Litz wire winding calculator

Purpose

The output is a wire construction (strand diameter, strand count, breakdown by stranding stages), marking per TU DSGT.685660.019, electrical parameters (R_DC, F_R, R_AC, P_Cu), wire and winding mass, and the F_R(f) curve over ±1 decade around the operating frequency.

For complex cases (an air gap, cores with distributed gaps, an asymmetric winding, shielding), two- or three-dimensional FEA modeling is required, which is beyond the scope of an online calculation. The tool does not account for: core loss, the effect of the air gap on field distribution in the winding, capacitive coupling between strands and turns, the thermal balance, or the spectral content of a non-sinusoidal current. A list of the implemented and not-implemented calculations, with justification, is given below.

Input parameters

Operating frequency, kHz

For PWM converters — the switching frequency; for resonant topologies — the center resonant frequency; for induction heaters — the inverter output frequency. If the winding operates over a frequency range, the center value is used in the calculation.

RMS current, A

The root-mean-square value of the winding current, not the peak. For a sinusoidal current, I_RMS = I_m/√2. For a non-sinusoidal current the calculator uses the specified value as the fundamental-harmonic current and does not account for the contribution of higher harmonics.

Winding voltage, V

The peak value. It is used for contextual checks against the strand insulation class and to warn of possible capacitive switching losses, but it does not enter the main calculation formulas.

Window width and height, mm

The internal dimensions of the core window into which the winding is placed. For typical ferrite cores these are taken from the manufacturer's datasheet. The window is used to estimate the mean turn length and the number of winding layers.

Number of turns, pcs

The physical number of winding turns, as specified in the requirements for the magnetic assembly.

Current density, A/mm²

The allowable current density set by cooling conditions. Approximate values: 3–5 for natural convection in an open enclosure, 6–8 for forced air, 10–12 for oil immersion or forced liquid cooling.

Implemented calculations

Skin depth

For copper at 20 °C, the standard formula is used, derived from the solution of the Helmholtz equation for a semi-infinite conductor:

where ρ = 1.724·10⁻⁸ Ω·m is the resistivity of copper, ω = 2πf is the angular frequency, and μ₀ = 4π·10⁻⁷ H/m is the magnetic constant. In engineering form the formula reduces to δ[mm] ≈ 66/√f[Hz].

Selecting the strand diameter

From the standard range of enamelled wires (0.040; 0.050; 0.063; 0.071; 0.080; 0.090; 0.100; 0.112; 0.125; 0.140; 0.160; 0.180; 0.200; 0.224; 0.250; 0.280; 0.315; 0.355; 0.400; 0.450; 0.500 mm) the largest diameter not exceeding the skin depth is selected. This is the strict criterion d ≤ δ, which keeps the resistance increase from the skin effect of an individual strand below 1%. The soft criterion d ≤ 2δ, often found in reference literature, gives an increase of up to 8% and is available in the calculator only as a comparison option. By default the Sullivan optimum criterion is used, which accounts for the number of layers in the window.

Calculating the strand count

The required copper cross-section is determined as S = I_RMS / J, where J is the specified current density. The strand count is estimated by dividing the total cross-section by the cross-section of a single strand: N_est = S / (πd²/4). The resulting value is rounded to the nearest number that breaks down correctly across the stranding stages.

Breakdown by stages

Per TU DSGT.685660.019 (clause 1.3.7), the first stranding stage contains up to 60 strands in a stochastic (wild) configuration; subsequent stages are strictly geometric with 3, 4, or 5 elements. Geometrically regular configurations of 6, 7, or 8 elements are prohibited at any transposing stage.

The breakdown algorithm iterates over numbers N' in the range [N_est, N_est·1.15], for each checks divisibility by products of {3, 4, 5}, and selects the option with the minimum cost function: a penalty for the deviation of the primary bundle from 25 strands (the geometric optimum), a penalty for the number of stages, and a penalty for the excess strand count above the original. The result is a specific construction of the form "24 strands in the primary bundle × 5 in the secondary stage" for N = 120.

DC resistance of the winding

Calculated by Ohm's law for the full wire length:

Full wire length: L_total = L_MTL · N_turns, where L_MTL is the mean turn length, estimated as 1.5·window perimeter (the factor of 1.5 accounts for the standoff from the bobbin walls and the thickness of the winding itself). Copper cross-section: S_Cu = N_strands · π·(d/2)².

