Air-Core Coil Inductance Calculator

A single-layer air-core solenoid is the simplest inductor to wind and the one RF circuits, crystal-set coils and filter prototypes use most. Its inductance is L = kN · µ0 · πr² · N² / l, where kN is Nagaoka's coefficient: exactly 1 for an infinitely long coil and less for real ones, because the field leaks out at the ends. This calculator evaluates kN exactly from complete elliptic integrals rather than from a table, so it is right for any shape from a long thin solenoid to a flat ring. Give the coil's mean diameter (to the centre of the wire), the number of turns and either a fixed length or the wire pitch — for a close-wound coil the pitch is the wire's outside diameter, and the length then grows with the turns. Or work backwards: enter a target such as 1u or 470n and it finds the turns, fractional and rounded up to a whole turn with the inductance that gives. Wheeler's 1928 formula is shown alongside for comparison; it is within 1 % once the coil is longer than 0.8 of its radius, but on a short coil it falls noticeably low. For example, 20 turns of 0.5 mm wire close-wound to a 10 mm mean diameter (a 9.5 mm former) give 2.72 µH, where Wheeler agrees to 0.1 %; squash 4 turns into 2 mm and Wheeler is 4 % low. The result is for a current sheet — the ideal of a thin continuous tape. Real round wire with gaps between turns has slightly less inductance (Rosa's corrections, typically a few per cent, more with widely spaced turns); the coil's self-capacitance lowers its self-resonant frequency, and at high frequency skin and proximity effects shift L a little. A ferrite or iron core multiplies L by an effective permeability that depends on the core's shape, not simply by the material's µr.