Currently, there is an increasing clinical demand for bone implants for several orthopedic and maxillofacial surgical procedures. Meeting these demands can be achieved with stem cells differentiated in vitro toward the osteogenic lineage to produce cells suitable for implantation in critical size bone defects. Toward this end, we present a population balance model (PBM) of the osteogenic differentiation of umbilical cord mesenchymal stem cells. Our experimental-modeling approach describes osteogenesis with a dynamic cell PBM incorporating the expression of key osteogenic genes and the activity of metabolic pathways involved in osteogenesis. In addition to accurately capturing the phenotypic heterogeneity of osteogenic differentiation, the model also predicts a delay for the onset of differentiation when the cells grow faster, thus a trade-off between proliferation and differentiation over the course of in vitro osteoinduction. The mathematical model from this work sets a solid foundation for future model-based culture or reactor optimization.