Abstract Using a data sample corresponding to an integrated luminosity of 2.0 $$\, \text {fb} ^{-1}$$ fb-1 , collected by the LHCb experiment, the production of the $${\eta _{c}} (1S)$$ ηc(1S) state in proton–proton collisions at a centre-of-mass energy of $$\sqrt{s} =13$$ s=13 $$\, \text {TeV}$$ TeV is studied in the rapidity range $$2.0< y < 4.5$$ 2.0<y<4.5 and in the transverse momentum range $$6.5< p_{\mathrm {T}} < 14.0 \, \text {GeV} $$ 6.5<pT<14.0GeV . The cross-section for prompt production of $${\eta _{c}} (1S)$$ ηc(1S) mesons relative to that of the $${J /\psi }$$ J/ψ meson is measured using the $$p $$ p $$\overline{{p}}$$ p¯ decay mode and is found to be $${\sigma _{{\eta _{c}} (1S)}/\sigma _{{{J /\psi }}} = 1.69 \pm 0.15 \pm 0.10 \pm 0.18}$$ σηc(1S)/σJ/ψ=1.69±0.15±0.10±0.18 . The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the $${{J /\psi }} \!\rightarrow {p} {\overline{{p}}} $$ J/ψ→pp¯ and $${\eta _{c}} \!\rightarrow {p} {\overline{{p}}} $$ ηc→pp¯ decays. The prompt $${\eta _{c}} (1S)$$ ηc(1S) production cross-section is determined to be $${\sigma _{{\eta _{c}} (1S)} = 1.26 \pm 0.11\pm 0.08\pm 0.14 \,\upmu \text {b}}$$ σηc(1S)=1.26±0.11±0.08±0.14μb , where the last uncertainty includes that on the $${J /\psi }$$ J/ψ meson cross-section. The ratio of the branching fractions of $$b $$ b -hadron decays to the $${\eta _{c}} (1S)$$ ηc(1S) and $${J /\psi }$$ J/ψ states is measured to be $${{\mathcal {B}} _{{b} \!\rightarrow {\eta _{c}} X}/{\mathcal {B}} _{{b} \!\rightarrow {{J /\psi }} X} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$$ Bb→ηcX/Bb→J/ψX=0.48±0.03±0.03±0.05 , where the last uncertainty is due to those on the branching fractions of the $${{J /\psi }} \!\rightarrow {p} {\overline{{p}}} $$ J/ψ→pp¯ and $${\eta _{c}} \!\rightarrow {p} {\overline{{p}}} $$ ηc→pp¯ decays. The difference between the $${J /\psi }$$ J/ψ and $${\eta _{c}} (1S)$$ ηc(1S) masses is also determined to be $$113.0 \pm 0.7 \pm 0.1 \, \text {MeV} $$ 113.0±0.7±0.1MeV , which is the most precise single measurement of this quantity to date.