Developments in the field of social robotics open interesting opportunities for applications in healthcare, education, and services. For this, studying engagement in humanrobot interaction (HRI) is crucial for improving the quality of interactive experiences. Questionnaires are powerful in describing voluntary behavior; however, engagement is often an implicit non-voluntary behavior that reaches awareness only once initiated. Inspired by research in cognitive psychology, we propose a behavioral feature to quantify engagement in HRI through the measurement of spontaneous movement and spectral wavelet analysis. For this, we conducted an experiment during which participants listened to sad stories narrated by a moving social robot. Throughout the experiment, we tracked the participants’ spontaneous and non-voluntary sway movements with a motion capture system. The experiments were conducted with three robotic platforms (Buddy, Pepper, and Nao). Results showed that spontaneous body sway can be modulated by social robots within no-goal-oriented interaction. This opens up the application possibility of our methodology to various modes of HRI such as collaboration.