This paper presents a new analytical technique for computing sonar performance which can be run on a programmable hand calculator. It is simple and rigorous, and does not require complex computer simulations which obscure the critical parameters. It allows the individual terms in the sonar equation to have two or more different relaxation times, and allows the Recognition differential (RD) term to be presented as a curve of probability of detection versus signal‐to‐noise ratio (SNR) rather than a jump in probability of detection versus SNR from 0 to 1. This method treats the sonar equation as a random process with a mean and standard deviation as in standard simplified techniques, but treats successive observations of received signals as a multivariate Gaussian distribution with observations correlated in accordance with the decorrelation times of the individual terms in the sonar equation. Restrictions of this method are twofold: the terms of the sonar equation are normally distributed (in dB) and the RD term is derived from a probability of detection versus SNR relationship which is represented by a straight line on normal probability paper.