We propose a novel epidemic routing policy, named energy optimal epidemic routing, for delay tolerant networks (DTNs). By investigating the tradeoff between delay and energy, we found the optimal transmission range as well as the optimal number of infected nodes for the minimal energy consumption, given a delivery requirement, specifically delay bound and delivery probability to the destination. We derive an analytic model of the Binary Spraying routing to find the optimal values, describing the delay distributions with respect to the number of infected nodes.