Phase change materials can improve the efficiency of energy systems by time shifting or reducing peak thermal loads. The value of a phase change material is defined by its energy and power density—the total available storage capacity and the speed at which it can be accessed. These are influenced by material properties but cannot be defined with these properties alone. Here we show the close link between energy and power density by developing thermal rate capability and Ragone plots, a framework widely used to describe the trade-off between energy and power in electrochemical storage systems (that is, batteries). Our results elucidate how material properties, geometry and operating conditions influence the performance of phase change thermal storage. This research sets a clear framework for comparing thermal storage materials and devices and can be used by researchers and designers to increase clean energy use with storage.