From sparse descriptions of events, observers can make systematic and nuanced predictions of what emotions the people involved will experience. We propose a formal model of emotion prediction in the context of a public high-stakes social dilemma. This model uses inverse planning to infer a person’s beliefs and preferences, including social preferences for equity and for maintaining a good reputation. The model then combines these inferred mental contents with the event to compute ‘appraisals’: whether the situation conformed to the expectations and fulfilled the preferences. We learn functions mapping computed appraisals to emotion labels, allowing the model to match human observers’ quantitative predictions of 20 emotions, including joy, relief, guilt and envy. Model comparison indicates that inferred monetary preferences are not sufficient to explain observers’ emotion predictions; inferred social preferences are factored into predictions for nearly every emotion. Human observers and the model both use minimal individualizing information to adjust predictions of how different people will respond to the same event. Thus, our framework integrates inverse planning, event appraisals and emotion concepts in a single computational model to reverse-engineer people’s intuitive theory of emotions.This article is part of a discussion meeting issue ‘Cognitive artificial intelligence’.