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Abstract Equilibrium geometry of single‐thread rivers with fixed width (engineered rivers) is determined with a flow resistance relation and a sediment transport relation, if characteristic discharge, sediment caliber and supply are specified. In self‐formed channels, however, channel width is not imposed, and one more relation is needed to predict equilibrium geometry. Specifying this relation remains an open problem. Here we present a new model that brings together a coherent train of research progress over 35 years to predict equilibrium geometry of single‐thread rivers from the conservation of channel and floodplain material. Predicted channel geometries are comparable with field observations. In response to increasing floodplain width, sand load and grain size, the equilibrium slope increases, bankfull depth and width decrease. As the volume fraction content of mud in the sediment load increases, bankfull width‐to‐depth ratio and slope decrease suggesting that mud load has a strong control on channel patterns and bankfull geometry.