Many combined heat and power (CHP) units have been installed in domestic buildings to increase energy efficiency and reduce energy costs. However, inappropriate sizing of a CHP may actually increase energy costs and reduce energy efficiency. Moreover, the high manufacturing cost of batteries makes batteries less affordable. Therefore, this paper will attempt to size the capacity of CHP and optimise daily energy costs for a domestic building with only CHP installed. In this paper, electricity and heat loads are firstly used as sizing criteria in finding the best capacities of different types of CHP with the help of the maximum rectangle (MR) method. Subsequently, the genetic algorithm (GA) will be used to optimise the daily energy costs of the different cases. Then, heat and electricity loads are jointly considered for sizing different types of CHP and for optimising the daily energy costs through the GA method. The optimisation results show that the GA sizing method gives a higher average daily energy cost saving, which is 13% reduction compared to a building without installing CHP. However, to achieve this, there will be about 3% energy efficiency reduction and 7% input power to rated power ratio reduction compared to using the MR method and heat demand in sizing CHP.