Power modelling is an important topic in many areas of computing, for example to save energy in texture streaming for gaming[1] or to select efficient H.264 video encoding parameters[2]. However, researchers' view of how hardware consume power is limited. They typically resort to rate­based models to describe the energy consumption of hardware, where power usage is correlated directly with hardware access rates (for example instructions or cache misses per second)[3,4,5,6]. This approach ignores many mechanisms that impact the power usage of a system, such as rail voltages, core­ and clock­ gating, frequency scaling and variable cost of instruction execution. Because of this, they can mispredict up to 70 % on the Tegra K1. We show that by taking all these factors into account with sufficient hardware knowledge, it is possible to bridge the gap between power usage and software execution to build power models which are over 98 % accurate over all CPU, GPU and memory frequency combinations.