Eurypterids—Palaeozoic marine and freshwater arthropods commonly known as sea scorpions—repeatedly evolved to remarkable sizes (over 0.5 m in length) and colonized continental aquatic habitats multiple times. We compiled data on the majority of eurypterid species and explored several previously proposed explanations for the evolution of giant size in the group, including the potential role of habitat, sea surface temperature and dissolved sea surface oxygen levels, using a phylogenetic comparative approach with a new tip-dated tree. There is no compelling evidence that the evolution of giant size was driven by temperature or oxygen levels, nor that it was coupled with the invasion of continental aquatic environments, latitude or local faunal diversity. Eurypterid body size evolution is best characterized by rapid bursts of change that occurred independently of habitat or environmental conditions. Intrinsic factors played a major role in determining the convergent origin of gigantism in eurypterids.