In this paper, mechanical thermal noise in micro-machined levitated two-axis rate gyroscopes (MLG) is comprehensively studied. Taking into account the gyroscopic nature and a type of electromagnetic levitation employed in MLG, effective damping coefficients are obtained for two cases corresponding to positive and negative angular position stiffness. According to obtained coefficients, expressions for the spectral density of the gyroscope noise floor and its angular random walk are derived. Moreover, an investigation of the response of an ideal levitated gyroscope to the fluctuating torque within the entire frequency domain shows a restriction of the detection of the measuring rate in order to preserve the same angular position stiffness. This response, a form of Johnson noise, provides an explanation of the mechanism of constraints in gyroscope resolution, which in turn limits the current performance of levitated gyroscopes. Also, using the Ising criterion, an alternative qualitative means to estimate the resolution is obtained. By joining the Johnson noise and Ising criterion techniques, a confidence range for the gyroscope resolut ... mehrion is proposed.