Energy correlators that describe energy-weighted distances between two or three particles in a hadronic jet are measured using an event sample of$\sqrt{s}=13\mathrm{TeV}$proton-proton collisions collected by the CMS experiment and corresponding to an integrated luminosity of$36.3{\mathrm{fb}}^{-1}$. The measured distributions are consistent with the trends in the simulation that reveal two key features of the strong interaction: confinement and asymptotic freedom. By comparing the ratio of the measured three- and two-particle energy correlator distributions with theoretical calculations that resum collinear emissions at approximate next-to-next-to-leading-logarithmic accuracy matched to a next-to-leading-order calculation, the strong coupling is determined at the$Z$boson mass:${\alpha }_S(m_Z)=0.1229_{-0.0050}^{+0.0040}$, the most precise${\alpha }_S(m_Z)$value obtained using jet substructure observables.