Summary Variation in angiosperm vessel diameter is of major functional significance. In the light of recent models predicting optimal vessel taper given resistance imposed by conductive path length, we tested the prediction that plant size should predict vessel diameter, with dryland plants having narrower vessels for their stem sizes. We assembled a comparative dataset including vessel and stem diameter measurements from 237 species from over 40 angiosperm orders across a wide range of habits and habitats. Stem diameter predicted vessel diameter across self‐supporting plants (slope 0.36, 95% CI 0.32–0.39). Samples from 142 species from five communities of differing water availability showed no tendency for dryland plants to have narrower vessels. Predictable relationships between vessel diameter and stem diameter mirrored predictable relationships between stem length and diameter across self‐supporting species. That vessels are proportional to stem diameter and stem diameter is proportional to stem length suggests that taper in relation to conductive path length gives rise to the vessel diameter–stem diameter relationship. In turn, plant size is related to climate, leading indirectly to the vessel–climate relationship: vessels are likely narrower in drier communities because dryland plants are on average smaller, not because they have narrow vessels for their stem sizes.