Abstract Analytical solutions for runoff caused by a moving rain storm of time-varying rain intensity from a complex drainage basin are derived assuming constant concentration times for the different systems within the basin. It is found that the runoff caused by a peaked rain intensity distribution is higher than that from a uniform distribution of the same mean intensity. It is also shown that the storm movement influences the runoff peak, especially in elongated basins. Correction factors for the non-uniform rain intensity distribution and for the storm movement are introduced allowing the rational formula to be used in its traditional way for the first design of a storm drainage system. The concept of effective kinematic time of concentration is introduced to be used in the rational formula.