Woody stems comprise a large biological carbon fraction and determine water transport between roots and leaves; their structure and function can influence both carbon and hydrological cycles. While angiosperm wood anatomy and density determine hydraulic conductivity and mechanical strength, little is known about interrelations across many species. We compiled a global data set comprising two anatomical traits for 3005 woody angiosperms: mean vessel lumen area (Ā) and number per unit area (N). From these, we calculated vessel lumen fraction (F = ĀN) and size to number ratio (S = Ā/N), a new vessel composition index. We examined the extent to which F and S influenced potential sapwood specific stem conductivity (KS) and wood density (D; dry mass/fresh volume). F and S varied essentially independently across angiosperms. Variation in KS was driven primarily by S, and variation in D was virtually unrelated to F and S. Tissue density outside vessel lumens (DN) must predominantly influence D. High S should confer faster KS but incur greater freeze–thaw embolism risk. F should also affect KS, and both F and DN should influence mechanical strength, capacitance, and construction costs. Improved theory and quantification are needed to better understand ecological costs and benefits of these three distinct dimensions.