Inductance formulas for circular and square coils

Abstract

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.