If the position of a vessel be determined from two or more position lines of known accuracy, it is possible to construct an error zone about the plotted fix, such that there is some given probability (for example 95 per cent) that the true position lies inside this zone. It is convenient for many purposes, such as ease of plotting, and preparation of accuracy diagrams, that this zone should be a circle, since in this case the figure of merit attaching to a fix is defined uniquely in terms of just one parameter, the radius of the circle. The object of this paper is the theoretical study, followed by practical example, of the circular zone round a vessel's plotted position inside which it may be asserted, with 95 per cent confidence, that the true position really lies.