This article presents a new EROI (energy return on investment) factor named the ideal EROI, or EROIide, that provides the theoretical upper boundary of the EROI of a given system. The EROIide is the ratio between the inputs within the EROIstna boundaries and the theoretical maximum output from a given system; i.e, all losses are omitted and the maximum theoretical energy output of the system is used. EROIide resembles the concept of the idealised Carnot heat engine. Although the EROI of a given system can never be equal to EROIide, the EROIide can be used to estimate the potential for improvement; e.g., if the difference between the EROIide and EROIstnd is small then little improvement can be expected from further research funding. Calculations using EROIide can add a valuable depth to the overall results of an EROI study, benefitting policy makers involved in energy policy planning. Three application examples of EROIide are provided, one for a hydroelectric power plant, one for a geothermal power plant and one example for a hypothetical wind farm. The calculations show that the hydro power plant could improve approximately 3 fold, whereas the geothermal plant had a potential of 27 fold improvement over its lifetime. (C) 2014 Elsevier Ltd. All rights reserved.