In practice, rainfall–runoff relationships are achieved through a simply defined runoff coefficient concept that is widely used in many engineering hydrological designs in urban and rural areas. The simplicity of the method, with the sole requirement of runoff coefficient assessment, is the main attractiveness, in addition to its successful prediction of average runoff rates for a given rainfall record. Unfortunately, in the classical regression approach of the rainfall–runoff relationship, internal variabilities are not taken into consideration explicitly. The runoff coefficient is considered a constant value, and it is used without distinction of antecedent conditions for the calculation of runoff from the rainfall record. In this paper, various other uncertainty embedded versions of the runoff coefficient, and hence rainfall–runoff formulation, are presented in terms of statistics, probability, perturbation and, finally, fuzzy system modelling. It is concluded that the fuzzy logic approach yields the least relative error among the various alternative runoff calculation methods; therefore, it is recommended for use in future studies. The application of various alternatives is presented for two monthly rainfall-runoff records around Istanbul, Turkey. Copyright © 2005 John Wiley & Sons, Ltd.