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Allometric relationships among the dimensions of leaves and their cells hold across diverse eudicotyledons, but have remained untested in the leaves of grasses. We hypothesised that geometric (proportional) allometries of cell sizes across tissues and of leaf dimensions would arise due to the coordination of cell development and that of cell functions such as water, nutrient and energy transport, and that cell sizes across tissues would be associated with light‐saturated photosynthetic rate. We tested predictions across 27 globally distributed C₃and C₄grass species grown in a common garden. We found positive relationships among average cell sizes within and across tissues, and of cell sizes with leaf dimensions. Grass leaf anatomical allometries were similar to those of eudicots, with exceptions consistent with the fewer cell layers and narrower form of grass leaves, and the specialised roles of epidermis and bundle sheath in storage and leaf movement. Across species, mean cell sizes in each tissue were associated with light‐saturated photosynthetic rate per leaf mass, supporting the functional coordination of cell sizes. These findings highlight the generality of evolutionary allometries within the grass lineage and their interlinkage with coordinated development and function.