Planar Inductor Calculator

About planar inductor estimates

L = µ₀ · n² · d_avg · c₁ / 2 · (ln(c₂/ρ) + c₃·ρ + c₄·ρ²)

ρ = (D_out − D_in) / (D_out + D_in)

Mohan's current-sheet expression estimates the inductance of a PCB spiral from turns, outer size, trace width, and spacing, with layout coefficients for square, hexagonal, octagonal, and circular shapes. The inner diameter must stay positive — the outer size has to fit all the turns and gaps.

How it works

A planar inductor is just a flat spiral of copper etched onto the board, so its inductance comes almost entirely from geometry rather than a core. Two numbers dominate: the number of turns, which enters as n² (doubling the turns roughly quadruples the inductance), and the fill ratio ρ, which describes how tightly wound the spiral is. A dense spiral with a small hole (ρ near 1) packs more mutual coupling between turns; an airy one with a big open centre (ρ near 0) gives less. The four shape coefficients simply adjust the constant for how "round" the winding is — a circular spiral is the most efficient, a square the least.

Worked example

A 4-turn square spiral 6 mm across, with 0.2 mm traces and 0.2 mm gaps, leaves an inner diameter of about 3.6 mm and lands near 90 nH. Add a turn and the n² term pushes it up steeply, but the inner hole shrinks — so beyond a point you gain more by growing the outer size than by cramming in turns.

Common mistakes and limits

The most common error is choosing an outer diameter too small for the turns and spacing you asked for: the spiral would overlap itself, the inner diameter goes negative, and the estimate is meaningless — the calculator flags this. Beyond that, spiral formulas are approximate and ignore nearby copper, ground planes, magnetic material, and high-frequency skin effect, all of which shift the real value. Treat the result as a starting point and prototype or simulate when the inductance tolerance actually matters.