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This paper introduces a function dedicated to the estimation of total energy expenditure (TEE) of daily activities based on data from accelerometers integrated into smartphones. The use of mass-market sensors such as accelerometers offers a promising solution for the general public due to the growing smartphone market over the last decade. The TEE estimation function quality was evaluated using data from intensive numerical experiments based, first, on 12 volunteers equipped with a smartphone and two research sensors (Armband and Actiheart) in controlled conditions (CC) and, then, on 30 other volunteers in free-living conditions (FLC). The TEE given by these two sensors in both conditions and estimated from the metabolic equivalent tasks (MET) in CC served as references during the creation and evaluation of the function. The TEE mean gap in absolute value between the function and the three references was 7.0%, 16.4% and 2.7% in CC, and 17.0% and 23.7% according to Armband and Actiheart, respectively, in FLC. This is the first step in the definition of a new feedback mechanism that promotes self-management and daily-efficiency evaluation of physical activity as part of an information system dedicated to the prevention of chronic diseases.