The inclusive jet cross-section has been measured in proton–proton collisions at s√=2.76 TeV in a dataset corresponding to an integrated luminosity of 0.20 pb−1 collected with the ATLAS detector at the Large Hadron Collider in 2011. Jets are identified using the anti-k t algorithm with two radius parameters of 0.4 and 0.6. The inclusive jet double-differential cross-section is presented as a function of the jet transverse momentum p T and jet rapidity y, covering a range of 20≤p T<430 GeV and |y|<4.4. The ratio of the cross-section to the inclusive jet cross-section measurement at s√=7 TeV , published by the ATLAS Collaboration, is calculated as a function of both transverse momentum and the dimensionless quantity xT=2pT/s√ , in bins of jet rapidity. The systematic uncertainties on the ratios are significantly reduced due to the cancellation of correlated uncertainties in the two measurements. Results are compared to the prediction from next-to-leading order perturbative QCD calculations corrected for non-perturbative effects, and next-to-leading order Monte Carlo simulation. Furthermore, the ATLAS jet cross-section measurements at s√=2.76 TeV and s√=7 TeV are analysed within a framework of next-to-leading order perturbative QCD calculations to determine parton distribution functions of the proton, taking into account the correlations between the measurements.