A prominent feature of comparative life histories is the well documented negative correlation between growth rate and life span. Patterns of resource allocation during growth and reproduction reflect life-history differences between species. This is particularly striking in tropical forests, where tree species can differ greatly in their rates of growth and ages of maturity but still attain similar canopy sizes. Here we provide a theoretical framework for relating life-history variables to rates of production, dM/dt, where M is above-ground mass and t is time. As metabolic rate limits production as an individual grows, dM/dt ~ M3/4. Incorporating interspecific variation in resource allocation to wood density, we derive a universal growth law that quantitatively fits data for a large sample of tropical tree species with diverse life histories. Combined with evolutionary life-history theory, the growth law also predicts several qualitative features of tree demography and reproduction. This framework also provides a general quantitative answer to why relative growth rate (1/M)(dM/df) decreases with increasing plant size (~M-1/4) and how it varies with differing allocation strategies.