This paper presents a new and accurate algorithm for assessing circularity tolerance from a set of data points obtained from a Coordinate Measuring Machine (CMM). This method, called Selective Zone Search algorithm, divides the workspace into small sectors called search zones and searches for the extreme points in these zones. These extreme points are used to draw a pair of concentric circles with minimum radial separation. The radial difference gives the circularity. The methodology has been tested with several example data sets and the results have been compared with the Least Squares method, Minimum Spanning Circle method and the Voronoi Diagram method.