The methylotrophic yeast Pichia pastoris is widely used as a microbial host for recombinant protein production. Bioreactor models for P. pastoris can inform understanding of cellular metabolism and can be used to optimize bioreactor operation. This article constructs an extensive macroscopic bioreactor model for P. pastoris which describes substrates, biomass, total protein, other medium components, and off-gas components. Species and elemental balances are introduced to describe uptake and evolution rates for medium components and off-gas components. Additionally, a pH model is constructed using an overall charge balance, acid/base equilibria, and activity coefficients to describe production of recombinant protein and precipitation of medium components. The extent of run-to-run variability is modeled by distributions of a subset of the model parameters, which are estimated using the maximum likelihood method. Model prediction from the extensive macroscopic bioreactor model well describes experimental data with different operating conditions. The probability distributions of the model predictions quantified from the parameter distribution are quantifiably consistent with the run-to-run variability observed in the experimental data. The uncertainty description in this macroscopic bioreactor model identifies the model parameters that have large variability and provides guidance as to which aspects of cellular metabolism should be the focus of additional experimental studies. The model for medium components with pH and precipitation can be used for improving chemically defined medium by minimizing the amount of components needed while meeting cellular requirements.