Inductance formulas for circular and square coils

Some simple inductance formulas are given for a circular or square coil of any shape ratio. Each one represents a continuous transition between the extremes of a long coil and a short coil. A unique case is a cubic coil whose inductance is 2/3 the reference value based on area/length. For any shape, the relative error is very small and is stated. The theoretical formulas are given for comparison.

[1]  E. B. Rosa,et al.  Formulas and tables for the calculation of mutual and self-inductance (Revised) , 1912 .

[2]  H. A. Wheeler.  Simple Inductance Formulas for Radio Coils , 1928, Proceedings of the Institute of Radio Engineers.

[3]  H.A. Wheeler.  Inductance Chart for Solenoid Coil , 1950, Proceedings of the IRE.

[4]  H. A. Wheeler,et al.  The Spherical Coil as an Inductor, Shield, or Antenna , 1958, Proceedings of the IRE.