The dependence of inclusive jet production in proton-proton collisions with a center-of-mass energy of 13 TeV on the distance parameter R of the anti-kT algorithm is studied using data corresponding to integrated luminosities up to 35.9 fb−1 collected by the CMS experiment in 2016. The ratios of the inclusive cross sections as functions of transverse momentum pT and rapidity y, for R in the range 0.1 to 1.2 to those using R = 0.4 are presented in the region 84 < pT< 1588 GeV and |y|< 2.0. The results are compared to calculations at leading and next-to-leading order in the strong coupling constant using different parton shower models. The variation of the ratio of cross sections with R is well described by calculations including a parton shower model, but not by a leading-order quantum chromodynamics calculation including nonperturbative effects. The agreement between the data and the theoretical predictions for the ratios of cross sections is significantly improved when next-to-leading order calculations with nonperturbative effects are used. [Figure not available: see fulltext.].