Abstract: Based on the viewpoint of interaction energy of the current element，the integral expression of the self

-inductance for a tightly wound ellipsoidal coil is derived. By using mathematica 10.3，the integral result for the azimuth

angle  is expressed as the linear combination of the first and the second kinds of complete elliptic integral，

and then the self-inductance is numerically investigated. The axis ratio ( c /a) dependence of the self-inductance is

calculated and discussed. This result shows that when c /a = 1. 7，the self - inductance per unit volume is the

minimum. Finally，a convenient and practical polynomial interpolation function for self-inductance is given.

Key words: ellipsoidal coil, self - inductance, Elliptic integral, numerical analysis, polynomial interpolation function