In this article, we explore how Twitter engagements can demonstrate different types and extent of research impact. It can be simple to demonstrate social media activity through quantitative metrics; however, it is more complex and challenging to evidence the impact that this activity can have. We start by exploring definitions of impact and public engagement. We then present an analysis of a selection of Twitter interactions from the @BarbieReports Art Activist Barbie account, creating a typology consisting of four categories: change tweet, cheer tweet, comment tweet and conversation tweet. These categories demonstrate different types of engagement and impact, enabling an understanding of how impact can be claimed from contextual social media analysis. This typology can be used by researchers to analyse tweet interactions in three ways: (1) as indicators of two-way engagement; (2) as evidence of impact; and (3) as part of a wider story of change and influence. The typology presented in this article is intended as a foundation which people can adapt and add to, making it an evolving tool for social media impact analysis.