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Flat spiral Tesla coil calculator

When you need this

A «pancake» spiral: every turn lies in the same plane. The same calculation works for a spiderweb coil.

Flat spiral coil: inner diameter Di, outer Do, gap between turns s
Di — inner diameter, Do — outer, s — gap between turns
Required inductance L (µH)
Spiral inner diameter Di (mm)
Wire diameter d (mm)
Gap between turns s (mm)
Result
Number of turns N
Outer diameter Do
Wire length Lth

📐 Formulas​

The model is the same as for a multilayer coil, but the geometry is simpler: the turns are coplanar, so the axial distance between them is zero.

pitch:  k = s + d
radius: rₙ = (Di + d)/2 + k·(n − 1)

L = Σ Lself(rₙ) + 2·Σ M(rᵢ, rⱼ; Δz = 0),   i less than j

Outer diameter:

Do = Di + 2·k·N

The wire length is the arc length of an Archimedean spiral, not the sum of the circumferences. For φ = 2πn:

Sp(n) = k/(4π) · [ φ·√(1+φ²) + ln(φ + √(1+φ²)) ]
n₀ = ceil(Di / (2k))
Lth = Sp(n₀ + N) − Sp(n₀)

Notation:​

  • L — inductance [µH]
  • Di — inner diameter of the spiral [mm]
  • Do — outer diameter [mm]
  • d — wire diameter [mm]
  • s — gap between turns [mm]
  • Lth — wire length
Limits of the calculator:
  • The wire is round and solid: strip conductor needs a separate calculation
  • The spiral is assumed to be strictly flat
  • The model is for an air-cored coil with no core and no shield
  • The calculation is capped at 5000 turns

🎯 Where it is used​

  • The primary of a flat-format Tesla coil.
  • Spiderweb coils in TRF receivers.
  • Work coils for induction heating and wireless power transfer.
Practical notes:
  1. The common calculators use Wheeler's simplified formula. It is fast, but with a large gap between turns and a small inner diameter it can be tens of per cent out.
  2. The wire length here is the arc of the spiral: with a large pitch it is noticeably longer than the sum of the circumferences, and that already matters when you buy the wire.
  3. Widening the gap between turns lowers the self-capacitance and raises the self-resonant frequency — for a Tesla coil that is often worth more than compactness.

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

How to cite this calculator
UR3PKI. «Flat spiral Tesla coil calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/flat_spiral (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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