Societal benefits of public engagement were recognized as 'impact' from research in the UK's recent Research Excellence Framework (REF), which determines an allocation of central government funding for universities and shapes the landscape for university researchers undertaking such activities. This paper shares experience from a successful REF Impact Case Study based on a programme of informing/inspiring-type public engagement, illustrating how engagement goals can match definitions of impact for the REF, and summarizing types of evidence used to demonstrate 'reach' and 'significance' of impact in media engagement, face-to-face engagement and online engagement, which represent common activities undertaken by many researchers.