Residential battery energy storage systems (BESS) are having an important role in transitioning towards low carbon communities. However, BESS capital cost remains questionable. In this work, an optimization-based BESS sizing algorithm is developed to maximize the customer's profitability by minimizing the electricity import for 162 combinations of demand, solar photovoltaic (PV) and electric vehicle (EV). The sizing algorithm results are utilized in introducing empirical formulas that ease the determination of the near-optimal BESS capacity. The annual savings are quantified for various cases under different tariff rates and the BESS viability is investigated for new installations over the next 10 years. The results show that the residential BESS can be profitable in the UK starting from 2024 without any subsidy for the time of use tariffs.