There is huge uncertainty about how global exchanges of carbon between the atmosphere and land will respond to continuing environmental change. A better representation of photosynthetic capacity is required for Earth System models to simulate carbon assimilation reliably. Here we use a global leaf-trait dataset to test whether photosynthetic capacity is quantitatively predictable from climate, based on optimality principles; and to explore how this prediction is modified by soil properties, including indices of nitrogen and phosphorus availability, measured in situ. The maximum rate of carboxylation standardized to 25 °C (Vcmax25) was found to be proportional to growing-season irradiance, and to increase-as predicted-towards both colder and drier climates. Individual species' departures from predicted Vcmax25 covaried with area-based leaf nitrogen (Narea) but community-mean Vcmax25 was unrelated to Narea, which in turn was unrelated to the soil C:N ratio. In contrast, leaves with low area-based phosphorus (Parea) had low Vcmax25 (both between and within communities), and Parea increased with total soil P. These findings do not support the assumption, adopted in some ecosystem and Earth System models, that leaf-level photosynthetic capacity depends on soil N supply. They do, however, support a previously-noted relationship between photosynthesis and soil P supply.