Abstract: A computer (21) processes the time between ultrasonic echoes received at a transducer (19) indicative of the outer radius and wall thickness of a workpiece (10) by subtracting (69) the weighted average (80-90) wall thickness from the weighted average outer radius to generate an internal radius for a large number of points around a spiral slice of the workpiece. The internal radii and angles are converted (69) to x and y coordinates. The centroid (X, Y) of each slice of data indicating workpiece cavity internal radii is determined (71) as twice the summation of the x coordinates and twice the summation of the y coordinates of all of the datum points of the slice. The least squares fit (73) of the X coordinates of the centroids of all of the slices and the least squares fit (74) of the Y coordinates of the centroids of all of the slices are then used to determine the average axis of the cavity of the workpiece.