Passive ring resonator (PRR) is the critical sensing component of a resonator optic gyroscope (ROG) and the scale factor of a resonator optic gyroscope is mainly determined by the coupling coefficient through the full width at half maximum of the passive ring resonators transfer function. A method to determine the optimal value of coupling coefficient is elaborated based on the theory of coupled-mode theory and frequency-modulation (FM) spectroscopy. Finally, emulation results is given to verify the method and prove that the value of about 5% is only correct in the situation of fiber optic gyros (FOG).