Litz Wire and Skin Depth Calculator

Skin depth first, because that is the number everything else hangs on — then the strand diameter as a fraction of it, the strands you need for a given copper area, the bundle’s DC resistance and outside diameter, and the AC-to-DC resistance ratio with the proximity term from Sullivan’s litz formula.

Last updated 24 Sep 2026

Skin depth, strands and AC resistance

Frequency → skin depth → strands

Frequency (kHz)The frequency of the current in the winding. For a converter that is the switching frequency; for a resonant converter, the resonant frequency; for a mains transformer, 50 or 60 Hz — enter 0.05 or 0.06.

ConductorCopper is 1.724×10⁻⁸ Ω·m at 20 °C, aluminium 2.65×10⁻⁸. Aluminium’s skin depth is about 24% larger for the same frequency, which is the one thing it has going for it here.

Conductor temperature (°C)Resistivity rises about 0.39% per degree for copper, so a winding at 100 °C has 31% more resistance than at 20 °C and a 15% larger skin depth. Design at the hot temperature, not the bench temperature.

How is the copper area set?

Target equivalent copper area (mm²)The total copper cross-section of the bundle, adding all the strands up. It is what sets the DC resistance.

Winding RMS current (A)Used to set the copper area in the second mode, and to work out the winding loss in both.

Current density (A/mm²)3–5 A/mm² is a common starting point for a transformer in still air; 6–10 with forced air or a short duty cycle. It is a proxy for temperature rise, not a limit in itself.

Candidate strand AWGLitz is built from AWG 32 to about AWG 50. The page shows what New England Wire recommends for your frequency, and how your choice compares with a skin depth.

Turns in this winding section, NₛThe turns of the winding you are designing, in the section that faces the other winding. Proximity loss goes as the square of this, which is why interleaving — which halves the turns per section — quarters it.

Winding breadth b (mm)The width of the winding window, across the face where one winding faces the other. 25.7 mm for a Ferroxcube ETD 39/20/13 coil former, which is the default here. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Mean length of a turn (mm)69 mm for the same ETD 39 coil former. Times the turns, this is how much wire you need. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Packing factor — copper ÷ bundle cross-section0.4 to 0.55 for a served litz bundle once the strand insulation, the twisting and the serving are counted. A real construction’s outside diameter comes from the maker’s own table; this is an estimate.

Target AC-to-DC resistance ratio1.05 means you will accept 5% more loss than the DC resistance implies. The page works back to the strand diameter and count that achieve it.

A geometry rather than a circuit, and schematic rather than to scale. On the left, one solid conductor: at high frequency the current keeps to a shell about one skin depth deep and the middle carries almost nothing. On the right, the same copper area as a transposed bundle, every strand inside a skin depth and every strand spending an equal length at each position. Underneath, the ramp is the magnetomotive force across the winding breadth b — it is that field, not the conductor's own current, that drives the proximity loss the resistance ratio below is mostly made of.

239.6µmExample

100 kHz in a copper winding at 100 °C, 5 A rms at 4 A/mm², 20 turns of AWG 38 strand across a 25.7 mm ETD 39 window

Skin depth, then everything else

δ = √( ρ ÷ (π · f · µ) ) with µ = µ₀ for copper and aluminium
ρ(T) = ρ₂₀ · (1 + α(T − 20))
d_AWG = 0.127 mm · 92^(36−n)/39
R_dc = ρ · N_s · MLT ÷ (n · πd_s²/4)
F_R = R_ac/R_dc = 1 + (π·n·N_s)² · d_s⁶ ÷ (192 · δ⁴ · b²)

delta: skin depth: the depth at which the current density has fallen to 1/e of its surface value. Exact, and the only exact thing on this page
n: strands in the bundle
Ns: turns in the winding section. Proximity loss goes as its SQUARE, which is the whole argument for interleaving
b: the winding breadth — the width of the face where one winding looks at the other. A wider window spreads the same MMF over more distance and lowers the field everywhere
ds: the strand’s copper diameter. It enters to the SIXTH power, so one gauge finer (a factor of 0.891) cuts the proximity term by 30%

