We present a novel technique that unobtrusively estimates forces exerted by human participants in multicontact interaction with rigid environments. Our method uses motion capture only, thus circumventing the need to set up cumbersome force transducers at all potential contacts between the human body and the environment. This problem is particularly challenging, as the knowledge of a given motion only characterizes the resultant force, which can generally be caused by an infinity of force distributions over individual contacts. We collect and release a large-scale dataset on how humans instinctively regulate interaction forces on diverse multicontact tasks and motions. The force estimation framework we propose leverages physics-based optimization and neural networks to reconstruct force distributions that are physically realistic and compatible with real interaction force patterns. We show the effectiveness of our approach on various locomotion and multicontact scenarios.