A measurement of the energy density in proton–proton collisions at a centre-of-mass energy of $\sqrt{s} =13$ $,\text {TeV}$ is presented. The data have been recorded with the CMS experiment at the LHC during low luminosity operations in 2015. The energy density is studied as a function of pseudorapidity in the ranges $-,6.6<\eta <-,5.2$ and $3.15<|\eta |<5.20$ . The results are compared with the predictions of several models. All the models considered suggest a different shape of the pseudorapidity dependence compared to that observed in the data. A comparison with LHC proton–proton collision data at $\sqrt{s} =0.9$ and $7,\text {TeV} $ confirms the compatibility of the data with the hypothesis of limiting fragmentation.