In this paper we present a novel mathematical approach to evaluate the degree of connectivity of a multi-sink wireless sensor network. We consider both unbounded and bounded domains, specifically squares and rectangles, and the impact of border effects is also shown. Our channel model takes random fluctuations into account, as well as a distance-dependent deterministic path-loss. In particular, we deal with randomly shaped wireless footprints, rather than with the less realistic (yet widely adopted) disk model, which is a special case of our channel model. Our performance metric is based on the probability that a randomly chosen sensor is not isolated, from which the probability that a certain amount of nodes are connected can be easily derived.