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Single-layer inductor calculator

When you need this

When you are winding a tuned-circuit coil on a round former and need to know how many turns to lay down. Or the other way round — to find out what you have already wound.

Single-layer coil: former diameter D, winding length l, wire diameter d
D — former diameter, l — winding length, d — wire diameter
Number of turns for a given inductance
Required inductance L (µH)
Former diameter D (mm)
Wire diameter over copper d (mm)
Winding pitch p — diameter over insulation (mm)
Estimate the pitch automatically
Number of turns N
Winding length l
Inductance from the dimensions of a finished coil
Number of turns N
Former diameter D (mm)
Winding length l (mm)
Inductance L

📐 Formulas​

The design diameter is taken between the wire axes:

Dk = D + p

The inductance of an ideal solenoid — Lundin's approximation, where u = l/Dk:

L₀ [µH] = 2·10⁻⁴ · π · Dk · N² · [ ln(1 + π/(2u)) + 1/F(u) ]
F(u) = 2.3004 + 3.437·u + 1.763·u² − 0.47/(0.755 + 1/u)^1.44

Rosa's correction accounts for the winding being made of separate turns of round wire rather than a continuous current sheet:

Ks = 1.25 − ln(2·p/d)
Km = ln(2π) − 3/2 − ln(N)/(6N) − 0.33084236/N − 1/(120N³) + 1/(504N⁵) − …
ΔL = 2·10⁻⁴ · π · Dk · N · (Ks + Km)

Together:

L = L₀ − ΔL

Notation:​

  • L — inductance [µH]
  • D — former diameter [mm]
  • d — wire diameter over copper [mm]
  • p — winding pitch, i.e. the diameter over the insulation [mm]
  • N — number of turns
  • l — winding length [mm]
Limits of the calculator:
  • The model is for a single-layer winding on a non-magnetic former: a core, a shield and a second winding are not taken into account
  • The winding pitch cannot be smaller than the wire diameter
  • In «dimensions → inductance» mode the wire diameter is unknown, so a close-wound coil with a pitch/wire ratio of 1.07 is assumed
  • In practice the error is set by how evenly you wind, not by the formula: expect a few per cent

🎯 Where it is used​

  • Tuned-circuit coils in local oscillators and RF amplifiers.
  • Matching-network coils in antenna tuners.
  • Checking a coil that is already wound, when there is no meter at hand.
Practical notes:
  1. The number of turns comes out fractional — round down and trim the inductance by stretching the winding. Stretching a coil by 10 % of its length is roughly the same as removing half a turn.
  2. Lundin's formula itself is accurate to better than 3·10⁻⁶, so everything you see on the meter is the error of your winding, not of the calculation.
  3. For a spaced winding (wire not laid turn against turn) always enter the real pitch: it matters more than it looks.

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

How to cite this calculator
UR3PKI. «Single-layer inductor calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/one_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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