The inclusive jet cross section for proton–proton collisions at a centre-of-mass energy of 7 $$\,\text {TeV}$$ was measured by the CMS Collaboration at the LHC with data corresponding to an integrated luminosity of 5.0 $$\,\text {fb}^{-1}$$ . The measurement covers a phase space up to 2 $$\,\text {TeV}$$ in jet transverse momentum and 2.5 in absolute jet rapidity. The statistical precision of these data leads to stringent constraints on the parton distribution functions of the proton. The data provide important input for the gluon density at high fractions of the proton momentum and for the strong coupling constant at large energy scales. Using predictions from perturbative quantum chromodynamics at next-to-leading order, complemented with electroweak corrections, the constraining power of these data is investigated and the strong coupling constant at the Z boson mass $$M_{\mathrm{Z}}$$ is determined to be $$\alpha _S(M_{\mathrm{Z}}) = 0.1185\pm 0.0019\,(\text {exp})^{+0.0060}_{-0.0037}\,\text {(theo)} $$ , which is in agreement with the world average.