Pumped heat electricity storage (PHES) has been recently suggested as a potential solution to the large-scale energy storage problem. PHES requires neither underground caverns as compressed air energy storage (CAES) nor kilometer-sized water reservoirs like pumped hydrostorage and can therefore be constructed anywhere in the world. However, since no large PHES system exists yet, and theoretical predictions are scarce, the efficiency of such systems is unknown. Here we formulate a simple thermodynamic model that predicts the efficiency of PHES as a function of the temperature of the thermal energy storage at maximum output power. The resulting equation is free of adjustable parameters and nearly as simple as the well-known Carnot formula. Our theory predicts that for storage temperatures above 400 °C PHES has a higher efficiency than existing CAES and that PHES can even compete with the efficiencies predicted for advanced-adiabatic CAES.