A bstract A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron–muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb − 1 at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 7 TeV and about 20 fb − 1 at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 8 TeV for each experiment. The combined cross-sections are determined to be 178 . 5 ± 4 . 7 pb at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 7 TeV and $$ {243.3}_{-5.9}^{+6.0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mn>243.3</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5.9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>6.0</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> pb at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 8 TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections is determined to be R 8 / 7 = 1 . 363 ± 0 . 032. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark pole mass (with the strong coupling fixed at 0.118) and the strong coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from the combined results by fitting a next-to-next-to-leading-order plus next-to-next-to-leading-log QCD prediction to the measurements. Using a version of the NNPDF3.1 PDF set containing no top-quark measurements, the results obtained are $$ {m}_t^{\textrm{pole}}={173.4}_{-2.0}^{+1.8} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>t</mml:mi> <mml:mtext>pole</mml:mtext> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>173.4</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.8</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> GeV and $$ {\alpha}_{\textrm{s}}\left({m}_Z\right)={0.1170}_{-0.0018}^{+0.0021} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mfenced> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>Z</mml:mi> </mml:msub> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>0.1170</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.0018</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0021</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> .