Phenotypic traits and their associated trade-offs have been shown to have globally consistent effects on individual plant physiological functions, but how these effects scale up to influence competition, a key driver of community assembly in terrestrial vegetation, has remained unclear. Here we use growth data from more than 3 million trees in over 140,000 plots across the world to show how three key functional traits - wood density, specific leaf area and maximum height - consistently influence competitive interactions. Fast maximum growth of a species was correlated negatively with its wood density in all biomes, and positively with its specific leaf area in most biomes. Low wood density was also correlated with a low ability to tolerate competition and a low competitive effect on neighbours, while high specific leaf area was correlated with a low competitive effect. Thus, traits generate trade-offs between performance with competition versus performance without competition, a fundamental ingredient in the classical hypothesis that the coexistence of plant species is enabled via differentiation in their successional strategies. Competition within species was stronger than between species, but an increase in trait dissimilarity between species had little influence in weakening competition. No benefit of dissimilarity was detected for specific leaf area or wood density, and only a weak benefit for maximum height. Our trait-based approach to modelling competition makes generalization possible across the forest ecosystems of the world and their highly diverse species composition.