One of the most important features to model the total number of human travels is their dependence on the spatial density of both population and facility distribution. The parameter free radiation model utilizes these features and gives good origin-destination (OD) flow predictions at country level. But some extension is needed if we want to apply it to different scales and in diverse regions of the world. To achieve this we first show that the original radiation model can be derived using exponential survival function. Then we extend the model by using a more flexible Weibull survival function with one parameter α This extension predicts well the number of commuting trip OD flows. More importantly, the results show a clear functional relationship between α and the square root of the area L [km] by sampling randomly selected regions in the US with scales ranging from a few kilometers to the entire country. This makes the model applicable to regions where empirical OD matrices are not available for calibrating α. For regions even without population census data, we propose a cell phone user OD matrix expansion method to gain insights into these regions’ commuting flow characteristics and then apply it to three different countries: Rwanda, Dominican Republic, and Portugal. This study provides the first building blocks for a better understanding of human mobility and how it can be generalized in statistical laws tested in different countries.