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Single-Layer Solenoid Inductance Calculator

Calculate the inductance of air-core coils using Nagaoka coefficients and estimate self-resonance frequency to avoid parasitic capacitance effects.

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About

Designing RF circuits or crossover networks requires precise inductance values. Standard formulas often fail when the coil geometry deviates from an infinitely long solenoid. This tool utilizes Nagaoka's coefficient, a correction factor derived from the ratio of diameter to length, to provide high-accuracy results for short air-core coils. It helps engineers minimize trial-and-error winding.

A critical, often overlooked aspect of coil design is the self-resonant frequency (SRF). Above this frequency, the parasitic capacitance between turns dominates, and the inductor behaves like a capacitor. This calculator estimates the SRF based on wire length and coil geometry, flagging designs that may be unstable at the target operating frequency.

RF design coil winding electronics inductance nagaoka

Formulas

The inductance L of a single-layer air-core solenoid is calculated using the corrected formula:

L = μ0 N2 Al × KN

Where μ0 is the permeability of free space, N is the number of turns, A is the cross-sectional area, l is the coil length, and KN is the Nagaoka coefficient determined by the ratio D/l.

Reference Data

Diameter/Length Ratio (D/l)Nagaoka Coefficient (K)Typical Application
0.10.959Long Solenoids (Electromagnets)
0.50.818RF Chokes
1.00.688General RF Tuning Coils
2.00.526Antenna Loading Coils
5.00.320Pancake Coils (WPT)
10.00.203Flat Loop Antennas
20.00.128PCB Spiral Inductors
50.00.066Planar Microwave Elements

Frequently Asked Questions

Every physical inductor has parasitic capacitance between its windings. When the operating frequency exceeds the Self-Resonant Frequency (SRF), this capacitance dominates the impedance, causing the component to block DC but pass high-frequency AC, effectively acting as a capacitor.
Nagaoka's coefficient corrects for the magnetic field leakage at the ends of a finite-length solenoid. For single-layer air-core coils, it provides accuracy typically within 1% provided the winding pitch is small relative to the wire diameter.
Yes. The calculation relies on the center-to-center pitch of the turns. Thicker insulation increases the pitch and the coil length for a given number of turns, which lowers the inductance slightly compared to tightly packed bare wire.