This study evaluates the impact of students’ usage of generative artificial intelligence (GenAI) tools such as ChatGPT on their exam performance. We analyse student essays using GenAI detection systems to identify GenAI users among the cohort. Employing multivariate regression analysis, we find that students using GenAI tools score on average 6.71 (out of 100) points lower than non-users. While GenAI may offer benefits for learning and engagement, the way students actually use it correlates with diminished exam outcomes. Exploring the underlying mechanism, additional analyses show that the effect is particularly detrimental to students with high learning potential, suggesting an effect whereby GenAI tool usage hinders learning. Our findings provide important empirical evidence for the ongoing debate on the integration of GenAI in higher education and underscore the necessity for educators, institutions, and policymakers to carefully consider its implications for student performance.