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