In the QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property-activity relationship) study physico-chemical property, lipophilicity is used, to predict bioactivity of the newly synthesized coumarin compounds. Lipophilicity is a property of a molecule which depends on and can be changed by modifications in molecular structure. The parameter of the lipophilicity, partition coefficient (log P), is commonly used in drug designing and it is a numeric characteristic of lipophilicity of the examined substance, potential drug. The synthesis of 4-arylaminocoumarins derivatives from 4-hydroxycoumarin, has been carried out. In this work we described the fragmental method of calculation of partition coefficient according to the Rekker's method, because the best correlation between calculated and experimental values log P was determined according to the Rekker model. 4-Arylaminocoumarin has negative value of log P, but substitution with alkyl or allyl groups on the position 3 increases lipofilicity. Introduction of methyl or ethyl group into position 3 increases lipofilicity, suggesting that by increasing the chain length the values of log P become higher. The influence of allyl substituent in position three increases lipophilicity similar to methyl group. The aryl supstitent decreases lipoflicity, but a general relationship among them could not be established. The results obtained in this study enable further synthesis of new coumarin derivatives and predict their biological activity and properties.