A novel method for evaluating the circular error probability (CEP) integral using a recurrence relation is presented, This approach is highly efficient, accurate, and reliable, It can easily be used, in conjunction with the Newton-Raphson iteration, to determine the CEP, The CEP expressions have been generalized elsewhere to include correlation between x and y coordinate measurements, Since modern guidance and control techniques have greatly improved accuracy, we may also wish to generalize the 0.5 probability associated with the CEP to some other value, P. These generalizations are included in the presented technique.