In a series of steering gear reducer′s force transmitting experiment with circular grating sensor as rotating angle measuring device,when the concentricity of circular grating sens or,the read head′s readings and the instruments indicate errors,the combined effect of these facto rs will make the final measured angle distorted,and these errors will affect the sensor reducer angle′ s measurement precision.In this paper,with a circular grating sensor as the research object,th e factors leading to a variety of angle measurement errors are analyzed,which will be classified as systematic errors and random errors.The distribution characteristics of rotating angular error are obtained by means of physical analysis and numerical calculation,and the new method is proposed to achieve actual rotati ng angle error compensation amount,thereby enhancing rotating angle data processing capabilities and improv ing rotating angle measurement precision based on the Monte Carlo method (MCM). Experimental results indicate that the precision of the measured angle is improv ed to arc-seconds magnitude (10＂),and demonstrate the effectiveness of this me thod.