Skin Depth Calculator determines how deep alternating current penetrates a conductor, plus its surface resistance, reactance, and impedance from resistivity, permeability, and frequency.
Skin Depth Calculator: RF Conductor Penetration Depth and Surface Impedance
This calculator computes the skin depth, surface impedance, and current-penetration profile of a conductor carrying alternating current, based on its resistivity, relative permeability, and the signal frequency. RF and microwave engineers, PCB trace designers, antenna builders, and induction-heating engineers use it to size conductors, estimate AC resistance, and predict shielding performance at a given frequency.
Skin Depth Calculator Inputs and Outputs
Enter resistivity $\rho$ in nΩ·m (or pick a material preset like annealed copper), relative permeability $\mu_r$ (1 for non-magnetic metals), and operating frequency in MHz. The calculator returns skin depth in µm, surface resistance and reactance in µΩ/sq, the guided wavelength, and the percentage of surface current remaining at 3δ and 5δ.
How the Skin Depth Formula Works
Per Pozar’s Microwave Engineering (the standard RF/microwave textbook treatment of skin depth and surface impedance), skin depth is:
$$\delta = \sqrt{\dfrac{\rho}{\pi f \mu_0 \mu_r}}$$
where $\mu_0 = 4\pi \times 10^{-7}$ H/m. For a good conductor, the surface impedance has equal resistive and reactive parts, $Z_s = R_s + jX_s$, with $R_s = X_s = \rho/\delta$, so $|Z_s| = R_s\sqrt{2}$.
The phase and attenuation constants are equal, $\beta = \alpha = 1/\delta$, giving a guided wavelength $\lambda = 2\pi\delta$. Current density decays exponentially with depth $x$: $J(x) = J_0 e^{-x/\delta}$, which is why current at 3δ is $e^{-3} \approx 4.98\%$ and at 5δ is $e^{-5} \approx 0.67\%$ of the surface value.
Loss per unit depth in dB/m is the attenuation constant in Np/m multiplied by 8.686, the standard Np-to-dB conversion factor.
The most common input mistake is a resistivity unit mismatch — entering a value in Ω·cm or µΩ·cm instead of nΩ·m (or off by a factor of 10 between “pure” and “annealed” datasheet values). Because $\delta \propto \sqrt{\rho}$, a 10x resistivity error only shifts the result by about 3.16x, which is easy to overlook as a plausible-looking but wrong answer rather than an obvious error.
One nuance specific to the $\mu_r$ input: for non-magnetic metals (copper, aluminum, silver, gold) $\mu_r = 1$ is a fixed constant, so resistivity alone drives the result.
For ferromagnetic materials (steel, nickel, mu-metal), $\mu_r$ is not a fixed material property — it depends on field amplitude and frequency, and typically drops toward 1 at high drive levels or high frequency (saturation and domain-wall lag).
Entering a textbook “typical” $\mu_r$ for steel gives a skin depth that can be off by a large factor from the real operating value, unlike copper where the calculation is exact.
Current Density Decay Inside the Conductor
Resistivity Reference Values for Common Conductor Materials
Resistivity values below are from the CRC Handbook of Chemistry and Physics (compiled reference tables). Skin depth is then calculated from the formula above at 1 MHz, $\mu_r = 1$; ferromagnetic materials like iron and steel are omitted because their permeability is not a fixed constant (see note above).
| Material | Resistivity ρ (nΩ·m) | Skin Depth at 1 MHz, μr = 1 (µm) |
|---|---|---|
| Silver | 15.9 | 63.5 |
| Copper (pure) | 16.8 | 65.2 |
| Copper (annealed) | 17.2 | 66.0 |
| Aluminum | 26.5 | 81.9 |
| Tungsten | 56.0 | 119.1 |
Skin Depth and Skin Effect: Common Questions
What does skin depth actually measure?
Skin depth is the distance below a conductor’s surface where AC current density has fallen to $1/e$, about 36.8%, of its value at the surface. Beyond a few skin depths, current contribution is negligible.
Why does higher frequency shrink skin depth?
Because $\delta \propto 1/\sqrt{f}$. Rising frequency strengthens induced eddy currents that oppose the field in the conductor’s interior, pushing current flow closer to the surface and shrinking the conducting layer.
How is skin depth different from surface resistance?
Skin depth is a length — how deep current penetrates. Surface resistance $R_s$ is the effective sheet resistance of that thin conducting layer, used to calculate AC power loss per unit area.
Does skin depth apply at DC?
No. At DC, current distributes uniformly across the full cross-section. Skin depth is an AC phenomenon; the formula’s frequency term means $\delta$ grows without bound as $f \to 0$.
Why does relative permeability matter more for steel than copper?
Magnetic materials have $\mu_r$ far above 1, which shrinks skin depth sharply, and unlike copper’s fixed $\mu_r = 1$, steel’s permeability shifts with field strength and frequency, so a single input value is only approximate.