The inclusive jet cross section is measured as a function of jet transverse momentum pT and rapidity y. The measurement is performed using proton-proton collision data at $$ \sqrt{s} $$= 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb−1. The jets are reconstructed with the anti-kT algorithm using a distance parameter of R = 0.4, within the rapidity interval |y| < 2, and across the kinematic range 0.06 < pT < 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling αS.