The UK government has recently made higher education funding of anthropological research partially dependent on its social ‘impact’. Based on work in higher education and fifty interviews with anthropologists trained in Britain, this article analyses the implications of these impact requirements. It shows that anthropologists generally share government desires for their work to have a societal effect, but that impact, as understood in the United Kingdom’s dominant research measurement exercise known as the Research Excellence Framework (REF), is marked by a series of important practical and conceptual limitations. On a practical level, it underestimates the social effects of teaching, relies on an overly limiting notion of evidence, and significantly restricts the scope of permissible research. On a conceptual level, impact measurement cannot fully grasp the nature or effect of anthropology, insofar as the latter is a critical science that contributes to the constant renewal of audit’s own politico-epistemic foundations. This exposes an important limitation of audit practices more widely, which has so far received little scholarly attention: audits are in several ways incapable of grasping sociocultural critique.