This paper focuses on the application of a novel mathematical limit approach derived for K/S values in reactive dyeing of cotton fabrics. The relation obtained from Kubelka-Munk equation is used because the Kubelka-Munk equation is the basic relationship among fabric reflectance, fabric dye content and dyestuff characteristics. The limit approach derived in a former paper is applied to the laboratory dyeings and the dyeing behavior of some reactive dyes on cotton knitted fabric has been obtained. The results of the laboratory experiments are discussed using the new mathematical approach. When the actual K/S values obtained from the dyeings and the calculated K/S values derived by the limit approach are considered independently, it is observed that the limit relation is val id for low dye concentration applications. When the K/S values are calculated taking the K/S value of the initial dyeing concentration $(0.1;\%;owf)$ as the starting concentration by applying the result of the derived limit approach, the calculated K/S values fit with the ones obtained in actual dyeings. It is concluded that the novel approach presented in the paper can be used in calculating the K/S values when the initial dyeings at low dye concentrations are carefully carried out.