The accurate evaluation of relative intensity noise (RIN) of broad-band sources and its effect mechanism on a fiber optic gyroscope (FOG) are key factors to further improve the performance of FOGs. An intensity noise measurement system is constructed and RINs of four sources with different spectral shapes and degree of polarizations are tested. Then the RINs are calculated with three different effective bandwidths and the accurate RIN model is confirmed by employing the power weighted average (PWA) bandwidth. Based on this research, the random walk coefficient (RWC) model of FOG is modified. A photoelectric detachment high precision FOG is constructed, and the RWC of FOG is tested with four broadband sources and calculated by using the modified model. It is shown that the calculation results are consistent with the experiment results. This indicates that the power weighted average bandwidth and the degree of polarization are key factors determining the RIN of broadband sources and this research is of great value in evaluating the RIN characteristics of different sources and designing high performance FOGs.