Ring strain energies (SEs) and enthalpies of hydrogenation (Delta H-hyd) of a series of E- and Z-alkenes, cyclic alkynes and allenes (C-5-C-9) are computed at the G3 level of theory. The SE for cycloheptyne, cyclohexyne, and cyclopentyne are calculated to be 25.4, 40.1, and 48.4 kcal/mol, respectively. The SE for E-cycloheptene and E-cyclohexene are calculated to be 25.2 and 49.3 kcal/mol (G3). The SE of cyclooctyne is 2.0 kcal/mol greater than that of E-cyclooctene (17.9 kcal/mol) but only 7.7 kcal/mol greater than that of cyclooctane. The SE of 3,3-difluorocyclooctyne (DIFO) is predicted to be slightly reduced (Delta SE = 2.6 kcal/mol) relative to the parent cyclooctyne to 17.3 kcal/mol. The SE and Delta H-hyd are correlated with activation barriers for the [3 + 2] cycloaddition of a series of azides to E- and Z-cycloalkenes and alkynes at the G3 level of theory. The energy barrier for the cycloaddition of methyl azide to cyclooctyne is 9.2 kcal/mol lower than addition to 4-octyne and 3.1 kcal/mol lower for reaction with E-cyclooctene. The activation energies for [3 + 2] cycloaddition of benzyl azide and acetamido azide (2HN(C=O)CH2-N-3) to DIFO are 2.3 and 5.3 kcal/mol lower in energy than cycloaddition to cyclooctyne [B3LYP/6-311+G(3df,2p)].