Worked example

100 kHz in a copper winding at 100 °C, 5 A rms at 4 A/mm², 20 turns of AWG 38 strand across a 25.7 mm ETD 39 window
Copper at 100 °C is 22.66 nΩ·m, so δ = √(22.66 nΩ·m ÷ (π × 100,000 Hz × µ₀)) = 239.6 µm — at 20 °C it would be 209 µm, so the hot winding has the deeper one
AWG 38 is 100.7 µm of copper, which is 0.420 of a skin depth — inside the range the formula is valid over, and close to what New England Wire recommends at this frequency
5 A at 4 A/mm² asks for 1.250 mm² of copper, which takes 157 of those strands and gives a bundle DC resistance of 25 mΩ over 1.38 m of turn length
Sullivan's proximity term makes that 1.2431 times worse in AC terms — 31.08 mΩ, or 777 mW of winding loss against 625 mW if the current were DC
To hold the ratio at 1.05 instead you would need a strand of 45.71 µm — AWG 45 — and 762 of them, which is what fine litz costs

New England Wire’s published strand table, measured against a skin depth

Skin depths computed here for copper at 20 °C at the top of each of New England Wire’s published bands. Every one of their recommended strands is BELOW one skin depth, between about 0.15 and 0.8 of one. The rule of thumb that a strand should be “one to two skin depths” is the crude solid-wire rule for picking a single conductor, not litz practice — Sullivan’s own guidance is strands “smaller than a skin depth, often by a factor of 4 or more”, and his formula stops being valid above one.
Frequency band	Strand	Diameter	Skin depth at the top of the band	d ÷ δ
up to 1 kHz	AWG 28	0.3211 mm	2.0897 mm	0.15
10 kHz	AWG 30	0.2546 mm	0.6608 mm	0.39
20 kHz	AWG 33	0.1798 mm	0.4673 mm	0.38
50 kHz	AWG 36	0.1270 mm	0.2955 mm	0.43
100 kHz	AWG 38	0.1007 mm	0.2090 mm	0.48
200 kHz	AWG 40	0.0799 mm	0.1478 mm	0.54
350 kHz	AWG 42	0.0633 mm	0.1117 mm	0.57
850 kHz	AWG 44	0.0502 mm	0.0717 mm	0.70
1,400 kHz	AWG 46	0.0398 mm	0.0559 mm	0.71
2,800 kHz	AWG 48	0.0316 mm	0.0395 mm	0.80

What moves the proximity term, and by how much

Computed from the exponents in Sullivan’s expression. The two entries worth remembering are that interleaving buys a factor of four for free, and that going finer buys much less than people expect — halving the strand diameter at a fixed copper area only halves the proximity term, because you have twice as many strands losing it.
Change	Effect on F_R − 1	Why
One AWG finer strand, same copper area	× 0.79	d⁶ falls by 0.891⁶ = 0.50 but the strand count rises by 1.26, and the term carries n²d⁶ at fixed area, so the net is d²
Twice the strands, same copper area	× 0.50	at fixed copper area, halving the strand diameter squared halves the term
Twice the turns in the section	× 4	Ns²
Interleaving — two sections instead of one	× 0.25	each section has half the turns, and Ns is squared
Twice the winding breadth	× 0.25	b², because the same MMF is spread over twice the distance
Twice the frequency	× 4	δ⁴ in the denominator and δ goes as 1/√f

Why current will not stay where you put it

Push alternating current into a conductor and it does not fill it. The changing field induces circulating currents that oppose it in the middle and reinforce it at the surface, so the current density falls exponentially inwards with a characteristic length δ = √(ρ ÷ πfµ). Copper at 100 kHz and room temperature has a skin depth of about 0.21 mm; at 1 MHz, 66 µm; at 50 Hz, 9.4 mm, which is why nobody worries about it in house wiring and everybody worries about it in a switching supply. A wire much thicker than δ is mostly decoration: its DC resistance says one thing and its AC resistance says another.

Litz wire is the answer to a second problem, not the first. Skin effect alone is dealt with by using any conductor thinner than a skin depth — foil, ribbon, several thin wires. What makes litz necessary is PROXIMITY effect: inside a winding, every strand sits in the field of every other strand, and that field induces eddy currents in it regardless of how thin it is. Simply paralleling thin wires makes this worse, because the outer ones end up carrying most of the current. Litz transposes the strands so each one spends an equal length at every position in the bundle, which forces the current to share and leaves only the eddy loss — which is what the formula on this page computes.

