How much does public capital matter for economic growth? How large should it be? This paper attempts to answer these questions, taking the case of Sub-Saharan African (SSA) countries. It develops and estimates a model that posits a non-linear relationship between public investment and growth, to determine the growth-maximizing public investment GDP share. It empirically also accounts for the crowding-in and crowding-out effects between public and private investment, with equations estimated separately and simultaneously, using System GMM. The paper further runs a simulation and examines the public investment GDP share that maximizes consumption. This is estimated to be between 8.4 percent and 11 percent. The results from estimating the growth model are in the middle of this range, which is larger than the observed value of 7.2 percent at the end of the sample period. These outcomes suggest that, on average, there has been public under-investment in Africa, contrary to previous findings.