Stomatal conductance (g s) is a key land-surface attribute as it links transpiration, the dominant component of global land evapotranspiration, and photosynthesis, the driving force of the global carbon cycle. Despite the pivotal role of g s in predictions of global water and carbon cycle changes, a global-scale database and an associated globally applicable model of g s that allow predictions of stomatal behaviour are lacking. Here, we present a database of globally distributed g s obtained in the field for a wide range of plant functional types (PFTs) and biomes. We find that stomatal behaviour differs among PFTs according to their marginal carbon cost of water use, as predicted by the theory underpinning the optimal stomatal model and the leaf and wood economics spectrum. We also demonstrate a global relationship with climate. These findings provide a robust theoretical framework for understanding and predicting the behaviour of g s across biomes and across PFTs that can be applied to regional, continental and global-scale modelling of ecosystem productivity, energy balance and ecohydrological processes in a future changing climate.