Brownian thermal noise is a severe limitation for the sensitivity of many optomechanical high-precision measurement systems. To push the sensitivity limit it is essential to quantify how device geometry and material properties affect thermal noise. As an important building block for optomechanical experiments, we present the analytical calculation of Brownian thermal noise of circular clamped reflective membranes in Fabry Perot cavities. To compute the thermal noise, we investigate the influence of the effective membrane position x (compare Fig. 1(a)) to the eigenfrequency of the cavity.