The hydroxyl radical (OH) largely determines the atmosphere's oxidative capacity and, thus, the lifetimes of numerous trace gases, including methane (CH₄). Hitherto, observation-based approaches for estimating the atmospheric oxidative capacity have primarily relied on using methyl chloroform (MCF), but as the atmospheric abundance of MCF has declined, the uncertainties associated with this method have increased. In this study, we examine the use of five hydrofluorocarbons (HFCs) (HFC-134a, HFC-152a, HFC-365mfc, HFC-245fa, and HFC-32) in multi-species inversions, which assimilate three HFCs simultaneously, as an alternative method to estimate atmospheric OH. We find robust estimates of OH regardless of which combination of the three HFCs are used in the inversions. Our results show that OH has remained fairly stable during our study period from 2004 to 2021, with variations of <2% and no significant trend. Inversions including HFC-32 and HFC-152a (the shortest-lived species) indicate a small reduction in OH in 2020 (1.6±0.9% relative to the mean over 2004-2021 and 0.6±0.9% lower than in 2019), but considering all inversions, the reduction was only 0.5±1.1%, and OH was at a similar level to that in 2019.