  Thermal noise of a mirror is one of the limiting noise sources in the high
precision measurement such as gravitational-wave detection, and the modeling of
thermal noise has been developed and refined over a decade. In this paper, we
present a derivation of coating thermal noise of a finite-size cylindrical
mirror based on the fluctuation-dissipation theorem. The result agrees to a
previous result with an infinite-size mirror in the limit of large thickness,
and also agrees to an independent result based on the mode expansion with a
thin-mirror approximation. Our study will play an important role not only to
accurately estimate the thermal-noise level of gravitational-wave detectors but
also to help analyzing thermal noise in quantum-measurement experiments with
lighter mirrors.
