The structures and conformations of ortho-, meta-, and para-methyl red (MR) upon proton gain and loss were studied by density functional calculations, and compared to methyl yellow for the effects of a carboxyl substitution. Internal hydrogen bonding causes the geometry of neutral o-MR planar, otherwise twist. Monoprotonated species of MR are planar where the proton is attached to $eta$-azo nitrogen. This loses its azo character a bit, and shows strong delocalization characterized as a quinonoid canonical structure. Di-protonated species of MR is proved to hold two protons at the amino and $alpha$-azo nitrogen atoms, and planar. It regains somewhat of its azo character, but still shows fairly delocalized property in terms of carbocationic canonical structures. The carboxyl substitution on 4-dimethylamino-trans-azobenzene structure has some delocalization effects on the geometry or conformation of MR derivatives whether neutral, mono-, di- or de-protonated.