Abstract Turbidity currents are destructive flows that are hazardous to critical seafloor infrastructure on submarine slopes because run‐up heights can be 10–100s of meters, as their relative density is 2–3 orders of magnitude lower than terrestrial flows. Currently, risk analysis is hindered by poor prediction of run‐up heights that are mainly derived from confined 2D experiments, and/or numerical models, and are restricted to a specific configuration whereby the flow strikes topographic barriers orthogonally. Here, a new analytical model is presented, informed by and validated against physical experiments, which predicts run‐up heights for flows encountering three‐dimensional slopes as a function of any slope angle, and incidence angle, of the impinging turbidity current. This has important implications for reducing geohazards by informing routing and positioning of seafloor infrastructure, and for more accurately interpreting submarine landscapes and their deposits.

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