Measurement of Energy Correlators inside Jets and Determination of the Strong Coupling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>Z</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>

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 TeV proton-proton collisions collected by the CMS experiment and corresponding to an integrated luminosity of 36.3 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: α_{S}(m_{Z})=0.1229_{-0.0050}^{+0.0040}, the most precise α_{S}(m_{Z}) value obtained using jet substructure observables.