Geometric and thermal errors are key contributors to the errors of a computer numerically controlled turning center. A planar error synthesis model is obtained by synthesizing 11 geometric and thermal error components of a turning center with homogeneous coordinate transformation method. This paper shows the sensitivity analysis on the temperature change, the confidence evaluation on the uncertainty Of measurement systems, and the error contribution analysis from the planar error synthesis model. Planar error in the z direction was very sensitive to the temperature change. and planar errors in the x and z directions were not affected by the uncertainty of measurement systems. The error contribution analysis ,which is applicable to designing a new turning center, was helpful to find the large error components which affect planar errors of the turning center.