Calculate the inductance, wire length, DC resistance, Q factor, and self-resonant frequency of a helical (solenoid) coil using the Nagaoka correction.
Helical coils — cylindrical solenoids wound with wire — are the most common form of inductor in electronics. They appear in RF circuits, power supplies, filters, sensors, and Tesla coils. Calculating their inductance accurately requires more than the simple solenoid formula; the Nagaoka correction factor accounts for the finite length of real coils.
This Helical Coil Inductance Calculator computes the inductance using both the ideal solenoid formula and the Nagaoka-corrected formula, along with the total wire length, DC resistance, estimated Q factor at 1 MHz, self-resonant frequency, and winding pitch. Simply enter the coil diameter, wire diameter, number of turns, winding length, and core permeability.
Whether you are designing an RF tank coil, winding a power inductor, or building a Tesla coil secondary, this tool gives you the essential parameters in seconds. Preset buttons cover common coil types, and a wire gauge reference table helps you select the right magnet wire for your application.
Use this page to estimate air-core or simple-core coil inductance, wire length, resistance, and rough RF behavior from the winding geometry you plan to build. It is a quick pre-build check for whether a coil will land near the inductance and frequency range you need. That helps you compare winding choices before buying wire or winding the coil.
Solenoid (ideal): L = µ₀ × µᵣ × N² × A / l Nagaoka correction: L_corr = L × k_N, where k_N ≈ 1 / (1 + 0.9 × D/l) Wire Length: l_wire = N × π × D DC Resistance: R = ρ × l_wire / A_wire (ρ_Cu = 1.72 × 10⁻⁸ Ω·m) Q at f: Q = 2πfL / R
Result: L_corrected = 0.65 µH, Wire Length = 0.628 m, R = 0.095 Ω
A 20-turn air-core coil on a 10 mm form spanning 15 mm yields about 0.65 µH of inductance with 63 cm of wire.
Inductance grows with turn count and magnetic coupling, but the exact geometry determines how efficient that turn count really is. Real coils are finite in length, so some flux leaks out of the ends and the ideal long-solenoid equation tends to overstate inductance for short windings.
The same winding that increases inductance also increases wire length and resistance. In RF designs, that affects Q factor and resonance. In power designs, the priorities may shift toward copper loss, current handling, and core saturation instead.
This calculator is useful for coil planning and quick comparison, but parasitic capacitance, skin effect, proximity effect, and real core losses can move the built result away from the estimate. Prototype and measure if the coil is part of a frequency-critical design.
A correction factor (< 1) that accounts for the magnetic flux leaking out the ends of a finite-length solenoid. Short, fat coils have a lower Nagaoka coefficient.
Marginally — thicker wire slightly increases the effective coil diameter. The main effect is on resistance and Q factor.
The frequency at which the coil's parasitic inter-turn capacitance resonates with its inductance. Above the SRF, the coil behaves as a capacitor.
The inductance is multiplied by the relative permeability µᵣ of the core material. Ferrite cores have µᵣ from 100 to 10,000.
For RF coils, Q > 100 is good; Q > 300 is excellent. For power inductors, Q is less critical than saturation current.
Set the winding length equal to N × wire diameter. The pitch equals the wire diameter, giving adjacent turns with no gap.