Clinical research on the deposition of inhaled substances (e.g. inhaled medications, airborne contaminants, fumes) in the lungs necessitates anatomical models of the airways. Current conducting airway models lack three‐dimensional (3D) reality as little information is available in the literature on the distribution of the airways in space. This is a limitation to the assessment or predictions of the particle deposition in relation to the subject’s anatomy. Detailed information on the full topology and morphology of the airways is thus required to model the airway tree realistically. This paper presents the length, diameter, gravity, coronal and sagittal angles that together describe completely the airways in 3D space. The angle at which the airways branch out from their parent (branching angle) and the rotation angle between successive bifurcation planes are also included. These data are from the study of two sets of airways computed tomography (CT) images. One CT scan was performed on a human tracheobronchial tree cast and the other on a healthy male volunteer. The airways in the first nine generations of the cast and in the first six conducting generations of the volunteer were measured using a computer‐based algorithm. The data contribute to the knowledge of the lung anatomy. In particular, the spatial structure of the airways is shown to be strongly defined by the central airways with clear angular lobar patterns. Such patterns tend to disappear with a mean gravity, coronal and sagittal angles of 90° in each generation higher than 13–15. The mean branching angle per generation appears independent of the lobe to which the airways belong. Non‐planar geometry at bifurcation is observed with the mean (± SD) bifurcation plane rotation angle of 79 ± 41° (n = 229). This angle appears constant over the generations studied. The data are useful for improving the 3D realism of the conducting airway structure modelling as well as for studying aerosol deposition, flow and biological significance of non‐planar airway trees using analytical and computational flow dynamics modelling.