In this study an analytical tbol that combines two models for determination of thermal performance of a direct expansion-solar assisted heat pump (DX-SAHP) domestic hot water heater is presented. The first method-the quadratic model developed in this study-predicts the approximate value of the collector fluid temperature, from the known values of solar radiation in the collector plane (I-coll), condensing temperature and the ambient air temperature. The predicted value of collector fluid temperature is used as an input in a companion model that, using the second law, predicts the system coefficient of performance (COP) from the known values of condensing temperature, compressor efficiency and refrigerant properties. The combined method presented in this study is ideally suited for preliminary design calculations for a selected location or for comparison of different locations for determination of the energy conservation and carbon emission reduction potential of DX-SAHP hot water systems. The thermal performance results predicted from this combined method indicate that system COP ranging from 3.6 to 5.6 can be obtained for the month of January for locations such as New York City, Norfolk and Tampa. The carbon reduction factor (CRF), signifying reduced carbon emission due to switch from electric only water heater to much more efficient DX-SAHP water heater, ranged from 72% to 82% for the chosen locations. This narrow range for CRF indicates that regardless of geographical locations it is prudent to phase out electric only hot water heater and replace them by DX-SAHP water heaters. (C) 2016 Elsevier Ltd. All rights reserved.