© 2016 New Phytologist Trust. A long-standing research focus in phytology has been to understand how plants allocate leaf epidermal space to stomata in order to achieve an economic balance between the plant's carbon needs and water use. Here, we present a quantitative theoretical framework to predict allometric relationships between morphological stomatal traits in relation to leaf gas exchange and the required allocation of epidermal area to stomata. Our theoretical framework was derived from first principles of diffusion and geometry based on the hypothesis that selection for higher anatomical maximum stomatal conductance (gsmax) involves a trade-off to minimize the fraction of the epidermis that is allocated to stomata. Predicted allometric relationships between stomatal traits were tested with a comprehensive compilation of published and unpublished data on 1057 species from all major clades. In support of our theoretical framework, stomatal traits of this phylogenetically diverse sample reflect spatially optimal allometry that minimizes investment in the allocation of epidermal area when plants evolve towards higher gsmax. Our results specifically highlight that the stomatal morphology of angiosperms evolved along spatially optimal allometric relationships. We propose that the resulting wide range of viable stomatal trait combinations equips angiosperms with developmental and evolutionary flexibility in leaf gas exchange unrivalled by gymnosperms and pteridophytes.