A measurement of the W boson pair production cross section in proton-proton collisions at [Formula: see text] TeV is presented. The data collected with the CMS detector at the LHC correspond to an integrated luminosity of 19.4[Formula: see text]. The [Formula: see text] candidates are selected from events with two charged leptons, electrons or muons, and large missing transverse energy. The measured [Formula: see text] cross section is [Formula: see text], consistent with the standard model prediction. The [Formula: see text] cross sections are also measured in two different fiducial phase space regions. The normalized differential cross section is measured as a function of kinematic variables of the final-state charged leptons and compared with several perturbative QCD predictions. Limits on anomalous gauge couplings associated with dimension-six operators are also given in the framework of an effective field theory. The corresponding 95 % confidence level intervals are [Formula: see text], [Formula: see text], [Formula: see text], in the HISZ basis.