An illustrative example embodiment of a system for detecting drift of a building includes a detector that detects at least one horizontal position of elevator roping within a hoistway in or on the building at a selected vertical location. A processor determines at least one characteristic of drift of the building based on information from the detector regarding the detected at least one horizontal position, information regarding tension on the elevator roping, information regarding a density of the elevator roping, and a relationship between the selected vertical location and a length of the elevator roping.