Echolocating bats were trained to discriminate between two small, spherical targets, each separated by a different angle from a third spherical target fixed in one location between the other targets. The targets were all in the horizontal plane. The angle from the fixed target to one of the movable targets was kept constant at 19° of arc, while the angle from the fixed target to the other movable target was varied from 37° to 19° in small decrements. The acuity with which the bat could use sonar to discriminate the larger angle from the smaller, constant angle of 19° was experimentally determined to be 6° to 8° forEptesicus fuscusand 4° to 6° forPhyllostomus hastatus.Phyllostomushas a nose‐leaf through which it broadcasts its sonar cries, using a beamwidth (6 dB down) of 40° to 50° in this experimental setting.Eptesicusemits cries through its open mouth and, in the apparatus for angular discrimination, used a beamwidth of 55° to 65°. There are many other differences between these species in echolocation, but the data suggest that at least the width of a bat's beam of sound may be related to acuity of angular resolution.