A measurement of the ZZ production cross section in the ℓ−ℓ+ℓ′ −ℓ′ + and $$ {\ell}^{-}{\ell}^{+}\nu \overline{\nu} $$ channels (ℓ = e, μ) in proton-proton collisions at $$ \sqrt{s}=8 $$ TeV at the Large Hadron Collider at CERN, using data corresponding to an integrated luminosity of 20.3 fb−1 collected by the ATLAS experiment in 2012 is presented. The fiducial cross sections for ZZ → ℓ−ℓ+ℓ′ −ℓ′ + and $$ ZZ\to {\ell}^{-}{\ell}^{+}\nu \overline{\nu} $$ are measured in selected phase-space regions. The total cross section for ZZ events produced with both Z bosons in the mass range 66 to 116 GeV is measured from the combination of the two channels to be 7.3 ± 0.4(stat) ± 0.3(syst) − 0.1 − 0.2 (lumi) pb, which is consistent with the Standard Model prediction of 6. 6 − 0.6 + 0.7 pb. The differential cross sections in bins of various kinematic variables are presented. The differential event yield as a function of the transverse momentum of the leading Z boson is used to set limits on anomalous neutral triple gauge boson couplings in ZZ production.