Fermentation Scale-Up Calculator

Constant tip speed divides lab RPM by the linear scale factor so impeller-tip velocity (π × D × N) stays the same at both scales — the gentler option, generally preferred for shear-sensitive mammalian or insect cell cultures. Constant P/V instead scales RPM by the impeller diameter ratio raised to the 2/3 power to hold power input per unit volume constant, which is usually favored when oxygen transfer and mixing time matter more than protecting cells from shear, such as in many microbial fermentations.

The calculator assumes geometric similarity — the production vessel and impeller keep the same proportions as the lab vessel, just larger. Since volume scales with the cube of linear dimension, the linear scale factor is the volume ratio raised to the 1/3 power, and multiplying the lab impeller diameter by that factor gives a production impeller that preserves the same aspect ratio.

Power input in the turbulent regime follows P ∝ N³D⁵, so the calculator raises the RPM ratio to the third power and the impeller diameter ratio to the fifth power and multiplies them together. Because both RPM and diameter change between scales, and each is raised to a high exponent, total power draw at production scale typically grows far faster than the volume itself — a key reason large fermentors need proportionally much bigger motors.

The calculator computes it as (prodRpm × prodDiam²) ÷ (labRpm × labDiam²), which — assuming the same fluid properties at both scales — is proportional to the ratio of actual Reynolds numbers. A ratio far from 1 signals that the mixing regime (how turbulent the flow is) differs meaningfully between lab and production scale, which is a known limitation of geometric similarity scale-up since it's generally impossible to hold Reynolds number, tip speed, and P/V all constant simultaneously.