Wireless ad hoc sensor networks have recently emerged as a premier research topic. They have great long-term economic potential, ability to transform our lives, and pose many new system-building challenges. Sensor networks also pose a number of new conceptual and optimization problems. Here, we address one of the fundamental problems, namely, coverage. Sensor coverage, in general, answers the questions about the quality of service (surveillance) that can be provided by a particular sensor network. We briefly discuss the definition of the coverage problem from several points of view and formally define the worst and best-case coverage in a sensor network. By combining computational geometry and graph theoretic techniques, specifically the Voronoi diagram and graph search algorithms, we establish the main highlight of the paper—an optimal polynomial time worst and average case algorithm for coverage calculation for homogeneous isotropic sensors. We also present several experimental results and analyze potential applications, such as using best and worst-case coverage information as heuristics to deploy sensors to improve coverage.