What are the quantitative effects of countercyclical capital buffers (CCyB)? I study this question in the context of a nonlinear DSGE model with a financial sector that is subject to occasional panics. A calibrated version of the model is combined with US data to estimate sequences of structural shocks, allowing me to study policy counterfactuals. First, I show that raising capital buffers during leverage expansions can reduce the frequency of crises by more than half. Second, I show that lowering capital buffers during a panic can moderate the intensity of the resulting crisis. A quantitative application to the 2007-08 financial crisis shows that CCyB in the 2.5% range (as in the Federal Reserve's current framework) could have greatly mitigated the financial panic in 2007Q4-2008Q4, for a cumulative gain of 22% in aggregate consumption. These findings suggest that CCyB are a useful policy tool both ex-ante and ex-post.