To quantify the dose calculation error and resulting optimization uncertainty caused by performing inverse treatment planning on inaccurate electron density data (pseudo-CT) as needed for adaptive radiotherapy and Magnetic Resonance Imaging (MRI) based treatment planning. Planning Computer Tomography (CT) data from 10 cervix cancer patients was used to generate 4 pseudo-CT data sets. Each pseudo-CT was created based on an available method of assigning electron density to an anatomic image. An inversely modulated radiotherapy (IMRT) plan was developed on each planning CT. The dose calculation error caused by each pseudo-CT data set was quantified by comparing the dose calculated each pseudo-CT data set with that calculated on the original planning CT for the same IMRT plan. The optimization uncertainty introduced by the dose calculation error was quantified by re-optimizing the same optimization parameters on each pseudo-CT data set and comparing against the original planning CT. Dose differences were quantified by assessing the Equivalent Uniform Dose (EUD) for targets and relevant organs at risk. Across all pseudo-CT data sets and all organs, the absolute mean dose calculation error was 0.2 Gy, and was within 2 % of the prescription dose in 98.5 % of cases. Then absolute mean optimisation error was 0.3 Gy EUD, indicating that that inverse optimisation is impacted by the dose calculation error. However, the additional uncertainty introduced to plan optimisation is small compared the sources of variation which already exist. Use of inaccurate electron density data for inverse treatment planning results in a dose calculation error, which in turn introduces additional uncertainty into the plan optimization process. In this study, we showed that both of these effects are clinically acceptable for cervix cancer patients using four different pseudo-CT data sets. Dose calculation and inverse optimization on pseudo-CT is feasible for this patient cohort.