All sort of measurements ought to be traceable to the standard The equivalence of the standards used in different places is ascertained by round-robin comparisons. In the comparisons of the geometrical quantities, physical gauges (artifacts) are circulated and measured by all participants, and the measurement results are compared. The important matter is the shape and the dimension of the artifact do not change throughout the circulation. In this paper, the calibration procedure of the ball-plate and the estimation of the measurement uncertainty are studied. Finally, problems on the round-robin comparisons mainly about the stability of the artifact are discussed according to our experiences of international comparisons of a ball-plate.