How this calculator works
The wire follows a helix whose turn length combines the circular circumference and axial pitch. Wheeler's single-layer air-core approximation estimates inductance using mean radius, winding length and turns, with inches converted internally. Its accuracy is geometry-dependent and is best when winding length is not extremely short relative to radius. Resonance uses a separately entered total capacitance, including external and stray capacitance. This page does not infer coil self-capacitance from geometry.
Formula
p = wire diameter + clear spacing; h = Np; wire length = N sqrt[(pi D)²+p²]; wire volume = pi dw² length/4. Wheeler: L(microhenry) = r(in)² N²/[9r(in)+10h(in)]. f = 1/(2 pi sqrt(LC)).
Worked example
For mean radius 1 inch, winding length 2 inches and 10 turns, Wheeler gives 100/29 = 3.448276 microhenries. Separately, 0.001 H resonating with 0.000001 F gives 5032.921 Hz.
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Frequently asked questions
Is the diameter inside, outside or mean?
Use mean wire-centre diameter. Add one wire diameter to an inside diameter, or subtract one wire diameter from an outside diameter.
Why can turn count be fractional?
A winding can end partway around the form. The geometry output permits a fractional turn count, but requires at least one full turn.
Does the resonant frequency include coil self-capacitance?
Only if you include it in the entered total capacitance. Dielectric formers, spacing and surroundings influence stray capacitance and are not estimated here.