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