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Low energy buildings are usually characterized by a very well insulated building envelope and an efficient ventilation system that makes use of the heat in the exhaust air. Internal heat gains from residents and their use of appliances can cover the heating demand to a certain extent. The magnitude of internal heat gains that cover demand are often modelled in a simplified way and thus can be associated with a large uncertainty. Hourly measurements of household electricity use in over 1000 apartments over a year, serves as a foundation for this study. These measurements show a large variation between households with regard to the annual electricity-use. Furthermore, each measurement series representing the unique behaviour in an apartment, shows a variation in household electricity use over time. Through Monte Carlo simulations that use the measurements as stochastic input, this study shows that heating energy demand can vary by up to 50% due to the different habits of residents in a building. This study also shows that the detail at which internal heat gains are modelled is not negligible regarding relative impact on energy and power demands for low-energy buildings. Reducing the resolution of the measurements from hourly to monthly means neglects important variations in the data, which in turn underestimates the heating power-demand.