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Rectangular-former multilayer coil calculator

When you need this

When the former is rectangular rather than round — the usual case for home-made chokes on flat bobbins and for coils inside slim enclosures.

Multilayer coil on a rectangular former: width a, height b, winding length l
a — former width, b — former height, l — winding length
Required inductance L (µH)
Former width a (mm)
Former height b (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 method is the same as for a round former, but a turn is not a circle — it is a rectangle made of four straight segments. That is why Grover's formulas are used here instead of elliptic integrals.

A = a + k + 2·k·layer      the two sides «across the width»
B = b + k + 2·k·layer      the two sides «across the height»
r = k·layer                radial offset of the layer

Self-inductance of a segment:

r_gmd = 0.5·d·e^(1/4)
S(ℓ) = 0.002·[ ℓ·ln((ℓ + √(ℓ²+r²))/r) − √(ℓ²+r²) + ℓ/4 + r ]

The mutual inductance of two parallel segments of lengths m and n spaced s apart (half-lengths α = m/2, β = n/2):

M = 0.002·[ 2α·ln((α+β+√((α+β)²+s²))/s)
          + (α−β)·ln((α+β+√((α+β)²+s²)) / (α−β+√((α−β)²+s²)))
          + √((α−β)²+s²) − √((α+β)²+s²) ]

The inductance of a single turn — opposite sides carry current in opposite directions, so their mutual inductance is subtracted:

L_turn = 2·S(A) + 2·S(B) − 2·M(A,A; B) − 2·M(B,B; A)

Notation:​

  • L — inductance [µH]
  • a — former width [mm]
  • b — former height [mm]
  • l — winding length [mm]
  • d — wire diameter over copper [mm]
  • k — diameter over the insulation [mm]
Limits of the calculator:
  • A close winding, turn against turn, with no interlayer insulation and no sections
  • The former is non-magnetic
  • The stated accuracy of the method is about ±5 %
  • The calculation is capped at 8000 turns: beyond that it becomes too slow

🎯 Where it is used​

  • Chokes on flat bobbins in compact designs.
  • Coils in slim enclosures, where a round former does not fit.
  • Comparison with a round former: a rectangle of the same overall size encloses a larger area, so fewer turns are needed.
Practical notes:
  1. A single square turn of 12 × 12 mm in 1 mm wire gives 23.6 nH. The closed-form formula for a rectangular loop gives 23.1 nH on the same figures — two independent models agreeing to within 2 %.
  2. Sharp corners concentrate the field and make winding harder: if you have the choice, take a former with rounded edges.
  3. A rectangular coil radiates outwards more than a round one of the same inductance — in sensitive circuits it is worth shielding.

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

How to cite this calculator
UR3PKI. «Rectangular-former multilayer coil calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/multi_layer_rect (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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