Antioxidants are an important component of our ability to combat free radicals, an excess of which leads to oxidative stress that is related to aging and numerous human diseases. Oxidative damage also shortens the shelf-life of foods and other commodities. Understanding the structure–activity relationship of antioxidants and their mechanisms of action is important for designing more potent antioxidants for potential use as therapeutic agents as well as preservatives. We report the first computational study on the electronic effects of ortho-substituents in dendritic tri-phenolic antioxidants, comprising a common phenol moiety and two other phenol units with electron-donating or electron-withdrawing substituents. Among the three proposed antioxidant mechanisms, sequential proton loss electron transfer (SPLET) was found to be the preferred mechanism in methanol for the dendritic antioxidants based on calculations using Gaussian 16. We then computed the total enthalpy values by cumulatively running SPLET for all three rings to estimate electronic effects of substituents on overall antioxidant activity of each dendritic antioxidant and establish their structure–activity relationships. Our results show that the electron-donating o-OCH₃ group has a beneficial effect while the electron-withdrawing o-NO₂ group has a negative effect on the antioxidant activity of the dendritic antioxidant. The o-Br and o-Cl groups did not show any appreciable effects. These results indicate that electron-donating groups such as o-methoxy are useful for designing potent dendritic antioxidants while the nitro and halogens do not add value to the radical scavenging antioxidant activity. We also found that the half-maximal inhibitory concentration (IC50) values of 2,2-diphenyl-1-picrylhydrazyl (DPPH) better correlate with the second step (electron transfer enthalpy, ETE) than the first step (proton affinity, PA) of the SPLET mechanism, implying that ETE is the better measure for estimating overall radical scavenging antioxidant activities.