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Turbulent flows over rough surfaces can be encountered in a wide range of engineering applications. Despite the progress made after several decades of studies, the prediction of drag and roughness function from the surface geometrical parameters remains an open question. Several methods have shown encouraging results. However, they lack generality and present some scatter in the data. In this paper we propose a new parameter, the effective distribution ($$ED$$), which lays foundation on the effective slope with some changes to take into account the sheltering effect of large roughness elements and the drag induced by pinnacles higher than the average roughness elements. To develop this new correlation between geometrical features of the wall and the drag, we performed a set of simulations of the turbulent flow over a rough surface made of triangular elements varying their height and spatial distribution. The$$ED$$correlates quite well both with the drag and the roughness function for a wide range of cases having different mean roughness height, skewness and kurtosis. To further validate the$$ED$$, and assessing how it can be generalized to real rough wall, an irregular wall made from the superposition of random sinusoidal function was considered. Results were consistent with the correlation here presented.