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The measurement of the luminosity recorded by the CMS detector installed atLHC interaction point 5, using proton-proton collisions at $\sqrt{s} =$ 13 TeVin 2015 and 2016, is reported. The absolute luminosity scale is measured forindividual bunch crossings using beam-separation scans (the van der Meermethod), with a relative precision of 1.3% and 1.0% in 2015 and 2016,respectively. The dominant sources of uncertainty are related to residualdifferences between the measured beam positions and the ones provided by theoperational settings of the LHC magnets, the factorizability of the protonbunch spatial density functions in the coordinates transverse to the beamdirection, and the modeling of the effect of electromagnetic interactions amongprotons in the colliding bunches. When applying the van der Meer calibration tothe entire run periods, the integrated luminosities when CMS was fullyoperational are 2.27 and 36.3 fb$^{-1}$ in 2015 and 2016, with a relativeprecision of 1.6% and 1.2%, respectively. These are among the most preciseluminosity measurements at bunched-beam hadron colliders.

Precision luminosity measurement in proton-proton collisions at $\sqrt{s} =$ 13 TeV in 2015 and 2016 at CMS