Abstract The extraction of component errors of a machine tool’s axes is a critical step for the synthesis of 3D volumetric error mapping, which is a prerequisite to improve the machine tool accuracy by numerical error compensation. This paper presents a method for the extraction of machine tool component errors from a statistical point of view. First, the B-Spline mathematical model is established to represent the component error function, and the least-squares fitting method to measured data points is presented. Then, statistical analysis is used to select the B-Spline model with proper flexibility, so as to separate repeatable errors from random errors in the measured data. Finally, based on the component error extraction method, numerical error compensation experiments were conducted on the XY-plane of a high precision machine tool by using a cross-grid scale system. According to the statistical analysis of the experimental data, all repeatable errors except the dynamic errors caused by machine tool control system were compensated for.