In recent years, we have seen an uptrend in the popularity of UAVs driven by the desire to apply these aircraft to areas such as precision farming, infrastructure and environment monitoring, surveillance, surveying and mapping, search and rescue missions, weather forecasting, and more. These aircraft are more often being fully powered by electric power sources and a major technical hurdle is that of drastically reducing overall power consumption so they can be powered by solar arrays, and for long periods of time. To do so, the power requirement of an aircraft and the conversion efficiency of its propulsion system, from electrical energy to thrust, must be parametrized so that it can be improved. This paper describes a high-fidelity, low-order power model for electric, fixed-wing unmanned aircraft using flight path information. The motivation behind this work is the development of computationally-intensive, long-endurance solar-powered unmanned aircraft, the UIUC Solar Flyer, which will have continuous daylight ability to acquire and process high resolution visible and infrared imagery. Therefore, having an accurate power model will aid in providing the ability to predict power usage for future mission flight segments, which will be vital for energy-conscious path planning. Compared to works in the existing literature, the model presented follows a holistic approach for fixed-wing electric UAV power modeling that encompasses both aircraft aerodynamics and propulsion models under realistic assumptions. The model developed is able to very accurately estimate the power consumption of an electric UAV based on flight path state, without needing precise aerodynamic measurements, therefore doing so with minimal computation power. The propulsion power model was evaluated by means of flight testing as well as simulation and showed errors ranging from negligible to approximately 5%.