The energy optimized structure of sodium 1,4-dihydroxy-9,10-anthraquinone-2-sulphonate (QS) was determined using computational methods. The interaction of it with cationic surfactant cetyltrimethylammonium bromide was investigated in aqueous solution at pH 7.4. The aspect of the affinity of such molecule to cationic surfactant micelle is important in determining its biological action. The binding constant, partition coefficient and the stoichiometry were determined for molecule-CTAB interaction. The study showed that the hydrophobic interaction plays a major role in binding of QS to CTAB micelles. Gibbs free energy for the binding and distribution of QS between the bulk aqueous medium and surfactant micelles were calculated. (C) 2018 Elsevier B.V. All rights reserved.