Electrical energy storage could play a pivotal role in future low-carbon electricity systems, balancing inflexible or intermittent supply with demand. Cost projections are important for understanding this role, but data are scarce and uncertain. Here, we construct experience curves to project future prices for 11 electrical energy storage technologies. We find that, regardless of technology, capital costs are on a trajectory towards US$340 ± 60 kWh−1 for installed stationary systems and US$175 ± 25 kWh−1 for battery packs once 1 TWh of capacity is installed for each technology. Bottom-up assessment of material and production costs indicates this price range is not infeasible. Cumulative investments of US$175–510 billion would be needed for any technology to reach 1 TWh deployment, which could be achieved by 2027–2040 based on market growth projections. Finally, we explore how the derived rates of future cost reduction influence when storage becomes economically competitive in transport and residential applications. Thus, our experience-curve data set removes a barrier for further study by industry, policymakers and academics.