Resistance-rise factor F_R

The full Dowell formula (Proc. IEE, 1966, vol. 113) for a multilayer winding is applied, adapted to round wire via the reduced thickness Δ:

where m is the number of winding layers in the window and η is the layer fill factor (taken as 0.8 in the calculator for tight packing). The number of layers is estimated as m = ceil(N_turns / turns_per_layer), where turns_per_layer = floor(window_height / bundle_diameter).

The second bracket in the formula contains the factor (m² − 1). This means that for a single-layer winding the proximity-effect contribution is zero, for two layers it triples, and for five it exceeds the single-layer value by a factor of 24. From this follows a practical criterion: if the calculation gives F_R > 3, the winding is designed with an excessive number of layers and the geometry needs revision.

Litz bundle diameter

Estimated from the total strand area with a correction for a packing factor of 0.75 (tight random packing):

The value is used to estimate the number of layers and to visualize the cross-section.

Wire mass

Linear mass accounting for the enamel insulation and the length increment from stranding:

where ρ_Cu = 8960 kg/m³, k_enamel = 1.03 is the correction for the enamel mass (typically 2–4% of the copper mass), and K_Σ = 1.03 is the normative strand-length increment from stranding for round wires per TU DSGT.685660.019 (clause 1.3.8). Total winding mass: M_total = m_linear · L_total.

F_R(f) curve

The Dowell formula is recomputed at 50 points on a logarithmic grid over the range [f/10; f·10]. A plot is built with markers for the operating frequency and the F_R value at that point. The plot shows how the factor changes when the frequency deviates from the nominal — especially upward, where the rise is non-linear due to the approach to the region where Δ becomes of order unity.

Calculations not implemented, and why

Core loss

Not calculated, because it requires the specific-loss curves P_v(B, f, T) for a particular ferrite grade, which are not among the calculator's inputs. Above 50 kHz, core loss is often comparable to or greater than copper loss; ignoring it when optimizing the winding leads to wrong decisions. A full calculation requires specifying the core grade (3C90, 3C95, N87, N97, PC47, and equivalents) and using the manufacturer's curves (Ferroxcube, TDK-Epcos, Magnetics Inc., DMEGC).

The difference between close grades can be significant. At the operating point f = 200 kHz, B = 200 mT, the specific loss of 3C90 (Ferroxcube) is about 600 mW/cm³, while for 3C95 it is about 320 mW/cm³. For a core of 30 cm³ volume this is equivalent to a difference of 8 W of dissipated power for an identical winding. Choosing the core material correctly when calculating the winding is just as important as choosing the strand diameter correctly.

Effect of the air gap

The Dowell model assumes a uniform magnetic field in the window, corresponding to transformer geometry without a gap. In inductors with an air gap, a fringing field arises near it, locally increasing the loss in the nearest turns by a factor of 10–100. A correct calculation requires either spacing the winding away from the gap by at least 1.5–2 times its length (Sullivan's rule of thumb) or two-dimensional FEA modeling. Neither is accounted for in the one-dimensional Dowell model.

A quantitative illustration of the scale of the effect. For a 1 mH / 20 A PFC inductor on an ETD49 core with a 1.5 mm concentrated gap in the center leg, with litz wire wound right against the gap, the loss in the 2–3 nearest turns amounts to 30–50% of all copper loss, even though those turns number only 2–3 out of 30. Moving the winding 3 mm away from the gap (a bobbin with an extra flange) reduces this loss by a factor of 5–7. Without accounting for the fringing field, the calculation shows a uniform temperature distribution across the winding, whereas in reality a local hot spot forms, leading to insulation degradation in the 2–3 nearest turns and subsequent failure.

Inter-strand and inter-turn capacitance

Each pair of neighboring strands in litz wire forms a distributed capacitance through the enamel insulation. Above 1–2 MHz this capacitance begins to shunt the transposition, which is equivalent to reverting to solid-conductor behavior. The calculator issues a warning above 2 MHz, but it does not compute the capacitive effects numerically — that requires either 3D FEA or measurement of the finished coil on an impedance analyzer.

