Treadmill experiments suggest that left-dominant arm swing is common in healthy walking adults and is modulated by cognitive dual-tasking. Little is known about arm swing asymmetry in overground walking. We report directional (dASI) and non-directional arm swing symmetry indices (ndASI) from 334 adults (mean age 68.6 ± 5.9 y) walking overground at comfortable (NW) and fast (FW) speeds and while completing a serial subtraction task (DT). dASI and ndASI were calculated from sagittal shoulder range of motion data generated by inertial measurement units affixed to the wrist. Most (91%) participants were right-handed. Group mean arm swing amplitude was significantly larger on the left in all walking conditions. During NW, ndASI was 39.5 ± 21.8, with a dASI of 21.9 ± 39.5. Distribution of dASI was bimodal with an approximately 2:1 ratio of left:right-dominant arm swing. There were no differences in ndASI between conditions but dASI was smaller during DT compared to FW (15.2 vs 24.6; p = 0.009). Handedness was unrelated to ndASI, dASI or the change in ASI metrics under DT. Left-dominant arm swing is the norm in healthy human walking irrespective of walking condition or handedness. As disease markers, ndASI and dASI may have different and complementary roles.