Ethyl 3-formyl-1H-indol-2-carboxylate (FIC) and 2-(4-methoxyphenyl)-2,4-dihydropyrrolo [3,4-b]indol-3-ol (MPI) were synthesized as indole derivatives. The chemical structures of FIC and MPI were established through analytical and spectroscopic techniques. The inhibitory impacts of FIC and MPI on mild steel (MS) in an acidic environment (0.5 M HSO) were investigated by employing methodologies including open circuit potential (OCP), electrochemical impedance spectroscopy (EIS), and potentiodynamic polarization (PDP). As the studied indole derivatives adsorbed on the surface of MS, they created a barrier to mass and charge movement, shielding the MS from dangerous ions. It was observed that the inhibitory efficiency (%EF) values increased with the molar concentration of indole derivatives (FIC and MPI). At all concentrations, the two indole derivatives being studied, FIC and MPI, had high efficiency values. The highest efficiencies at 90 ppm were 81.2% with MPI and 76.2% with FIC. The polarization curves also clearly showed that MPI and FIC function as mixed-type inhibitors. Additionally, this study used density functional theory (DFT) and molecular dynamics (MD) simulations to investigate how well the two indole derivatives prevented mild steel corrosion.