A mathematical technique to determine quantitatively the optimum reach setting of the first zone of a distance relay is presented. The problem is formulated by considering the simultaneous effect of various system uncertainties. Also, the 'optimum sensitivity analysis' is introduced for distance relays. This analysis determines the variation range of system parameters over which the optimum reach setting remains near-optimal. Simulation results are presented to illustrate the application of this technique. The factors considered in this simulation are transmission line parameter uncertainties, metering errors, variations in load and charging currents, and changes in zero-sequence mutual coupling. © 1989.