RF Skin Depth Calculator
Enter material, frequency and conductor geometry to find skin depth, AC resistance and the current-carrying derating.
Step-by-step
- Enter valid values to begin.
Skin depth δ = √(ρ/(π f μ0μr)) with μ0 = 4π×10−7 H/m. Resistivities are 20 °C typical values (aluminium alloys run 26.5–28.2 nΩ·m, brass about 64–70 nΩ·m); iron and steel μr are typical only and fall with frequency and vary widely by alloy. Round wire uses the annulus approximation Rac = Rdc·r²/(2rδ−δ²) for δ<r. Flat traces use effective area = perimeter × δ (limited to the DC area). Proximity effect, ground-plane current crowding and temperature are not modelled. Roughness uses the Hammerstad factor 1+(2/π)atan(1.4(Δ/δ)²), maximum 2.
RF Skin Depth: Why Thick Copper Doesn’t Help at Frequency
Core Engineering Principles
At DC the current spreads evenly through the whole conductor. Alternating current makes changing flux inside the metal, and the eddy currents it drives oppose the current in the middle while reinforcing it near the surface. The density falls off exponentially with depth, and the skin depth δ = √(ρ/(π f μ0μr)) is where it has dropped to 37% of the surface value. For copper that is about 8.4 mm at 60 Hz, 65 µm at 1 MHz, 6.5 µm at 100 MHz and 2.1 µm at 1 GHz.
The consequence is that resistance rises with the square root of frequency while the copper in the middle carries nothing. A 1 mm wire at 100 MHz has an effective cross-section of about 0.02 mm², not 0.785 mm², so its resistance is about 39 times the DC value. That is why RF builders use thin strip, tubing and plated surfaces, and why Litz wire only works from audio up to a few megahertz. Steel is a trap: with μr around 100 the skin depth shrinks tenfold, so steel conductors are lossy at RF. On circuit boards, rough copper foil adds up to a factor of two at GHz once the roughness approaches δ.
Flat trace: Aeff = min(Adc, perimeter × δ) • Roughness = 1 + (2/π) atan(1.4(Δ/δ)²)
NEC & Standard References
IEEE Std 100 defines skin effect and skin depth. IEC 60287-1-1 gives skin- and proximity-effect factors for power cables, which matter at 50/60 Hz in large conductors. IPC-2152 covers the DC temperature rise and current capacity of printed conductors, and IPC-2221 the general design rules. Neither addresses RF conduction loss, so treat their ampacity as a DC baseline and derate for the AC resistance this tool reports. Verify material resistivity against the supplier’s data sheet.1. δ = √(1.68×10−8 / (π × 108 × 1.2566×10−6)) = 6.52 µm.
2. DC area = 0.7854 mm²; AC annulus area = π(2rδ − δ²) = 0.02036 mm².
3. Rdc = 0.02139 Ω/m; Rac = 0.825 Ω/m (0.0210 Ω/inch).
4. Rac/Rdc = 38.6, so for equal heating the wire carries only 1/√38.6 = 16.1% of its DC current.
5. Plating of 3δ = 19.6 µm carries 95% of the current.
- Plating must be thick enough. A silver layer thinner than about 3δ lets current dive into the base metal; silver’s 5% lower resistivity gains little, so it mainly buys oxidation resistance.
- Hollow is as good as solid. At RF a tube with wall thickness above 3δ carries the same current as a rod, so save the copper.
- Steel and iron are poor RF conductors. High permeability shrinks δ, and μr itself falls with frequency, so the preset values are only typical.
- Joints and corners add loss. Oxidised or painted contact faces put resistance exactly where the current flows.