Physical activity (PA) is a main determinant of total energy expenditure (TEE) and has been suggested to play a key role in body weight regulation. However, thus far it has been challenging to determine what part of the expended energy is due to activity in freely moving subjects. We developed a computational method to estimate activity related energy expenditure (AEE) and resting metabolic rate (RMR) in mice from activity and indirect calorimetry data. The method is based on penalised spline regression and takes the time dependency of the RMR into account. In addition, estimates of AEE and RMR are corrected for the regression dilution bias that results from inaccurate PA measurements. We evaluated the performance of our method based on 500 simulated metabolic chamber datasets and compared it to that of conventional methods. It was found that for a sample time of 10 minutes the penalised spline model estimated the time-dependent RMR with 1.7 times higher accuracy than the Kalman filter and with 2.7 times higher accuracy than linear regression. We assessed the applicability of our method on experimental data in a case study involving high fat diet fed male and female C57Bl/6J mice. We found that TEE in male mice was higher due to a difference in RMR while AEE levels were similar in both groups, even though female mice were more active. Interestingly, the higher activity did not result in a difference in AEE because female mice had a lower caloric cost of activity, which was likely due to their lower body weight. In conclusion, TEE decomposition by means of penalised spline regression provides robust estimates of the time-dependent AEE and RMR and can be applied to data generated with generic metabolic chamber and indirect calorimetry set-ups.