As online spatial datasets grow both in number and sophistication, it becomes increasingly difficult for users to decide whether a dataset is suitable for their tasks, especially when they do not have prior knowledge of the dataset. The GeoBrowsing service developed for the ADL project provides users an effective and efficient way to explore the content of a spatial dataset. In this paper, we identify a set of spatial relations that need to be supported in browsing applications, namely, the contains, contained and the overlap relations. We prove a storage lower bound to answer queries about the contains relation accurately at a given grid resolution. We then present three storage-efficient approximation algorithms which we believe to be the first to estimate query selectivities about these spatial relations. Experimental results show that these algorithms provide highly accurate estimates in real time for a wide range of datasets with various characteristics.