Calculators / 08
Skin Depth and Surface Roughness Calculator
At high frequency, current crowds into a thin layer at the conductor's surface — the skin depth δ, which shrinks as 1/√f. Once δ is smaller than the copper, the copper's thickness stops mattering and its surface starts to: a rough surface makes the current travel further, and loss rises.
Reading the numbers
- Copper's skin depth is 2.06 µm at 1 GHz — thinner than the roughness of standard foil.
- Skin effect sets in where δ falls to half the thickness: above it, resistance grows as √f.
- The roughness multiplier saturates at 2: once the bumps are much taller than δ, the path cannot get much longer.
Every value is in the address bar as you change it, so a link reproduces the calculation exactly.
Type values with SI prefixes — 100n, 2.2p, 16G — or
drag the sliders; a bare number keeps the prefix already shown.
The formulas
Go deeper — assumptions, how it is checked, and sources
Assumptions. Copper at 20 °C; resistivity rises about 0.4% per °C. The roughness model is a fit that works up to a few tens of GHz and saturates at 2; the Huray model describes very rough foils better at higher frequency.
How it is checked. δ falls as 1/√f exactly; it matches the textbook 8.4 mm at 60 Hz and the 2.06 µm used elsewhere on this site; the roughness multiplier is 1 for smooth copper and tends to 2 for very rough copper.
Sources. S. Ramo, J. R. Whinnery and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., Wiley, 1994; E. Hammerstad and Ø. Bekkadal, Microstrip Handbook, ELAB report STF44 A74169, University of Trondheim, 1975.