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Multilayer inductor calculator

When you need this

When a single layer is no longer enough: chokes, loudspeaker crossover coils, high-inductance windings on a short former.

Multilayer coil: former diameter D, winding length l, winding thickness c
D — former diameter, l — winding length, c — winding thickness
Required inductance L (µH)
Former diameter D (mm)
Winding length l (mm)
Wire diameter over copper d (mm)
Wire diameter over insulation k (mm)
Estimate the diameter over insulation automatically
Result
Number of turns N
Number of layers n
Winding thickness c
Wire length Lw
DC resistance of the winding

📐 Formulas​

The coil is not worked out from a single empirical formula — it is literally wound in memory, turn by turn. Each turn is a circular loop with a known radius and position:

turns per layer: Nl = floor(l / k)
layer number:    layer = floor((n − 1) / Nl)
turn radius:     r = (D + k)/2 + k·layer
position:        z = k · ((n − 1) mod Nl)

The inductance is the sum of the self-inductances of the turns plus twice the mutual inductance of every pair:

L = Σ Lself(i) + 2·Σ M(i, j),   i less than j

The mutual inductance of two coaxial turns (Maxwell):

k = 2·√(r₁r₂) / √((r₁+r₂)² + (s − g)²)
M [µH] = −0.004π·√(r₁r₂) · [ (k − 2/k)·K(k) + (2/k)·E(k) ]

where K and E are the complete elliptic integrals and g is the geometric mean distance of the wire cross-section, g = e^(−1/4)·d/2.

Derived quantities:

winding thickness: c = n·k
wire length:       Lw = Σ 2πr
resistance:        R = ρ·Lw/S,  ρ(copper) = 0.0175 Ω·mm²/m

Notation:​

  • L — inductance [µH]
  • D — former diameter [mm]
  • l — winding length [mm]
  • d — wire diameter over copper [mm]
  • k — diameter over the insulation, i.e. the pitch [mm]
  • n — number of layers, c — winding thickness [mm]
Limits of the calculator:
  • The winding is assumed close-wound, turn against turn and row against row: a random («jumble») winding will give a different result
  • Interlayer insulation and sectioning are not taken into account
  • The former is non-magnetic, there is no core and no shield
  • A realistic error for a neat winding is about ±5 %

🎯 Where it is used​

  • Chokes in supply filters and decoupling.
  • Crossover coils in loudspeaker systems.
  • High-inductance windings where the former length is limited.
Practical notes:
  1. The computation is quadratic in the number of turns: for coils of a few thousand turns the page will think for a second or two.
  2. The resistance shown is the DC value. At the working frequency the skin effect and proximity effect make it noticeably higher — which is exactly why multilayer coils have a low Q.
  3. If the coil comes out too «fat», try a longer former: for the same inductance, fewer layers mean lower resistance and lower self-capacitance.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Multilayer inductor calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/multi_layer (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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