Data on the number of floors is required for several applications, for instance, energy demand estimation, population estimation, and flood response plans. Despite this, open data on the number of floors is very rare, even when a 3D city model is available. In practice, it is most often inferred with a geometric method: elevation data is used to estimate the height of a building, which is divided by an assumed storey height and rounded. However, as we demonstrate in this paper with a large dataset of residential buildings, this method is unreliable: <70% of the buildings have a correct estimate. We demonstrate that other attributes and characteristics of buildings can help us better predict the number of floors. We propose several indicators (e.g. construction year, cadastral attributes, building geometry, and neighbourhood census data), and we present a predictive model that was trained with 172,000 buildings in the Netherlands. Our model achieves an accuracy of 94.5% for residential buildings with five floors or less, which is an improvement of about 25% over the geometric approach. Above five floors, our model has only a slight improvement on the geometric approach (5%). The main culprit is the lack of training data for tall buildings, which is uncommon in the Netherlands.