In hot dry climates, it is estimated that almost half the urban peak load of energy consumption is used to satisfy air-conditioning cooling demands in summer time. Since the urbanization rate in developing countries – like the case in Egypt – is rising rapidly, the pressure placed on energy resources to satisfy inhabitants’ indoor comfort requirements is consequently increasing too. This paper introduces passive cool roof as a means of reducing energy cooling loads for satisfying human comfort requirements in a hot climate. A designed algorithmic hybrid matrix was used to simulate 37 roof design probabilities alternating roof shape, roof material and construction. The result of using a vault roof with high albedo coating shows a fall of 53% in discomfort hours and saves 826 kW h during the summer season compared to the base case of the conventional non insulated flat roof in a typical Cairo residential buildings. It is recommended that the selected cool roof solution be combined with natural ventilation to increase the indoor thermal comfort, and with passive heating strategies to compensate the increase in heating hours. The application is intended for low cost residential buildings in a hot dry climate.