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As previous self-calibration technologies are mostly limited to 1-D or 2-D metrology systems, a holistic and explicit self-calibration strategy is proposed for 3-D precision metrology stages in this paper. With different alignments of a rigid cubic artifact on the uncalibrated 3-D stage, four measurement views are constructed to provide the symmetry, transitivity, and redundancy of the 3-D stage error. The first-order components of the stage error, i.e., the nonorthogonality and the scale difference, are determined through the first three measurement views with mathematical processing. The residual components of the stage error are then determined through a least square-based calculation law. Additionally, the misalignment error and the artifact error are all identified through rigorous algebraic manipulation, which may be useful as foundation for synthesis of other self-calibration algorithms. Computer simulation is carried out, and the results validate that the proposed scheme can achieve good calibration accuracy even under the existence of various random measurement noises. Experimental results are also presented to provide a preliminary illustration and validation of the proposed approach in practical applications.