temperature here, because a trace running at 105 °C has roughly a third more resistivity than one at 20 °C, and that shifts both the skin depth and the resistance.

One limitation worth keeping in mind: this models a smooth conductor. As skin depth shrinks toward the roughness profile of the copper foil, the real AC resistance rises above what this ratio predicts, and on rough foil at high frequency the difference is substantial.

Worked Example

Take 1 oz copper — 35 µm — at 1 GHz, at room temperature.

The skin depth works out to 2.090 µm. As a fraction of the conductor:

2.090 / 35 × 100 = 5.97%

So about six percent of the thickness is doing the conducting. The effective conducting depth, counting both faces, is 4.178 µm, and the AC to DC resistance ratio is:

35 / 4.178 = 8.376

The sheet resistance tells the same story in units you can use directly: 0.4926 mΩ per square at DC, 4.126 mΩ per square at 1 GHz.

Sweeping frequency on the same 35 µm copper makes the transition visible:

1 MHz — δ = 66.08 µm, 188.8% of thickness, ratio 1.138 100 MHz — δ = 6.608 µm, 18.88%, ratio 2.850 1 GHz — δ = 2.090 µm, 5.971%, ratio 8.376 10 GHz — δ = 0.6608 µm, 1.888%, ratio 26.48

At 1 MHz the skin depth is nearly twice the thickness and the trace is behaving much as it does at DC. By 10 GHz the current is confined to under two percent of the copper, and the resistance is twenty-six times the DC value.

Practical Tips

  • ✓Use the percentage as a design gate: above 100%, copper weight matters proportionally; below a third, it barely matters electrically.
  • ✓For loss-critical high-frequency work, choose the copper foil by its roughness profile rather than its weight — at that point the surface matters more than the bulk.
  • ✓Evaluate at the highest frequency of interest, not the fundamental. A 1 GHz clock has significant energy well into its harmonics.
  • ✓Compare the AC sheet resistance directly against your loss budget rather than converting through the ratio; it is the number that multiplies your trace length.
  • ✓Run the calculation at operating temperature, not ambient, for anything carrying meaningful current.
  • ✓Where the percentage is near 100%, the frequency is in the transition region and neither the DC nor the fully-skin-limited approximation is accurate — use the ratio directly.

Common Mistakes

  • ✗Quoting skin depth without the conductor thickness. The number is meaningless in isolation — the comparison is the whole point.
  • ✗Assuming heavier copper always reduces high-frequency loss. Once the skin depth is a small fraction of the thickness, extra copper adds cross-section that carries almost no current.
  • ✗Using the simple ratio thickness/skin depth as the AC resistance ratio. A flat conductor conducts on both faces, so the effective depth is roughly twice the skin depth until the thickness runs out.
  • ✗Working at 20 °C when the trace runs hot. Resistivity rises about 0.39% per degree, so a trace at 105 °C has noticeably higher loss than the room-temperature figure suggests.
  • ✗Ignoring surface roughness at high frequency. Once the skin depth approaches the roughness profile, measured loss exceeds the smooth-conductor prediction significantly.

Frequently Asked Questions

Because the number that matters is the comparison. A skin depth of 2 µm means nothing until you know whether the copper is 17.5 µm or 105 µm thick. The percentage tells you directly whether the conductor is being used or whether most of it is idle.
Once the skin depth is well under a third of the thickness, extra copper adds cross-section that carries almost no current at that frequency. It still helps thermally and at DC, so heavier copper is not wasted — it just stops helping AC resistance.
Yes, and increasingly so as skin depth shrinks toward the roughness profile. This calculator models a smooth conductor, so at high frequencies on a rough foil the real AC resistance will be higher than the ratio here suggests.
Because a flat conductor conducts on both its faces. Each face contributes an exponentially decaying layer, and the two add until they meet in the middle — at which point the effective depth is capped at the real thickness.
The skin depth itself does, since it depends only on material and frequency. The effective-depth expression here assumes a flat conductor conducting on two faces, so for round wire the geometry factor differs.

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