Accurately predicting contact between our bodies and environmental objects is paramount to our evolutionary survival. It has been hypothesized that multisensory neurons responding both to touch on the body, and to auditory or visual stimuli occurring near them-thus delineating our peripersonal space (PPS)-may be a critical player in this computation. However, we lack a normative account (i.e., a model specifying how we ought to compute) linking impact prediction and PPS encoding. Here, we leverage Bayesian Decision Theory to develop such a model and show that it recapitulates many of the characteristics of PPS. Namely, a normative model of impact prediction (i) delineates a graded boundary between near and far space, (ii) demonstrates an enlargement of PPS as the speed of incoming stimuli increases, (iii) shows stronger contact prediction for looming than receding stimuli-but critically is still present for receding stimuli when observation uncertainty is non-zero-, (iv) scales with the value we attribute to environmental objects, and finally (v) can account for the differing sizes of PPS for different body parts. Together, these modeling results support the conjecture that PPS reflects the computation of impact prediction, and make a number of testable predictions for future empirical studies.