DBSCAN is one of the most popular clustering algorithms amongst practitioners, but it has received comparatively less theoretical treatment. We show that given \(\lambda > 0\) and its parameters set under appropriate ranges, DBSCAN estimates the connected components of the \(\lambda\)-density level set (i.e. \(\{ x : f(x) \ge \lambda \}\) where \(f\) is the density). We characterize the regularity of the level set boundaries using parameter \(\beta > 0\) and analyze the estimation error under the Hausdorff metric. When the data lies in \(\mathbb{R}^D\) we obtain an estimation rate of \(O(n^{-1/(2\beta + D)})\), which matches known lower bounds up to logarithmic factors. When the data lies on an embedded unknown \(d\)-dimensional manifold in \(\mathbb{R}^D\), then we obtain an estimation rate of \(O(n^{-1/(2\beta + d\cdot \max\{1, \beta \})})\). Finally, we provide adaptive parameter tuning in order to attain these rates with no a priori knowledge of the intrinsic dimension, density, or \(\beta\).