With the aim of decreasing the corrosion of metal specimens, two polyesters, namely 4-(1-(4-methoxyphenyl)cyclohexyl)phenyl 3-oxobutanoate (MPOB) and 4-(1-(4-methoxyphenyl)cyclohexyl)phenyl 10-oxoundecanoate (MPOU), were synthesized and utilized as corrosion inhibitors. The synthesized polyesters were characterized by Fourier-transform infrared (FT-IR) and nuclear magnetic resonance spectral analyses, followed by thermogravimetric and differential scanning calorimetry analyses. The protective effect of the polyesters on mild-steel specimens in 0.5 M H2SO4 medium was evaluated by nonelectrochemical and electrochemical methods. Gravimetric measurements revealed a decreased corrosion rate with increasing concentration of the inhibitors, reaching a maximum inhibition efficiency of 79.88% for MPOB and 92.98% for MPOU at 1000 ppm concentration at room temperature. The obtained experimental data were best fit by the Langmuir adsorption isotherm, suggesting monolayer adsorption. Thermodynamic parameters supported a physisorption mechanism. Electrochemical impedance spectroscopy showed increased charge-transfer resistance (Rct), in turn decreasing the double-layer capacitance and thereby favoring good inhibition of corrosion of mild steel. Mixed-type inhibition was revealed by potentiodynamic polarization analysis, suppressing anodic metal dissolution and cathodic hydrogen evolution. The mode of adsorption of the inhibitors on the mild-steel surface was additionally evaluated by morphological study using FT-IR and atomic force microscopy (AFM) analyses. © 2019, Springer Nature B.V.