Humans use carefully chosen step locations to restore their balance during locomotion and in response to perturbations. Understanding the relationship between foot placement and balance restoration is key to developing useful dynamic human balance diagnostic tests and balance rehabilitation treatments. The link between foot placement and balance restoration is studied in this paper using a simplified monopedal model that has a circular foot, coined the Euler pendulum. The Euler pendulum provides a convenient method of studying the stability properties of three-dimensional (3D) bipedal systems without the burden of large system equations typical of multibody systems. The Euler pendulum has unstable regions of its state-space that can be made to transition to a statically stable region using an appropriate foot placement location prior to contacting the ground. The planar foot placement estimator (FPE) method developed by Wight is extended in this work in order to find foot placement locations in 3D to balance the 3D Euler pendulum. Preliminary experimental data shows that the 3D foot placement estimator (3DFPE) location corresponds very well with human foot placement during walking, gait termination, and when landing from a jump. In addition, a sensitivity analysis revealed that the assumptions of the 3DFPE are reasonable for human movement. Metrics for bipedal instability and balance performance suggested in this work could be of practical significance for health care professionals.