Every source of liquid pollutants lies somewhere on a watershed. Leachwaters derived from water percolating through solid waste deposits and liquid effluents from industry are diluted on their way down the river until they interact with man or particular environmental systems. This environmental dilution of potentially toxic effluents has to be estimated in assessing health and environmental risks. The problem for the risk assessor is to find an appropriate mathematical model. In this paper, the recent mathematical theory of fractal objects is used to demonstrate that, within certain limits, rivers of all lengths and their river basins are self‐similar. Simple general relations exist, therefore, between the length and drainage area of rivers both large and small. These relations and a few additional assumptions are then used to derive an improved set of models for estimating environmental dilution of some pollutant