Using first principles structure searching with density-functional theory (DFT) we identify a novel Fm-3m phase of Cu2P and two low-lying metastable structures, an I-43d–Cu3P phase, and a Cm–Cu3P11 phase. The computed pair distribution function of the novel Cm–Cu3P11 phase shows its structural similarity to the experimentally identified Cm–Cu2P7 phase. The relative stability of all Cu–P phases at finite temperatures is determined by calculating the Gibbs free energy using vibrational effects from phonon modes at 0 K. From this, a finite-temperature convex hull is created, on which Fm-3m–Cu2P is dynamically stable and the Cu3−xP (x < 1) defect phase Cmc21–Cu8P3 remains metastable (within 20 meV/atom of the convex hull) across a temperature range from 0 K to 600 K. Both CuP2 and Cu3P exhibit theoretical gravimetric capacities higher than contemporary graphite anodes for Li-ion batteries; the predicted Cu2P phase has a theoretical gravimetric capacity of 508 mAh/g as a Li-ion battery electrode, greater than both Cu3P (363 mAh/g) and graphite (372 mAh/g). Cu2P is also predicted to be both non-magnetic and metallic, which should promote efficient electron transfer in the anode. Cu2P’s favorable properties as a metallic, high-capacity material suggest its use as a future conversion anode for Li-ion batteries; with a volume expansion of 99 % during complete cycling, Cu2P anodes could be more durable than other conversion anodes in the Cu–P system with volume expansions greater than 150 %. The structures and figures presented in this paper, and the code used to generate them, can be interactively explored online using Binder.