Contrary to expectations, a measurement of the random walk in the ring laser gyro (RLG) as a function of laser power P shows that it is not consistent with the P^{-1/2} rule. In the experiment, the random walk and laser power are tested and recorded at different discharge currents. The random walk decreases with increasing power, but with a rate much less than the theoretical value according to current literature. In order to solve the inconsistency above, we derive the expression for the random walk in RLGs based on laser theory. Theoretical analysis shows that, accumulating effects of lower energy level due to its limited lifetime lead to additional quantum noise from spontaneous emission. Results show that the random walk in the RLGs consists of two components. The former decreases with increasing power according to the P^{-1/2} rule, whereas the other is power-independent. Thus far, the power-independent quantum limit has not appeared in the literature; therefore, the expressions for RLGs should be modified to describe the low-loss RLGs exactly, where the power-independent term takes a relatively larger proportion. The findings are significant to the further reduction of quantum limit in low-loss RLGs.