In this paper, we study the one-dimensional coverage problem in a wireless sensor network (WSN) and consider a network deployed along a one-dimensional line according to a Poisson distribution. We analyze three important parameters that are related to the problem, i.e., expected k-coverage proportion, full k-coverage probability, and partial k-coverage probability, and derive mathematical models that describe the relationships between the node density in the network and these parameters. The purpose is to calculate or estimate the node density required for achieving a given coverage probability, which is useful in the deployment of a one-dimensional network for many applications. We first analyze the expected k-coverage proportion, then analyze the full k-coverage probability for k = 1 and the lower bound to the full k-coverage probability for k > 1, and finally analyze the partial k-coverage probability for k = 1 and give a brief discussion of the partial k-coverage probability for k > 1. The mathematical models are validated through simulation. Copyright © 2011 John Wiley & Sons, Ltd.