Coils wound on forms such that each turn incloses' a regular polygon are finding frequent use in radio circuits. Not only are they easy to construct, but support for the wires of the coil is necessary only at the vertices of the polygon. Thus, the amount of dielectric near the wires is small, making it easy to reduce energy losses in the dielectric to a very small amount. In this paper formulas are derived for the calculation of the inductance of such coils. The cases treated are triangular, square, hexagonal, and octagonal coils. It is found that a circular coil inclosing the same area as the polygonal coil, the length and the number of turns being the same in both cases, has nearly the same inductance as the polygonal coil.