Activity cliffs (ACs) are an important type of structure-activity relationship in medicinal chemistry where small structural changes result in unexpectedly large differences in biological activity. Being able to predict these changes would have a profound impact on lead optimization of drug candidates. Free-energy perturbation is an ideal tool for predicting relative binding energy differences for small structural modifications, but its performance for ACs is unknown. Here, we show that FEP can on average predict ACs to within 1.39 kcal/mol of experiment (∼1 log unit of activity). We performed FEP calculations with two different software methods: Schrödinger-Desmond FEP+ and GROMACS implementations. There was qualitative agreement in the results from the two methods, and quantitatively the error for one data set was identical, 1.43 kcal/mol, but FEP+ performed better in the second, with errors of 1.17 versus 1.90 kcal/mol. The results have far-reaching implications, suggesting well-implemented FEP calculations can have a major impact on computational drug design.