The ray angle diagram presents loci as a function of depth of the angles which selected rays make with the horizontal as sound propagates in the ocean. It provides useful qualitative information about deep ocean propagation and the vertical distribution of signal and ambient noise power. The loci are based on Snell’s law. It is shown that an approximate ray angle diagram (ARAD) can be easily constructed directly from the sound‐velocity profile since on an appropriate scale the loci of one minus the cosine of the ray angle versus depth are approximately mirror images of the sound‐velocity profile. The approximations are shown to involve negligible errors for cases of interest in underwater acoustics. The use and construction of the ARAD are illustrated with examples. A simple graphical technique is presented for annotating the ARAD with range information from which rays may be plotted without the use of a computer.