Calculating the dexterity value of a certain point is the foundation for demonstrating the dexterity of the robot. Furthermore, the criteria for calculating the dexterity value of the given point determines the authenticity of the capability map. Traditional methods that use Jacobian matrix to find inverse kinematic to determine whether a pose is reachable exhibit uncertainty around singularities. Thus, this article proposes an approach for calculating the dexterity of points based on a serial-parallel hybrid 7-degree-of-freedom robot. By improving the inverse kinematics solving process and selecting the optimal solutions, this method addresses the issues of low efficiency and inaccuracy in calculations near singular points. Additionally, this method does not require consideration of the configuration of the robot’s end-effector axis, thus offering broader applicability. By analyzing the characteristics of the capability map and explaining the reasons behind their formation, verify the practicality and potential applications of this criteria.