Background Slow degradation of synthetic plastics represents a high environmental hazard; therefore, there is an essential requirement to substitute them with eco-friendly products. Polyhydroxybutyrate (PHB) is a biodegradable biopolymer and also has several industrial, agricultural, and medical applications. Scaling up the production of PHB is still a problem due to the numerous parameters tangled in the fermentation processes. Objective The present work seeks to scale up polyhydroxybutyrate production by Bacillus aryabhattai MH997667.1 from shaken flasks to a 5L-bench top bioreactor with previously optimized media by applying a batch fermentation strategy. Materials and methods Different agitation speeds (200, 250 and 300 rpm) were tested in a 5L-bench-top bioreactor with a working volume of 3L. A kinetic model (logistic and Luedeking–Piret) that describes the microbial biomass and polyhydroxybutyrate (PHB) production is used to expect the performance of batch fermentation of Bacillus aryabhattai MH997667.1. Results and conclusion The optimum PHB yield (2.32 g/l) was expressed at 250 rpm agitation after 28 hours of fermentation. The experimental data were also fitted with the logistic and Luedeking–Piret equations for growth and PHB formation, respectively. The mathematical model proposed for batch fermentation revealed that the simulated data showed a good fit with the experimental results obtained during the first 24 h of PHB production at 250 rpm, where the productivity was 0.095 g L−1h−1. Our data suggest that agitation speed had a significant effect on PHB production and the 250 rpm agitation speed is the optimum speed for PHB production using Bacillus aryabhattai MH997667.1 in batch fermentation.