In this work the single and ternary removal of sulfonamides (sulfamethoxazole, sulfadiazine and sulfametazine) from water was investigated using granular activated carbon. The single adsorption mechanism was elucidated by obtaining the adsorption isotherms supported by computational calculations. The ternary adsorption was analyzed by using an experimental Box-Behnken type response surface design. The results showed that the total adsorption capacity of activated carbon duplicates in ternary systems compared to single systems. Besides, in both cases the activated carbon showed a greater affinity for removing sulfamethoxazole followed by sulfadiazine and sulfametazine, correspondingly. It was shown that hydrogen bonding interactions presented the highest adsorption energies followed by π-π interactions. From the design of experiments three statistically reliable mathematical models were proposed to estimate the adsorption capacity for each sulfonamide as a function of the solution pH, temperature and initial concentration. Finally, it was shown that sulfonamide ternary adsorption is an endothermic process and that the adsorption rate decreases as a result of partial blockage of the pores due to simultaneous adsorption.