Reactive oxygen species (ROS) play a critical role in the chemical transformation of atmospheric secondary organic aerosols (SOA) and aerosol health effects by causing oxidative stress in vivo. Acidity is an important physicochemical property of atmospheric aerosols, but its effects on the ROS formation from SOA have been poorly characterized. By applying the electron paramagnetic resonance spin-trapping technique and the Diogenes chemiluminescence assay, we find highly distinct radical yields and composition at different pH values in the range of 1-7.4 from SOA generated by oxidation of isoprene, α-terpineol, α-pinene, β-pinene, toluene, and naphthalene. We observe that isoprene SOA has substantial hydroxyl radical (•OH) and organic radical yields at neutral pH, which are 1.5-2 times higher compared to acidic conditions in total radical yields. Superoxide (O2 •-) is found to be the dominant species generated by all types of SOAs at lower pH. At neutral pH, α-terpineol SOA exhibits a substantial yield of carbon-centered organic radicals, while no radical formation is observed by aromatic SOA. Further experiments with model compounds show that the decomposition of organic peroxide leading to radical formation may be suppressed at lower pH due to acid-catalyzed rearrangement of peroxides. We also observe 1.5-3 times higher molar yields of hydrogen peroxide (H2O2) in acidic conditions compared to neutral pH by biogenic and aromatic SOA, likely due to enhanced decomposition of α-hydroxyhydroperoxides and quinone redox cycling, respectively. These findings are critical to bridge the gap in understanding ROS formation mechanisms and kinetics in atmospheric and physiological environments.