A circular flexure hinge is a core element for force transmission and relative motion of precision stages used in semiconductor processes. When designing a circular flexure hinge, calculation formulas for axial and rotational compliance are essential. However, in the case of axial compliance, results of the existing calculation formulas have significant differences from reliable finite element analysis results. In this study, calculation formulas for axial compliance of the circular flexure hinges were derived based on stress distribution phenomenon. Comparison with finite element analysis results confirmed that the newly developed calculation formulas were more accurate than existing ones. It is anticipated that these enhanced formulas will lead to more precise designs, ultimately reducing both time and costs in research and industry.