Wireless sensor networks are consist of large number of embedded devices that are each capable of sensing, communicating, and computing. Sensor networks have a wide variety of applications in both military and civil environment[1]. most sensors are equipped with non-rechargeable batteries that have limited lifetime[18]. Sensor nodes monitor some surrounding environmental phenomenon, process the data obtained and forward this data towards a base station located on the periphery of the sensor network. Base station(s) collect the data from the sensor nodes and transmit this data to some remote control station. Sensor network models considered by most researchers have a single static base station located on the periphery of the sensor network [2], [3], [4], [5]. Following development of technology, the number of the nodes would increase highly. The upper bound of the number of the nodes becoming more and more important. In this work, we develop closed-form expressions of the upper bound of the number of nodes in energy-efficient wireless sensor networks.