<p>The outcomes of modern particle physics experiments, such as proton–proton collisions at the Large Hadron Collider at CERN (European Organization for Nuclear Research), depend crucially on the precise description of the scattering processes in terms of the fundamental forces. Among all the known forces that contribute, the limited understanding of the strong nuclear force is a key source of inaccuracy. At the fundamental level, the strong force is described by quantum chromodynamics, the theory of quarks and gluons. Their coupling, <i>α</i>_s, becomes weaker at high energies (asymptotic freedom), enabling power series expansions in <i>α</i>_s, but the confinement of quarks in hadronic bound states usually requires additional model assumptions. Consequently, determinations of <i>α</i>_s from experiment mostly remain with large systematic theory errors^{<CitationRef CitationID="CR1">1</CitationRef>,<CitationRef CitationID="CR2">2</CitationRef>}. Here we report the model-free determination of <i>α</i>_s with unprecedented precision from low-energy experimental input combined with large-scale numerical simulations of the first-principles formulation of quantum chromodynamics on a space–time lattice. The uncertainty, about half that of all other results combined^{<CitationRef CitationID="CR3">3</CitationRef>}, originates predominantly from the statistical Monte Carlo evaluation and has a clear probabilistic interpretation. The result for <i>α</i>_s describes both low-energy hadronic physics with the help of lattice quantum chromodynamics and high-energy scattering using the perturbative expansion. By removing a source of theoretical uncertainty, our estimate of <i>α</i>_s could enable markedly improved analyses of many high-energy experiments^{<CitationRef CitationID="CR4">4</CitationRef>}. This will contribute to the likelihood that small effects of yet unknown physics are uncovered, as well as enable stringent precision tests of the Standard Model.</p>