Capacitive switching losses

Calculated by the formula P_C = C·V²·f, but they require knowledge of the actual inter-turn capacitance, which depends on the bobbin geometry, the winding scheme (layer, sectioned, cross-wound), and the inter-layer insulation material. In a one-dimensional model without detailed winding geometry this quantity is undefined.

Thermal balance

Loss calculated in watts gives no information about winding temperature without a heat-transfer model. Heat-transfer coefficients depend on cooling conditions, enclosure geometry, the presence of impregnation, and thermally conductive potting. The calculator indirectly accounts for cooling through the choice of allowable current density, but it does not build a full thermal circuit.

Typical values of specific heat transfer from the winding surface: 5–10 W/dm² for natural convection in an open enclosure, up to 50 W/dm² for forced air at 20 m/s, 80–120 W/dm² for potting in a thermally conductive compound (for example, Silagum DS-250 or an equivalent with λ ≈ 2 W/m·K), up to 200 W/dm² for immersion in transformer oil. The corresponding range of allowable winding current density is from 3–4 A/mm² to 10–12 A/mm². This means the same litz construction in different thermal regimes can carry a current in the range of 10 to 40 A without changing the wire construction itself. With cooling conditions unspecified, the correct decision is to design for the most conservative scenario, which inevitably leads to excess copper consumption.

Non-sinusoidal current spectrum

For a current with a non-trivial shape (PWM, trapezoidal, triangular), the loss is calculated for each harmonic separately and then summed. The calculator works only with the fundamental harmonic. For PWM with edges ≤ 100 ns, the loss can be underestimated by up to 30–50% due to harmonics.

A numerical example for a trapezoidal current of 30 A RMS at a 100 kHz switching frequency with 100 ns edges. The spectrum of such a current contains significant harmonics up to 3–5 MHz. At the fundamental of 100 kHz, the F_R factor in a typical litz construction is about 1.1, whereas at 3 MHz in the same construction it is 8–12. Although the amplitude of the higher harmonics is a smaller part of the RMS current, the product I²·R_AC at these frequencies can make a significant and sometimes dominant contribution to total copper loss. Calculating from the fundamental harmonic alone systematically underestimates the heat dissipation in such cases.

Data for an extended calculation

Four parameters beyond the basic six are required for a full calculation that accounts for the effects listed above.

Current waveform

An oscillogram, an export from a simulator (LTspice, PLECS, Simulink), or an analytical description in the form of Fourier coefficients. Used to decompose the current into harmonics and sum the loss over each.

Air-gap length and location

A value in millimeters and the type (concentrated in the center leg / distributed / multiple). Used to estimate the fringing field and the zone of increased loss in the winding.

Core material grade

The exact designation (3C90, 3C95, N87, N97, PC47, etc.) and the operating temperature. Allows the P_v(B, f, T) curves to be extracted from the manufacturer's datasheet and the core loss to be computed using Steinmetz parameters or their modern modifications (iGSE, i²GSE).

Cooling conditions

The type of cooling (natural convection / forced air / compound potting / oil / water), the ambient temperature, and the specified maximum allowable winding temperature. Allows a thermal model to be built and the real allowable current density to be set for a specific product.

When this data is available, the calculation is performed outside the online calculator — using FEA modeling (Ansys Maxwell, FEMM) together with in-house software in Python. The turnaround for such a calculation is 3 to 10 business days depending on the complexity of the magnetic assembly.

Implementation details

All the math is implemented client-side in JavaScript. The source code of the JavaScript and the reference Python implementation is open. The Python version is covered by regression tests on six scenarios of different character (an induction heater, Qi charging, an OBC PFC inductor, a resonant LLC converter, an HF transformer at the limit of litz applicability at 1 MHz, and an additional control case); the JavaScript and Python results match to the last digit.

The calculator page uses no external libraries except for fonts (Inter Tight and JetBrains Mono from Google Fonts), makes no requests to a server — all parameters and results stay in the user's browser. It works in any modern browser without special setup.

Output formats

The result is presented in three ways.

