A wireless system is considered, where, computationally complex algorithms are offloaded from user devices to an edge cloud server, for the purpose of efficient battery usage. The main focus of this paper is to characterize and analyze, the trade-off between the energy consumed for processing the data locally, and for offloading. An analytical framework is presented, that minimizes the in-device energy consumption, by providing an optimal offloading decision for multiple user devices. A closed form solution is obtained for the offloading decision. The solution also provides the amount of computational data that should be offloaded, for the given computational and communication resources. Consequently, reduction in the energy consumption is observed.