Abstract: A method of determining the coordinates of the center of curvature of the curved surface of a workpiece on a surface measurement instrument of the type having a workpiece table rotatably mounted on a main spindle, and a sensor for contacting the surface of a workpiece mounted on the table. The method comprises the steps of traversing the sensor over the workpiece surface and deriving three signals representing the value of the radial distance from the spindle to the workpiece surface at three points spaced along the traverse. From these values, and a knowledge of the angular separation of the three points an approximation for the coordinates of the center of the curved surface of the workpiece with respect to the spindle can be derived using the algorithm ##EQU1## WHERE X AND Y RESPECTIVELY REPRESENT THE COORDINATES OF THE CENTER OF THE WORKPIECE, R.sub.1, R.sub.2, R.sub.3 REPRESENT THE RADIAL DISTANCE FROM THE SPINDLE AXIS TO THE WORKPIECE SURFACE AT THE THREE POINTS ALONG THE TRAVERSE, AND .phi.