Marking per TU — a string of the form Литц ПЭПЭТ-155-М 120×0,180 ДСГТ.685660.019ТУ, where the first group denotes the insulation class (modified polyester, 155 °C), then after a space — the strand count and the diameter of a single strand in millimeters, and at the end — the technical specification number. In parallel, the closest standard item from Table 2 of TU DSGT.685660.019 is shown — the calculator displays both the theoretical optimum (which may land on an arbitrary diameter from the enamelled-wire range) and the closest actually manufacturable item from the product range.

Parameter table: δ, d, N, R_DC, F_R, R_AC, P_Cu, mass per 1 m of wire, winding mass, and the actual current density after the breakdown.

Visualization — a schematic image of the bundle cross-section with hexagonal strand packing, plus the F_R(f) plot with the operating point marked.

FAQ

What method does the calculator use?

Skin depth — from the classical formula for a non-magnetic conductor. The optimal strand diameter — by Sullivan-Zhang (APEC 2014) with iteration over the number of layers in the window. F_R — from the simplified Dowell formula (1966) with a porosity factor η = 0.8. Marking and product range — per TU DSGT.685660.019 (Diada-Electro, 2025).

How accurate is the calculation?

±20–30% for typical E-core window geometry. The model does not account for air-gap fringing fields, core loss, or the thermal regime — for a full calculation, contact our engineering department.

How does the “ideal calculated” litz wire differ from the “closest per TU”?

The calculator first computes the theoretically optimal strand diameter (for example, 0.090 mm by Sullivan-Zhang), then matches it to the closest actually manufacturable item from Table 2 of TU DSGT.685660.019 — where only 0.071 / 0.100 / 0.150 / 0.200 / 0.250 mm are standardized.

How do you choose the litz wire strand diameter for a given frequency?

Start from the skin depth δ at the operating frequency: for copper at 20 °C, δ[mm] ≈ 66/√f[Hz]. The strand diameter must stay below δ so the current spreads evenly across the strand. The strict rule is d ≤ δ; for multilayer windings d ≤ δ/2. The calculator uses the Sullivan-Zhang optimum by default, which sets d as a function of skin depth and the number of layers m in the window, because the proximity effect grows with m. At 120 kHz the skin depth is about 0.19 mm, so a typical strand is 0.071–0.10 mm.

How many strands does a litz wire need?

The strand count follows from the copper cross-section the winding must carry. Required cross-section S = I_RMS / J, where I_RMS is the winding current and J is the allowable current density (3–5 A/mm² for convection, 6–8 for forced air, up to 12 for oil). The number of strands is then N = S / (π·d²/4), rounded to a count that breaks down across the stranding stages. For 18 A at 6 A/mm² with 0.071 mm strands the calculator returns roughly 760 strands; raising the strand diameter or the current density lowers the count.

How is the AC resistance of litz wire calculated?

AC resistance is the DC resistance multiplied by the resistance-rise factor F_R: R_AC = R_DC · F_R. The DC part is R_DC = ρ·L/S_Cu from Ohm's law. F_R comes from the Dowell formula (Proc. IEE, 1966), which accounts for skin and proximity effects through the reduced strand thickness Δ = (d/δ)·√(πη/4) and the number of winding layers m, with porosity factor η = 0.8. A well-sized litz winding keeps F_R close to 1; F_R above 3 means the strands are too thick or there are too many layers.

References

1. Dowell P.L. Effects of eddy currents in transformer windings. Proc. IEE, 1966, vol. 113, no. 8, pp. 1387–1394.
2. Sullivan C.R., Zhang R.Y. Simplified Design Method for Litz Wire. Thayer School of Engineering, Dartmouth College, IEEE APEC, 2014.
3. Sullivan C.R. Optimal Choice for Number of Strands in a Litz-Wire Transformer Winding. IEEE Trans. Power Electron., 1999.
4. Wojda R.P., Kazimierczuk M.K. Winding resistance and power loss for inductors with litz and solid-round wires. IEEE / IET Power Electron., 2012–2016.
5. TU 27.32.11-019-59596873-2025 (DSGT.685660.019TU). High-frequency continuously transposed winding wires. DIADA LLC, 2025.

Related materials

• What is litz wire — the transposition principle, applications, and the 52 grades in the Diada-Electro catalog.
• Skin effect and proximity effect — the physics of the phenomena, formulas, and the link to copper loss.
• LITZ.PRO products — round and rectangular litz wire, thermal classes up to 200 °C.