Based on the theory of spatial conjugate curves, this study selects the circular arc as the normal profile to construct a gear pair using the method of normal equidistance. By integrating the characteristics of their meshing contact, the force situation of the teeth during the meshing process is analyzed. The contact between the two tooth surfaces of this gear pair is point contact, and according to the Hertz contact theory, the contact area is approximated as an ellipse. Taking into account the variation of the contact position at each moment, the contact elliptical area is divided using the slicing method, and the tooth stiffness is calculated through the potential energy method. The calculated results are compared with those from finite element analysis to verify the accuracy of the computational method. Furthermore, this approach is utilized to analyze the impact of the equidistant distance on the meshing stiffness.