A Quantitative Structure-Activity Relationship (QSAR) of coumarins by genetic algorithms employing physicochemical, topological, lipophilic and electronic descriptors was performed. We have used experimental antioxidant activities of specific coumarin derivatives against the DPPH· radical molecule. Molecular descriptors such as Randic Path/Walk, hydrophilic factor and chemical hardness were selected to propose a mathematical model. We obtained a linear correlation with R2 = 96.65 and Q
LOO2 = 93.14 values. The evaluation of the predictive ability of the model was performed by applying the Q
ASYM2, $\hat r^2 $ and Δr
m2 methods. Fukui functions were calculated here for coumarin derivatives in order to delve into the mechanics by which they work as primary antioxidants. We also investigated xanthine oxidase inhibition with these coumarins by molecular docking. Our results show that hydrophobic, electrostatic and hydrogen bond interactions are crucial in the inhibition of xanthine oxidase by coumarins.