Due to water scarcity, in the last few decades, air-to-water generator (AWG) technology, whose useful effect is the extraction of water from air, has been improved. In particular, in the last few years, advanced AWG integrated systems have been developed. Such systems permit, not only to condense water from air, but also the smart use of the by-side effects of the process in order to partially or totally cover the heating ventilation air conditioning (HVAC) needs of a building. Presently, there are no evaluation tools that permit a complete comparison among AWG machines, taking into account all the useful effects that can be obtained at the same time and with the same energy input. The current work, starting from the need for such a tool, proposes a global index whose formulation considers all useful effects of an integrated system, the energy required to obtain them, and the integration degree of the machine. The index translates into a single number the system global efficiency, by means of a particular combination of existing efficiency indicators. In its extended formulation, it can be applied, not only to AWGs, but also to other HVAC integrated systems, as well as to combinations of non-integrated and integrated solutions. In addition to equations, the paper provides calculation examples and a case study in order to show the practical application and advantages of GEI.