The stiffness coefficient on the contact point of the gear pairs is defined based on the Hertz Elastic Contact Theory, which can be used to calculate the meshing force of the gear pairs. Then, the characteristics of the working flanks of the involute ring tooth spherical gear are analyzed and the equations to calculate the master curvature radius are derived. Afterwards, the contact ratio, a key factor in the calculation of the stiffness coefficient, is studied and the method on how to find the position of inverse meshing point is given. Finally, the result of an example is presented to demonstrate the time-variable characteristic of the stiffness coefficient in spherical gears transmission.