This study assesses the risk of parametric roll in large container ships and examines the feasibility of applying a cloud-based ship safety operation service based on that assessment. Actual accident cases were analyzed to confirm the potentially severe consequences of parametric roll. We then derived approximate probabilities of occurrence by analyzing the relationship between the vessel’s natural roll frequency and the wave encounter frequency. To evaluate the accuracy of these approximate calculations, the results were validated against previously reported Computational Fluid Dynamics (CFD) simulations and additional CFD simulations performed for the KRISO Container Ship (KCS) hull form. For risk assessment, we propose four indices: (1) Roll Motion Amplification Index (RMAI), (2) Probability of Occurrence (PI), (3) Exceedance Probability (P_exceed) relative to safety limits, and (4) an integrated Risk Level Index (RLI). In particular, RMAI is referenced to the ±25° safety limit specified in the International Maritime Organization (IMO)’s second-generation intact stability guidance. Based on these metrics, we propose a method to compare live ship environmental data with a CFD result database in the cloud to evaluate parametric-roll risk in real time. The proposed service architecture comprises three layers - data collection, risk analysis, and user service - enabling operators to monitor parametric-roll risk intuitively via a dashboard and alarm system. Finally, we discuss how integrating the proposed framework with Artificial Intelligence (AI)-based predictive analysis could extend the functionality and practical utility of cloud-based safe-navigation services.