This study examines how variation of within-day cognitive function affects human capital accumulation. Cognitive function, which neurobiologists have found varies widely across the day, has thus far been an important omission in the economics literature. We quantify its role on human capital accumulation using data from five cohorts of college freshman at the United States Air Force Academy, where students face randomized scheduling and a common set of classes and exams. We find clear evidence that daily fluctuations in cognitive function affects academic achievement-a student does 0.25 standard deviations better at her highest observed ability than at her worst. Cognitive function is affected by the time of day that learning takes place, but also importantly, by the context of a student's schedule and the degree of cognitive fatigue at that time of day- students perform 0.05 standard deviations worse if they have back-to-back classes than if they just had a break. Differences in effects along the ability distribution suggest that overall effi- ciency gains are possible. Prioritizing the schedules of those most impacted by cognitive fatigue would be equivalent to improving their teacher quality by a standard deviation in 40% of offered classes. Findings suggest that a re-organization of students' daily school schedules is a promising and potentially low-cost educational intervention.