A measurement of the inclusive top-pair production cross-section (σ) with a data sample of 78 pb−1 of proton-proton collisions at a centre-of-mass energy of 13 TeV, collected in 2015 by the ATLAS detector, using tt events with an opposite-sign electron-muon pair in the final state is presented. Jets containing b-quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b-tagged jets were counted and used to determine simultaneously σ and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be:
σ=825±49 (stat)±60(syst)±83(lumi) pb,
where the three uncertainties arise from data statistics, experimental and theoretical systematic effects, and the integrated luminosity, giving a total relative uncertainty of 14%. The result is consistent with recent theoretical QCD calculations at next-to-next-to-leading order.