Abstract Measuring circular shape is a main task of dimensional metrology, characterized by circle diameter and its roundness, both for full circles and circle arcs. Point coordinates allows measuring both arcs and full circle, by fitting to substitution geometry, in many cases by least-squares criteria and fitting. Nevertheless, circle shape can be also characterized by the minimum zone, minimum circumscribed and maximum inscribed circles. This research presents a systematic experimental analysis of results of normal distributed points around the substitution circle through simulation, for different circle arc angles to the full circle and for the four mentioned fitting criteria. The results show the influence of arc angle in the variability of the results across criteria and the different behaviour depending on the arc amplitude. The results confirm the good stability and behaviour of least squares and minimum zone criteria, while warns the use of minimum circumscribed and maximum inscribed circles over half circumference. Experimental regression facilitates estimation of the minimum zone criteria from the least squares fitting that are independently verified with literature datasets with good results.