The adsorption of Cd2+ and Co2+ using alginic acid (AA) was performed by density functional theory (DFT) calculations. To validate the theoretical findings, Cd2+ and Co2+ were extracted from aqueous solutions using brown algae, where AA constituted the major component. The study encompassed both experimental and theoretical aspects, addressing single and binary systems. Various parameters, including adsorption energy, thermodynamics, quantum chemical, natural bond orbital, quantum theory of atoms, electron-localization-function, non-covalent interaction, UV–vis, and restrained electrostatic potential (RESP), were calculated using a DFT-based method to assess the adsorption of heavy metals (Cd2+ and Co2+) onto AA in both single and binary systems. The DFT calculations confirmed higher Co2+ adsorption onto AA compared to Cd2+. Moreover, the determination of the charge distribution on the adsorbent atoms, accomplished through the RESP method, revealed that oxygen atoms within AA allocate more negative charge for Co2+ adsorption than Cd2+, signifying a stronger affinity for Co2+ than Cd2+. The computed adsorption energies were −25.40 and −9.32 kcal/mol for the Co2+-AA and Cd2+-AA complexes, respectively. AA, the predominant compound in brown algae, has been recognized for its significant capability in adsorbing heavy metals. To further verify the accuracy of the DFT calculations, batch adsorption processes of Co2+ and Cd2+ were conducted using brown algae. Isothermal and kinetic studies demonstrated higher Co2+ adsorption (single = 102.10 mg/g and binary = 85.20 mg/g) on brown algae than Cd2+ (single = 60.01 mg/g and binary = 41.12 mg/g). The close agreement between the DFT-based calculations and experimental data underscored the remarkable potential of AA in removing heavy metals. Furthermore, the RESP method exhibited excellent predictive ability for heavy metal adsorption in single and binary systems.