Abstract: A method is provided for virtual machining which helps predict the accuracy of parts to be made on machine tools, allocates errors in design and manufacture of machine tools, and diagnoses the source of errors in machine tools. More particularly, the present invention relates to a method which calculates the "error shape" of a part being manufactured based upon the position, orientation, velocity and shape of the machine tool. The method predicts the statistical distribution of part size, form, and profile errors in a population of parts by superposing "error shapes." The machine errors are diagnosed by matching post process gauging data with a linear combination of "error shapes." The method predicts the magnitude and pattern of errors in a machined part, performs a simulation taking into account the geometry of the machine, the commanded machine motions as a function of time, error motions of the machine's components as a function of time, and the shape of the tool.