Aerostatic planar XY stages are frequently used as the main frames of precision positioning systems. The machining and assembly process of the rails and bed of the stage is one of first processes performed when the system is built. When the system is complete, the 2D position, motion, and stage flatness errors are measured in tests. If the stage errors exceed the application requirements, the stage must be remachined and the assembly process must be repeated. This is difficult and time-consuming work. In this paper, a method for estimating the errors of a planar XY stage is proposed that can be applied when the rails and bed of the stage are evaluated. Profile measurements, estimates of the motion error, and 2D position estimation models were considered. A comparison of experimental results and our estimates indicated that the estimated errors were within $1{mu}m$ of their true values. Thus, the proposed estimation method for 2D position and flatness errors of an aerostatic planar XY stage is expected to be a useful tool during the assembly process of guideways.