Jet energy scale measurements and their systematic uncertainties are reported for jets measured with the ATLAS detector using proton-proton collision data with a center-of-mass energy of s=13 TeV, corresponding to an integrated luminosity of 3.2 fb-1 collected during 2015 at the LHC. Jets are reconstructed from energy deposits forming topological clusters of calorimeter cells, using the anti-kt algorithm with radius parameter R=0.4. Jets are calibrated with a series of simulation-based corrections and in situ techniques. In situ techniques exploit the transverse momentum balance between a jet and a reference object such as a photon, Z boson, or multijet system for jets with 20<pT<2000 GeV and pseudorapidities of |η|<4.5, using both data and simulation. An uncertainty in the jet energy scale of less than 1% is found in the central calorimeter region (|η|<1.2) for jets with 100<pT<500 GeV. An uncertainty of about 4.5% is found for low-pT jets with pT=20 GeV in the central region, dominated by uncertainties in the corrections for multiple proton-proton interactions. The calibration of forward jets (|η|>0.8) is derived from dijet pT balance measurements. For jets of pT=80 GeV, the additional uncertainty for the forward jet calibration reaches its largest value of about 2% in the range |η|>3.5 and in a narrow slice of 2.2<|η|<2.4.