Despite global efforts to harmonize international trade statistics, our understanding of digital trade and its implications remains limited. Here, we introduce a method to estimate bilateral exports and imports for dozens of sectors starting from the corporate revenue data of large digital firms. This method allows us to provide estimates for digitally ordered and delivered trade involving digital goods (e.g. video games), productized services (e.g. digital advertising), and digital intermediation fees (e.g. hotel rental), which together we call digital products. We use these estimates to study five key aspects of digital trade. We find that, compared to trade in physical goods, digital product exports are more spatially concentrated, have been growing faster, and can offset trade balance estimates, like the United States trade deficit on physical goods. We also find that countries that have decoupled economic growth from greenhouse gas emissions tend to have larger digital exports and that digital products exports contribute positively to the complexity of economies. This method, dataset, and findings provide a new lens to understand the impact of international trade in digital products.