Leaf size and venation show remarkable diversity across dicotyledons, and are key determinants of plant adaptation in ecosystems past and present. Here we present global scaling relationships of venation traits with leaf size. Across a new database for 485 globally distributed species, larger leaves had major veins of larger diameter, but lower length per leaf area, whereas minor vein traits were independent of leaf size. These scaling relationships allow estimation of intact leaf size from fragments, to improve hindcasting of past climate and biodiversity from fossil remains. The vein scaling relationships can be explained by a uniquely synthetic model for leaf anatomy and development derived from published data for numerous species. Vein scaling relationships can explain the global biogeographical trend for smaller leaves in drier areas, the greater construction cost of larger leaves and the ability of angiosperms to develop larger and more densely vascularised lamina to outcompete earlier-evolved plant lineages.