Skin Depth Calculator
From the frequency, the conductor's resistivity, and its relative permeability, get the skin depth — how far an AC current penetrates below the surface — in micrometres and millimetres.
Three inputs, one depth
Enter the frequency, the resistivity, and the relative permeability and the calculator returns the skin depth δ = √(ρ / (π × f × µ₀ × µr)) in both µm and mm.
Higher frequency, thinner skin
Skin depth falls as the square root of frequency — raise the frequency 100× and the current crowds into a layer 10× thinner near the surface.
What is a skin depth calculator?
Frequency, resistivity, and permeability in, depth out
When alternating current flows in a conductor, it does not spread evenly across the cross-section — it crowds toward the surface. This is the skin effect, and the skin depth is the measure of it: the distance below the surface at which the current density has fallen to about 37 % (1/e) of its surface value. A skin depth calculator turns three inputs into that distance, so you can see how thin the conducting layer really is. That matters for sizing RF conductors, choosing wire or tubing for high-frequency power, understanding why hollow tubes carry RF as well as solid rods, and estimating high-frequency losses.
Enter the frequency, the resistivity, and the relative permeability to get the skin depth in micrometres and millimetres instantly.
One formula built from the frequency, the material properties, and the constant µ₀ (the permeability of free space, 4π × 10⁻⁷ H/m).
δ = √(ρ / (π × f × µ₀ × µr))ρ is the conductor's resistivity in ohm-metres, f is the frequency in hertz, µr is the dimensionless relative permeability, and µ₀ is the fixed permeability of free space. Because frequency and permeability sit under a square root in the denominator, skin depth falls as 1/√f — quadruple the frequency and the depth halves. A more resistive material has a deeper skin depth, while a magnetic material (high µr) has a much shallower one.
Suppose you have a copper conductor (ρ = 1.68 × 10⁻⁸ Ω·m, µr = 1) carrying a 1 MHz signal.
Build the denominator
π × f × µ₀ × µr = π × 1 000 000 × (4π × 10⁻⁷) × 1 ≈ 3.948 (in 1/m² units).
Divide and take the root
δ = √(1.68 × 10⁻⁸ / 3.948) ≈ √(4.256 × 10⁻⁹) ≈ 6.523 × 10⁻⁵ m.
Scale the units
6.523 × 10⁻⁵ m = 65.234115 µm = 0.065234 mm.
The skin depth tells you how thin the layer is that actually carries most of the AC current — a smaller number means the current crowds into a thinner shell at the surface and the interior of the conductor barely contributes. The example value (about 65 µm for copper at 1 MHz) means nearly all the current flows in roughly the outer tenth of a millimetre, so a solid wire much thicker than that is mostly wasted copper at this frequency. The single most useful insight is the 1/√f trend: because skin depth falls as the square root of frequency, the conducting layer thins steadily as you climb in frequency — at the mains 50 Hz it is around 9 mm in copper, but by 1 GHz it is barely 2 µm. That is why RF engineers use hollow tubes, silver plating, and Litz wire — the centre of a conductor is dead weight once the skin depth is much smaller than the radius. A magnetic conductor (high µr) pushes the current even closer to the surface, which is why steel makes a poor RF conductor despite carrying DC well.
The formula is the standard good-conductor approximation, so a couple of practical points are worth keeping in mind.
Good-conductor model and consistent units
This formula is the good-conductor approximation: it assumes a non-magnetic or linear-magnetic material with a constant resistivity and a frequency well below where the material stops behaving as a simple conductor. Real conductors have resistivity that rises with temperature, and ferromagnetic metals have a µr that changes with field strength, so treat high-µr results as estimates. Enter the resistivity in ohm-metres (Ω·m) and the frequency in hertz (Hz) as labelled; using Ω·cm or megahertz directly will throw the answer off by powers of ten.