Skin depth calculator
Skin depth is how far RF current flows into a conductor. At one skin depth the current density has fallen to 37 % of its surface value. It shrinks with the square root of frequency, so copper carries 1 GHz current in its outer two micrometres. This calculator gives δ, surface resistance and the plating thickness worth paying for.
High-purity copper at 20 °C. Commercial annealed copper (100 % IACS, exactly 58 MS/m) is 1.72×10⁻⁸ Ω·m, which adds about 1 % to the skin depth. Hard-drawn copper adds a little more.
The curve is the current density J(x) dying away into the metal, and the bar below is the same conductor in cross-section, shaded by that current. The profile depends only on x/δ, so it keeps its shape: what changes with frequency and material is the ruler underneath, whose decade marks slide as δ grows or shrinks. Amber marks one skin depth, grey marks five. The depth axis is logarithmic, so the surface itself sits just off the left edge.
Assumes a smooth, isotropic conductor thicker than a few skin depths, unsaturated if magnetic, and resistivity at 20 °C. Real plating is layered, real surfaces are rough, and resistivity climbs about 0.4 % per kelvin, so treat δ as a design figure with a few per cent of uncertainty. The material list quotes published table values, re-checked on 18 August 2026 and credited under Sources. Brass and carbon steel are nominal alloy figures rather than specifications, so use the custom entry when you have a measured resistivity.
Skin depth by frequency
| Frequency | Skin depth δ | Surface resistance Rs | Minimum plating 5δ |
|---|---|---|---|
| 1 MHz | 65.2 µm | 258 µΩ/sq | 326 µm |
| 10 MHz | 20.6 µm | 814 µΩ/sq | 103 µm |
| 100 MHz | 6.52 µm | 2.58 mΩ/sq | 32.6 µm |
| 1 GHz | 2.06 µm | 8.14 mΩ/sq | 10.3 µm |
| 10 GHz | 652 nm | 25.8 mΩ/sq | 3.26 µm |
The selected material from 1 MHz to 10 GHz. Ten times the frequency means 3.16 times less depth and 3.16 times more surface resistance.
How it works
- 01
Pick the conductor
Each metal brings a resistivity ρ, quoted at 20 °C, and a relative permeability μr. Silver, copper, gold, aluminium, brass, zinc and tin all have μr = 1. Nickel and carbon steel are ferromagnetic, with μr in the hundreds, which squeezes the current into a far thinner layer.
- 02
Compute the skin depth
The current density decays into the metal as J(x) = J0·e−x/δ, with δ = ρ / (π·f·μ0·μr). Because δ goes with the square root of frequency, ten times the frequency leaves 3.16 times less depth. Copper carries 1 MHz current in 65 µm and 1 GHz current in 2.06 µm.
- 03
Read the surface resistance
Rs = ρ/δ is the resistance of any square patch of a thick conductor, in ohms per square, and it is the number that sets conductor loss in coax, waveguide and microstrip. It rises as the square root of frequency. Copper at 1 GHz gives 8.14 mΩ per square, brass 1.9 times more, mild steel nearly 30 times more.
- 04
Choose the plating thickness
A layer 3δ thick carries 95 % of the current, 5δ carries 99.3 %. Five skin depths of a good conductor is the standard target. Thicker plating changes nothing, and thinner plating lets the base metal underneath carry current and add its own loss.
Formulas
- δ — skin depth, m
- ρ — resistivity, Ω·m (copper: 1.68×10−8)
- f — frequency, Hz
- μ0 — 4π×10−7 H/m
- μr — relative permeability, 1 for non-magnetic metals
- Rs — surface resistance, Ω per square
- conductor loss is proportional to Rs, so it grows as f
- t = δ → 63.2 %
- t = 3δ → 95.0 %
- t = 5δ → 99.3 %
Worked example
- ρ = 1.68×10−8 Ω·m, μr = 1, f = 1 GHz
- π · f · μ0 = π · 109 · 4π×10−7 = 3947.8
- δ = 1.68×10−8 / 3947.8 = 2.0629×10−6 m = 2.06 µm (81.2 µin)
- Rs = 1.68×10−8 / 2.0629×10−6 = 8.14 mΩ per square
- 5δ = 10.3 µm → thicker copper plating adds nothing
FAQ
- How thick does RF plating need to be?
- Five skin depths of the plated metal is the working rule: that layer carries 99.3 % of the current, and anything thicker is metal you paid for and cannot use. Three skin depths already carry 95 %. For copper at 1 GHz five skin depths is about 10 µm, or 400 µin.
- Does silver plating really lower loss?
- Not much over copper. Silver is 5 % less resistive, and surface resistance follows the square root of that, so Rs drops by only 2.7 %. Silver plating pays off on brass and steel hardware such as connectors, waveguide and filter cavities, where the bulk metal has roughly 1.9 and 30 times copper’s surface resistance. Silver tarnish also stays conductive, while copper oxide does not.
- Why are steel and nickel such poor RF conductors?
- Both are ferromagnetic. A relative permeability near 100 divides the skin depth by ten and multiplies the surface resistance by ten on top of the material’s own resistivity. Nickel at 1 GHz has about 166 mΩ per square against copper’s 8.14 mΩ. That is why a nickel barrier layer under gold plating quietly ruins a microwave circuit. The gold is far thinner than a skin depth, so the RF current runs in the nickel.
- Does surface roughness change the result?
- Yes, once the roughness is comparable to δ. The current follows the contour of the surface, so a rough conductor gives it a longer path. The usual correction saturates at about twice the smooth-metal surface resistance for roughness of a couple of skin depths. Copper at 5.8 GHz has δ = 0.86 µm, which a 1–2 µm PCB foil tooth profile already rivals.
- How does skin depth relate to coax cable loss?
- Directly. The conductor part of coax attenuation is proportional to Rs, so it rises as the square root of frequency, which is the √f term in every cable model. The dielectric part rises linearly with frequency and takes over higher up. Skin effect is also why the centre conductor of a quality cable is silver-plated or copper-clad. Only its outer skin carries current.
Skin effect decides how much of your power survives the feedline. Where the rest of it lands is a terrain question — Waveshed maps line-of-sight and RF coverage over real elevation data, free in your browser.
Open the coverage simulator →Related guides
- Plan radio coverage (RF / ITM) — skin effect is where feedline and connector loss comes from — subtract it before you enter radiated power
Sources & further reading
- NIST/CODATA — vacuum magnetic permeability ↗ — 2022 recommended value 1.256 637 061 27(20)×10⁻⁶ N·A⁻², which the exact 4π×10⁻⁷ used here matches to ten digits
- Microwaves101 — Skin Depth ↗ — the five-skin-depth plating rule of thumb, and what nickel under gold does to loss
- Microwaves101 — High Permeability Materials ↗ — source of μr = 100 for nickel and mild steel: “Permeability of most metals is 1.0. However, metals such as nickel are a special case, and can have permeability as high as 100 or more.”
- Copper Development Association — C26000, Cartridge Brass 70 % ↗ — the brass row: 28 % IACS at 68 °F, and 100 % IACS is exactly 58 MS/m, so ρ = 6.16×10⁻⁸ Ω·m
- CRC Handbook of Chemistry and Physics — Electrical Resistivity of Pure Metals — the 293 K reference values the material list is cross-checked against (printed only, no public URL)
- Electrical resistivity and conductivity — Wikipedia ↗ — source of every other resistivity in the material list, tabulated at 20 °C and re-read on 18 August 2026. Text there is CC BY-SA 4.0; measured constants carry no copyright, so this credit is courtesy rather than obligation
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