Abstract: Annular contact surface is widely used in mechanical engineering, and in mechanical design, it is usually necessary to calculate the friction torque of annular contact surface. The key to the calculation of friction torque lies in the determination of friction radius, and in many cases, for the convenience of calculation, the friction radius of the annular contact surface is regarded as the average friction radius of the mean value of the inner radius and the outer radius. However, some design manuals give a very different formula for the calculation of the equivalent friction radius. Aiming at this problem, the mechanical model of contact surface friction torque is established, and the same result as the equivalent friction radius given in the manual is derived by means of torque integration. The two formulas are compared, and the error caused by the average friction radius is evaluated, and suggestions are given for the selection of the friction radius formula of the annular contact surface.