In this paper we investigate whether partial reconfiguration can be used to reduce FPGA energy consumption. The core idea is that within a hardware design there are a number of independent circuits, and some can be idle for long periods of time. Idle circuits still consume power though, especially through clock oscillation and static leakage. Using partial reconfiguration we can replace these circuits during their idle time with others that consume much less power. Since the reconfiguration process itself introduces energy overhead, it is unclear whether this approach actually leads to an overall energy saving or to a loss. This study identifies the precise conditions under which partial reconfiguration reduces the total energy consumption, and proposes solutions that minimize the configuration energy overhead. Partial reconfiguration is compared against clock gating to evaluate its effectiveness. We apply these techniques to an existing embedded microprocessor design, and show how FPGAs can be used to accelerate application performance while also reducing overall energy consumption.