Yb-doped fibers are widely used in laser applications requiring high average output powers and high-peak-power pulse amplification. Photodarkening (PD) is recognized as one limiting factor in these fibers when pumped with high-intensity radiation. We describe an approach for performing quantitative PD studies of fibers, and we present measurements of the rate of PD in Yb-doped single-mode fibers with varying inversion levels. The method is applicable to large-mode-area fibers. We observed a seventh-order dependence of the PD rate on the excited-state Yb concentration for two different fibers; this result implies that PD of a Yb-doped fiber source fabricated using a particular fiber will be strongly dependent on the configuration of the device.