An accurate approximation for calculating bit error rates in direct sequence code division multiple access (CDMA) radio systems using binary phase shift keyed (BPSK) signaling is presented. All interfering users are assumed to employ random signature sequences, but the desired signal can be structured with either a random or a deterministic spreading code. Bit error probabilities are given for signals having carrier phase or chip offsets that are either deterministic or random, Computational complexity of all calculations is O(1).