Aircraft trajectory prediction is a feature at the core of most Air Traffic Management (ATM) applications. This process is strongly affected by stochastic sources that impact the accuracy of the predictions. The work presented hereafter focuses on application of the Polynomial Chaos theory to the quantification of the estimated time of arrival at designated waypoints throughout the trajectory. This methodology returns very accurate polynomial representations of trajectory uncertainties with very low computational requirements. This highly efficient approach enables the capability of quantifying the trajectory prediction uncertainties of a real traffic sample (i.e., thousands of flights) within seconds, which is fully compliant with the requirements of future advanced automation tools envisioned in future Trajectory Based Operations (TBO) environment. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.