The structural vibration due to earthquake or outside impact causes serious problem for building safety. A dynamic model of a friction damper which can be constructed and installed easily is needed to reduce the vibration of the building. In this paper, the experimental equation of a circular friction damper is derived and designed for reduction of a earthquake vibration of a building. The developed experimental equation is defined to simply design the capacity on design of the circular friction damper based on the results of the performance test. Finally this experimental equation can be used for the design of a circular friction damper.