Despite numerous studies, the link between verbal working memory (WM) and calculation abilities remains poorly understood. The present longitudinal study focuses specifically on the role of serial order retention capacities, based on recent findings suggesting a link between ordinal processing in verbal WM and numerical processing tasks. Children were tested when they were in 3rd-year kindergarten (Time 1 [T1]), 1st grade (Time 2 [T2]), and 2nd grade of primary school (Time 3 [T3]), with WM tasks maximizing retention of serial order or item information, as well as with numerical judgment and calculation tasks. We observed that order WM measures at T1 provided a robust predictor of calculation abilities at T2 and T3. Numerical ordinal and magnitude judgment abilities were also associated with calculation abilities and this, independently of order WM abilities. This study highlights the important role of WM for order in early calculation acquisition, in addition to numerical ordinal and magnitude representations, and provides new perspectives for our understanding of the link between verbal WM and numerical abilities.