Skin depth calculator

Current in a wire makes a magnetic field around it and inside it. When the current alternates, that field changes, and a changing field inside the metal drives eddy currents. Near the axis they oppose the main current; near the surface they add to it. So the current density is highest at the skin and falls off toward the centre, and the faster the field changes, the thinner the busy layer gets.

The skin depth δ = √(ρ / (π f μ0 μr)) is how far in the density drops to 1/e, about 37 % of its surface value. For annealed copper at 20 °C it is 9.35 mm at 50 Hz, 209 µm at 100 kHz and 66.1 µm at 1 MHz. Each fourfold step in frequency halves it.

Because δ goes as one over the square root of frequency, a log-log plot is a straight line. Aluminium sits above copper by √(2.8264 / 1.7241) = 1.28, the square root of the ratio of their resistivities. Heat does the same thing: copper at 100 °C has a skin depth 1.15 times the 20 °C figure.

The quick estimate treats the wire as a tube one skin depth thick and ignores the rest. That is fine for thick wire at high frequency, and poor in the range most hobby and power electronics work sits in. It says nothing happens until the radius reaches δ, and at a radius of 2δ it gives 1.33 × the DC resistance where the exact answer is 1.26 ×.

The calculator uses the exact solution for a lone round wire, written with Kelvin functions (the Bessel functions of a complex argument). It reproduces Terman's published table: 1.08 × at x = 2, 1.32 × at x = 3 and 2.04 × at x = 5, where x = √2 × radius / δ. Above a radius of about 8.5δ it switches to the thick-wire expansion a/2δ + ¼ + 3δ/32a, which matches the series there to better than 0.01 %.

At 100 kHz, a common switching frequency, AWG 22 already runs at 1.11 × DC, and thicker wire is worse. That is why switch-mode windings often use several thin wires in parallel, or litz wire.

Turn it round and ask how thick a wire can be before its AC resistance is 10 % above DC. At mains frequency the answer is a bar 28.2 mm across across. At 1 MHz it is 200 µm across.

• Measure the bare copper. Enamel adds a few hundredths of a millimetre, which changes the DC resistance of fine wire by several per cent.
• Use the hot temperature for winding loss. Copper resistance rises about 0.4 % per °C, and the AC figure rises with it.
• Parallel strands only help if each one takes its turn at the outside of the bundle. Twist them, or buy litz.
• In a multi-layer winding, proximity effect usually costs more than skin effect. Fewer layers often help more than thinner wire.
• For a thick conductor at mains or audio frequency, a tube of the same outside size carries almost the same AC current with much less metal.
• An ordinary multimeter reads DC resistance. For the AC figure, measure at the working frequency with an LCR meter or work it out here.

The skin effect glossary entry covers the idea in a few paragraphs, and the lesson on resistivity and conductance gives the DC side. For winding work read wire and cable and transformer losses. The RC snubber calculator deals with ringing at the switch node of the same converters, and the PCB design rules page covers copper on the board.

Sources: IEC 60028, International Standard of Resistance for Copper (annealed copper 1/58 Ω·mm²/m at 20 °C, α = 0.00393 per °C); IEC 60889, Hard-drawn aluminium wire for overhead line conductors (0.028264 Ω·mm²/m at 20 °C, α = 0.00403 per °C); ASTM B258, standard nominal diameters of American Wire Gauge (d = 0.127 mm × 92^((36 − n)/39)); F. E. Terman, Radio Engineers' Handbook (McGraw-Hill, 1943), table of skin-effect resistance ratios for an isolated round wire. The curves and figures are our own computation of those formulas. Checked 31 October 2026.