The formula and where it stops. Sullivan’s simplified expression adds a term in (π·n·N_s)²·d_s⁶ ÷ (192·δ⁴·b²) to unity. It comes from the eddy loss of a small cylinder in a locally uniform field, summed over strands laid through the winding’s own MMF gradient — which is exactly how it was re-derived and checked when this page was built, without going anywhere near the published form. It is a small-strand expansion: valid while the strand is inside a skin depth, and it begins to overestimate the loss past about two. It also assumes a one-dimensional field, so it knows nothing about a gapped core’s fringing field, which can dwarf everything here if a winding sits across the gap.

What actually helps. The exponents say it plainly. Turns per winding section are squared, so interleaving a winding into two sections cuts proximity loss by four and costs nothing but build complexity. Winding breadth is squared in the denominator, so a wide flat window beats a tall narrow one. Frequency is effectively squared through δ⁴. Strand diameter is the sixth power, which sounds decisive until you notice that at a fixed copper area a finer strand also means more strands — the net is only the square, and finer strands cost money, pack worse and eventually lose more to insulation than they save in eddy currents. That trade is the subject of Sullivan’s 1999 paper on the optimal number of strands.

For the core beside the winding see the Steinmetz core loss calculator and the gapped core inductance calculator; for the turns and the window, the SMPS transformer calculator and the toroid inductor turns calculator; and for solid wire at DC, the AWG wire size calculator.

Frequently asked questions

What is the skin depth of copper at 100 kHz?

About 0.21 mm at 20 °C and 0.24 mm at 100 °C — the hot winding has the deeper one, because resistivity rises with temperature and skin depth goes as its square root. Scale as 1 over the square root of frequency: 0.66 mm at 10 kHz, 66 µm at 1 MHz.

How thin should litz strands be?

Below one skin depth, and usually well below. New England Wire’s published table works out at 0.15 to 0.8 skin depths at the top of each of its bands, and Sullivan recommends strands smaller than a skin depth “often by a factor of 4 or more”. The rule that a conductor should be one to two skin depths is for choosing a single solid wire, not for litz.

Does litz wire help at mains frequency?

Almost never. A skin depth in copper at 50 Hz is 9.4 mm, so any wire you can reasonably wind is already far inside it and litz buys nothing against skin effect. It can still help against proximity effect in a very heavily wound coil, but at 50 Hz that is a specialist case.

Why does adding more copper not fix my AC resistance?

Because the proximity term scales with the copper, not against it. More strands of the same size means more conductors sitting in the same field, each losing the same eddy power. What lowers the ratio is finer strands, fewer turns per winding section, a wider window, or interleaving — and interleaving is usually the cheapest of the four.

What is the difference between skin effect and proximity effect?

Skin effect is a conductor pushing its own current to its own surface. Proximity effect is a conductor being stirred by its neighbours’ field. In a multi-layer winding proximity effect is almost always the larger of the two, and it is the one that litz exists to fight — thin wire alone deals with skin effect, but only transposition deals with proximity.

How big will the finished litz bundle be?

The page gives an estimate from the copper area and a packing factor, which for a served bundle is around 0.4 to 0.55 once strand insulation, the twist and the serving are counted. It is an estimate only: the real outside diameter depends on the construction — how many strands per bunch, how many bunches per cable, whether it is served or not — and comes from the maker’s own table.

Related calculators

References

Sullivan C R. Simplified Design Method for Litz Wire. IEEE APEC 2014. The resistance factor used here, F_R = 1 + (π·n·N_s)²·d_s⁶ ÷ (192·δ⁴·b²), with its stated validity condition d_s < δ and the note that it “starts to overestimate loss for higher frequencies, beyond where d_s ≈ 2δ”, and the recommendation of strands “smaller than a skin depth, often by a factor of 4 or more”.
Sullivan C R. Optimal choice for number of strands in a litz-wire transformer winding. IEEE Transactions on Power Electronics, vol. 14 no. 2, 1999. The underlying proximity-loss expression and the cost-versus-loss optimum that decides how far to take stranding.
Dowell P L. Effects of eddy currents in transformer windings. Proceedings of the IEE, vol. 113 no. 8, 1966. The one-dimensional layer solution used here as the independent check on the skin-depth formula: a finite-difference solve of the field diffusion in a slab agrees with Dowell’s closed form to better than 0.2% over a 20 kHz to 1 MHz range.
New England Wire Technologies, Litz Wire Design & Engineering. The published strand-gauge-versus-frequency table reproduced and measured against a skin depth above: AWG 28 up to 1 kHz through AWG 48 at 1.4–2.8 MHz, and the statement that they design “with individual strands that are smaller than the skin depth”.