A simple optical field overlap method is reported to calculate the transfer coefficient of fiber ring resonator, the heart of the resonator fiber optic gyro. The results are applied to the investigation of influence of spectral linewidth of laser on resonance characteristics in fiber ring resonator. Furthermore, analysis has been made of relationship between the shot noise limited sensitivity of resonator fiber optic gyro and optical parameters in fiber ring resonator under some spectral linewidth of the laser conditions. The results are provided to theoretical basis for optimization design of resonator fiber optic gyro.