A pervasive dilemma in neuroimaging is whether to prioritize sample size or scan time given fixed resources. Here, we systematically investigate this trade-off in the context of brain-wide association studies (BWAS) using functional magnetic resonance imaging (fMRI). We find that total scan duration (sample size × scan time per participant) robustly explains individual-level phenotypic prediction accuracy via a logarithmic model, suggesting that sample size and scan time are broadly interchangeable up to 20-30 min of data. However, the returns of scan time diminish relative to sample size, which we explain with principled theoretical derivations. When accounting for fixed overhead costs associated with each participant (e.g., recruitment, non-imaging measures), prediction accuracy in many small-scale and some large-scale BWAS might benefit from longer scan time than typically assumed. These results generalize across phenotypic domains, scanners, acquisition protocols, racial groups, mental disorders, age groups, as well as resting-state and task-state functional connectivity. Overall, our study emphasizes the importance of scan time, which is ignored in standard power calculations. Standard power calculations maximize sample size, at the expense of scan time, which can result in sub-optimal prediction accuracies and inefficient use of resources. Our empirically informed reference is available for future study design: WEB_APPLICATION_LINK.