The 1,3-dipolar cycloaddition of cyclooctynes with azides, also called "copper-free click chemistry", is a bioorthogonal reaction with widespread applications in biological discovery. The kinetics of this reaction are of paramount importance for studies of dynamic processes, particularly in living subjects. Here we performed a systematic analysis of the effects of strain and electronics on the reactivity of cyclooctynes with azides through both experimental measurements and computational studies using a density functional theory (DFT) distortion/interaction transition state model. In particular, we focused on biarylazacyclooctynone (BARAC) because it reacts with azides faster than any other reported cyclooctyne and its modular synthesis facilitated rapid access to analogues. We found that substituents on BARAC's aryl rings can alter the calculated transition state interaction energy of the cycloaddition through electronic effects or the calculated distortion energy through steric effects. Experimental data confirmed that electronic perturbation of BARAC's aryl rings has a modest effect on reaction rate, whereas steric hindrance in the transition state can significantly retard the reaction. Drawing on these results, we analyzed the relationship between alkyne bond angles, which we determined using X-ray crystallography, and reactivity, quantified by experimental second-order rate constants, for a range of cyclooctynes. Our results suggest a correlation between decreased alkyne bond angle and increased cyclooctyne reactivity. Finally, we obtained structural and computational data that revealed the relationship between the conformation of BARAC's central lactam and compound reactivity. Collectively, these results indicate that the distortion/interaction model combined with bond angle analysis will enable predictions of cyclooctyne reactivity and the rational design of new reagents for copper-free click chemistry.