Air-Core Inductor Calculator

Harold A. Wheeler published his famous approximation for single-layer solenoid inductance in 1928 while working at the Hazeltine Corporation. Wheeler was a prodigy — he had already designed an automatic volume control circuit that Hazeltine licensed widely — and his single-line formula replaced laborious tables of elliptic integrals that radio engineers had been wrestling with since Maxwell and Nagaoka. His paper "Simple Inductance Formulas for Radio Coils" in the IRE Proceedings gave ±1% accuracy across the practical range of radio-era coil geometries and is still the starting point taught today.

The underlying physics goes back to Ampère's 1820s experiments on magnetic fields from current-carrying coils, then to James Clerk Maxwell's mathematical treatment in his 1873 Treatise on Electricity and Magnetism, and to Hidetsugu Nagaoka's correction factors for finite-length solenoids published in 1909. Wheeler's contribution was practical: distilling decades of pure-physics results into a calculator-friendly formula a radio engineer could use in the lab without a table.

Air-core coils remain the go-to choice for RF work — they have no saturation, no frequency-dependent core loss, and perfectly linear L-versus-current behavior. Most HF matching networks, tank circuits, and antenna traps still use hand-wound air solenoids designed with Wheeler's formula nearly a century after he published it.

Enter the number of turns, coil diameter, and coil length. The calculator applies Wheeler's metric-unit formula and returns inductance in microhenries, plus the total wire needed to wind the coil and the turn density. For tightly wound coils (length similar to diameter, like most RF tank circuits), accuracy is within 1%; very short or very long coils stray further and you'd need a finite-element EM solver for high precision.

This tool assumes a single-layer, close-wound air-core solenoid on a non-magnetic former. For multi-layer coils, toroidal windings, or cores with ferrite or powdered-iron material, the formulas change — use the appropriate core datasheet's A_L factor instead. Everything here runs client-side; no values leave your browser.