Clustering offers significant insights in data analysis. Density-based algorithms have emerged as flexible and efficient techniques, able to discover high-quality and potentially irregularly shaped clusters. Here, we present scalable density-based clustering algorithms using random projections. Our clustering methodology achieves a speedup of two orders of magnitude compared with equivalent state-of-art density-based techniques, while offering analytical guarantees on the clustering quality in Euclidean space. Moreover, it does not introduce difficult to set parameters. We provide a comprehensive analysis of our algorithms and comparison with existing density-based algorithms.