The geometrical parameters of the drill point, i.e., relief angles, chisel form, web size, and errors of symmetry have a major influence on drill performance. This paper deals with geometrical aspects of the drill point and with the development of fundamental mathematical definitions for the design of improved drill point grinders. A drill point grinder was built and a set of drills was ground and tested to find the optimum clearance angle. When compared with the standard commercial point, the new point with the optimum clearance angle gave an increase in tool life by more than a factor of two.