Much work has been done in the past to determine the conductor loss of microwave and millimeter-wave integrated circuits (MIMICs). However, much of this work is limited by constraints on the conductor thickness, skin depth, or the shape of the edge. In this paper, a technique will be presented that results virtually in a quasi-closed form expression for this loss in many cases. This expression will allow the calculation of the attenuation constant for a planar circuit for an arbitrarily shaped edge and any conductor thickness. The question of how different edge shapes affect the conductor loss will be addressed.