Abstract The rate of carbon uptake by land plants depends on the ratio of leaf-internal to ambient carbon dioxide partial pressures 1 , here termed χ . This quantity is a key determinant of both primary production and transpiration and the relationship between them. But current models for χ are empirical and incomplete, contributing to the many uncertainties afflicting model estimates and future projections of terrestrial carbon uptake 2 , 3 . Here we show that a simple evolutionary optimality hypothesis 4 , 5 generates functional relationships between χ and growth temperature, vapour pressure deficit and elevation that are precisely and quantitatively consistent with empirical χ values from a worldwide data set containing > 3500 stable carbon isotope measurements. A single global equation embodying these relationships then unifies the empirical light use efficiency model with the standard model of C 3 photosynthesis 1 , and successfully predicts gross primary production as measured at flux sites. This achievement is notable because of the equation′s simplicity (with just two parameters, both independently estimated) and applicability across biomes and plant functional types. Thereby it provides a theoretical underpinning, grounded in eco-evolutionary principles, for large-scale analysis of the CO 2 and water exchanges between atmosphere and land.