The paper derives the relationship between the angular distribution of incident signals plus noise and the measured angle of arrival, using a twin-beam amplitude-comparison direction-finding system. The analysis allows the aerial phase response and receiver noise to be taken into account. Examples of the use of the analysis are given which derive percentiles of measured angle for a point target, embedded in clutter and adjacent to a patch of clutter. The results give an indication of the signal/clutter ratio required for a particular system performance. The analysis is applicable to a wide range of amplitude-comparison systems and should therefore be of considerable value in system studies.