We perform a phenomenological study ofZplus jet, Higgs plus jet and di-jet production atthe Large Hadron Collider. We investigate in particular the dependence of the leading jet crosssection on the jet radius as a function of the jet transverse momentum. Theoretical predictionsare obtained using perturbative QCD calculations at the next-to and next-to-next-to-leading order,using a range of renormalization and factorization scales. The fixed order predictions are comparedto results obtained from matching next-to-leading order calculations to parton showers. A studyof the scale dependence as a function of the jet radius is used to provide a better estimate of thescale uncertainty for small jet sizes. The non-perturbative corrections as a function of jet radius areestimated from different generators.