Abstract: On the basis of thorough studying radial rotation error of the spindle and differentiation rule of error evaluation , a new method of minimum regional ring for calculating radial rotation error of the spindle is discussed．There needs no trial in this method and the best direction and step of the center trace of minimum regional ring can be determined immediately．As compared with the conventional methods, it has the features of high speed and accuracy of the calculation．

Key words: Concentric circle, Inclusion, Minimum regional ring, Radial rotation error of spindle, Step