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Abstract 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 ( V cmax25 ) 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 V cmax25 covaried with area-based leaf nitrogen ( N area ) but community-mean V cmax25 was unrelated to N area , which in turn was unrelated to the soil C:N ratio. In contrast, leaves with low area-based phosphorus ( P area ) had low V cmax25 (both between and within communities), and P area 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.