Phytoplankton size structure is key for the ecology and biogeochemistry of pelagic ecosystems, but the relationship between cell size and maximum growth rate (μmax) is not yet well understood. We used cultures of 22 species of marine phytoplankton from five phyla, ranging from 0.1 to 106 μm3 in cell volume (Vcell), to determine experimentally the size dependence of growth, metabolic rate, elemental stoichiometry and nutrient uptake. We show that both μmax and carbon-specific photosynthesis peak at intermediate cell sizes. Maximum nitrogen uptake rate (VmaxN) scales isometrically with Vcell, whereas nitrogen minimum quota scales as Vcell0.84. Large cells thus possess high ability to take up nitrogen, relative to their requirements, and large storage capacity, but their growth is limited by the conversion of nutrients into biomass. Small species show similar volume-specific VmaxN compared to their larger counterparts, but have higher nitrogen requirements. We suggest that the unimodal size scaling of phytoplankton growth arises from taxon-independent, size-related constraints in nutrient uptake, requirement and assimilation.