The prescribed dose in radiation therapy has to be converted into machine monitor units for patient treatment. This is done routinely for each spread-out Bragg peak (SOBP) field either by calibration measurements, by using analytical algorithms or by relying on empirical data. At the Northeast Proton Therapy Center, a monitor unit corresponds to a fixed amount of charge collected in a segmented transmission ionization chamber inside the treatment head. The goal of this work was to use a detailed Monte Carlo model of the treatment head to calculate the dose delivered to the patient as a function of ionization chamber reading, i.e. to yield absolute dose in patients in terms of machine monitor units. The results show excellent agreement with measurements. For 50 SOBP fields considered in this study, the mean absolute difference between the experimental and the calculated value is 1.5%, where approximately 50% of the fields agree within 1%. This is within the uncertainties of the data. The Monte Carlo method has advantages over analytical algorithms because it takes into account scattered and secondary radiation, does not rely on empirical parameters, and provides a tool to study the influence of parts of the treatment head on the ionization chamber reading. Compared to experimental methods the Monte Carlo method has the advantage of being able to verify the dose in the patient geometry.