For volumetric error measurement and calibration for machine tools, manufacturing machine or coordinate measuring machine (CMM), are studied using a Ball-bar artifact. A design of the Ball-bar is suggested manufactured by Invar, which is a low thermal expansion material, and precision steel balls. The uncertainty for the artifact method is discussed. A method of the Ball-bar artifact for obtaining 3-D position errors in CMM is proposed. The method of error vector measurement is shown using the Ball-bar artifact. Finally, the volumetric error is calculated from the error vectors and it can be used for Pitch error compensation in conventional NC machine and 3-D position Error map for calibration of NC machine tools.