Purpose We present a methodology to automatically detect falls on stairs, an application of computer vision and machine learning techniques with major real-world importance. Falls on the stairs, in particular, are a common cause of injury among older adults. Comprehending the conditions under which accidents take place could significantly aid in the prevention of falls, support independent living, and improve quality of life. Methods We extract a set of features, composed of Fourier coefficients and entropy metrics of instantaneous velocities from 3D motion sensor data, to encode lower body motion during stair navigation. A supervised learning algorithm is then trained on manually annotated data simulated in a home laboratory. Results In our empirical analysis, the algorithm obtains high fall detection accuracy (> 92%) and a low false positive rate (5-7%). In contrast with previous research, we identify that motion of the hips, rather than that of the feet, is the best indicator of dangerous activity given the 3D trajectory of various lower body joints. It is also shown that entropy measures alone provide sufficient information to detect abnormal events on stairs. Conclusions The study of falls is difficult due to their exceedingly sparse nature; but an automatic non-contact fall detection system can assist in data collection by sieving through large quantities of data, e.g., from public stairways.