Why do children learn some words earlier than others? Regularities and differences in the age of acquisition for words across languages yield insights regarding the mechanisms guiding word learning. In a large-scale corpus analysis, we estimate the ages at which 9,200 children learn 300-400 words in seven languages, predicting them on the basis of independently-derived linguistic, environmental, and conceptual factors. Predictors were surprisingly consistent across languages, but varied across development and as a function of lexical category (e.g., concreteness predicted nouns while linguistic structure predicted function words). By leveraging data at a significantly larger scale than previous work, our analyses highlight the power that emerges from unifying previously disparate theories, but also reveal the amount of reliable variation that still remains unexplained.