Abstract Deformation bands can influence fluid flow in sandstone hydrocarbon reservoirs and therefore, understanding the geometrical attributes of individual bands and their patterns is a critical step in quantifying their connectivity. We present a geometrical study of deformation band lozenges, which are rock volumes contained between deformation bands, and fault lenses, which are rock volumes bounded by slip surfaces in fault cores. We investigate the statistical trends among data sets for deformation band lozenges and fault lenses in sandstones from the Moray Firth (Scotland) and southeastern Utah (USA), and explore their potential correlation to other attributes of the fracture pattern and petrophysical properties. The aspect ratio of lozenges, that represents the ratio of length or height to the maximum thickness of a lozenge, displays an oblate-shaped geometry in relation to fault-zone orientation. The length–thickness scaling relationships of lozenges are statistically similar to lenses. The scaling relationships show a slope break between lozenges bounded by deformation bands and lenses bounded by slip surfaces in the fault core. This break is inferred to mark the boundary between the lozenge domain and lens domain, and is likely due to a deformation transition from distributed strain for deformation bands to localised strain for slip surfaces. Furthermore, the integration of geometrical analysis with an understanding of scaling properties can help to make better predictions of fractures and fault properties in subsurface reservoirs.