The oxygen status of a tumor has significant clinical implications for treatment prognosis, with well-oxygenated subvolumes responding markedly better to radiotherapy than poorly supplied regions. Oxygen is essential for tumor growth, yet estimation of local oxygen distribution can be difficult to ascertain in situ, due to chaotic patterns of vasculature. It is possible to avoid this confounding influence by using avascular tumor models, such as tumor spheroids, a much better approximation of realistic tumor dynamics than monolayers, where oxygen supply can be described by diffusion alone. Similar to in situ tumours, spheroids exhibit an approximately sigmoidal growth curve, often approximated and fitted by logistic and Gompertzian sigmoid functions. These describe the basic rate of growth well, but do not offer an explicitly mechanistic explanation. This work examines the oxygen dynamics of spheroids and demonstrates that this growth can be derived mechanistically with cellular doubling time and oxygen consumption rate (OCR) being key parameters. The model is fitted to growth curves for a range of cell lines and derived values of OCR are validated using clinical measurement. Finally, we illustrate how changes in OCR due to gemcitabine treatment can be directly inferred using this model.