PCB spiral inductance, two formulas.

The inductance of a planar spiral PCB coil depends mainly on its number of turns, its average diameter and how full the spiral is. Mohan, Hershenson, Boyd and Lee (1999) gave two simple expressions that are widely used: the modified Wheeler formula, L = K1·μ0·n²·d_avg / (1 + K2·ρ), and the current-sheet formula, which also covers circular spirals. Here n is the number of turns, d_avg the mean of the outer and inner diameters and ρ = (d_out − d_in)/(d_out + d_in) the fill ratio. Both are typically within a few percent of field-solver results when the trace spacing is small compared with the width and there is no ground plane or ferrite nearby. This calculator works out the inner diameter from your trace width and spacing and gives the inductance from both formulas, so you can see how close they agree.

A square spiral, 30 mm outer size, 0.3 mm traces and 0.3 mm gaps:

Inductance grows roughly with n², but each extra turn sits at a smaller diameter, so the growth slows as the spiral fills in.

This calculator is free to use and answers one question at a time. The full AirInduct Sim simulator goes further:

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