Lactic acid (LA) is a key product widely used in several industries and can be produced by aerobic microorganisms like the fungus Rhizopus oryzae NRRL 395. In this study, the effect of different oxygen transfer rates on the performance of R. oryzae was analyzed in a 3 L stirred tank bioreactor. Inoculum and sucrose initial concentrations were previously evaluated at the shake flask level in order to choose the initial culture conditions for the bioreactor trials. In bioreactor, evaluations showed a range of OTRmax between 0.13 and 0.28 kg m−3 h−1 and DOT of 72–83 %, in which were reached the best values of LA productivity (0.53 g L−1h−1), Yps (0.78–0.83 g g−1), and LA production (44 g L−1). Further, a dimensionless analysis determined that LA production is greater in Damköhler number (Da) ≈ 1 and effectiveness factor (ɳ) ≈ 0.14 conditions. Finally, these results were used in a comparative dimensionless analysis with other aerobic microbial systems reported in the literature. According to our knowledge, this is the first study in which the oxygen transfer/oxygen uptake relationships and their effects on R. oryzae are analyzed in-depth.