123 123Calculator

Helical Coil Calculator

Use the helical coil calculator to estimate the inductance and volume of coil springs.

Clear
Inductance10.8028 µH10.8028 µH by Wheeler's formula — an empirical fit, good to a few percent for a single-layer air coil
By the ideal solenoid formula13.8791 µHµN²A ÷ ℓ — this assumes an infinitely long coil, so it OVERSTATES a short one
Difference between the two28.48%the ideal formula ignores end effects, and the gap grows as the coil gets shorter relative to its diameter
Length to diameter ratio1.6long enough for either formula to be reasonable
Turns30
Turns per metre750
Wire length required2.3562 mπ × diameter × turns, ignoring the pitch
At twice the turns43.2111 µHfour times the inductance — it goes as the SQUARE of turns, which is the strongest lever available
Reactance at 7 MHz475.1304 Ω
Capacitance to resonate here47.853 pFthe tuning capacitor for a tank circuit at this frequency
Self-resonant frequency cautioncheck it exceeds your operating frequencyinter-turn capacitance makes every coil self-resonant, above which it behaves as a capacitor rather than an inductor

The formula

Wheeler: L(µH) = d²n² ÷ (18d + 40ℓ), inches

Two formulas, and when each fails

The textbook solenoid formula µN²A/ℓ assumes an infinitely long coil where every field line stays inside. Real coils leak at the ends, so the formula overstates the inductance — badly for a short fat coil, mildly for a long thin one.

Wheeler's formula is an empirical fit that accounts for that end effect, and it is accurate to about 1% for single-layer coils longer than about 0.4 diameters. It is stated in inches for historical reasons, which is why this page converts internally rather than pretending the constants are dimensionless.

Inductance goes as the square of turns and only linearly with length and area, so turns are the strongest lever by far. Doubling the turns quadruples the inductance.

Every real coil has capacitance between its turns and is therefore self-resonant at some frequency. Above it the winding behaves as a capacitor, not an inductor — so a coil must be used well below its self-resonance, and checking that is part of the design rather than an afterthought.