Abstract Two coumarin derivatives, namely, 3-(3-benzyl-4-hydroxy-2-thioxo-3,4-dihydro-2H-1,3-thiazin-6-yl)-8-methoxy-2H-chromen-2-one (BTMC) and 3-(3-benzyl-4-hydroxy-2 thioxo-3,4-dihydro-2H-1,3-thiazin-6-yl)-2H-chromen-2-one (BTC) were synthesized, characterized and applied as potential corrosion inhibitors for mild steel (MS) in molar hydrochloric acid (1M HCl). Different techniques including Potentiodynamic Polarization (PDP), Electrochemical Impedance Spectroscopy (EIS) and weight loss (WL) measurements were applied in order to prove the inhibition potential of BTMC and BTC against mild steel corrosion. PDP investigation suggests the mixed mode of inhibition by the studied coumarin derivatives. These compounds prevented the metal from corrosive attack of chloride anions (Cl−) by getting adsorbed on the metal surface following Langmuir isotherm adsorption model. The change in surface morphology was studied by Scanning Electron Microscopy (SEM) and Electron Dispersion Spectroscopy (EDS). Organic molecules formed a non-crystalline protective layer on the metal surface which was confirmed from X-ray Diffraction Analysis (XRD).The corrosive solution applied for descaling or acid pickling process dissolved the metal surface, until the inhibitor was not applied. The UV–Vis spectrum confirms the formation of a complex between the inhibitor and the iron cations present in the electrolytic medium. WL measurement revealed that BTMC and BTC exhibit a high inhibition efficiency (IE%) of 93.59% and 92.17% for BTMC and BTC, respectively, in their optimum concentration (300 ppm) at 298 K. Density Functional Theory (DFT) calculations and Monte Carlo (MC) simulations were employed to envisage the interactions of synthesized inhibitors with metal surface along with corrosive species as it happens in corrosive environment. In addition, The Fukui function and local softness indices were computed for the determination of the most plausible nucleophilic and electrophilic attack sites.