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 root 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-k(t) 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 < p(T) < 2000 GeV and pseudorapidities of vertical bar eta vertical bar < 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 (vertical bar eta vertical bar < 1.2) for jets with 100 < p(T) < 500 GeV. An uncertainty of about 4.5% is found for low-p(T) jets with p(T) = 20 GeV in the central region, dominated by uncertainties in the corrections for multiple proton-proton interactions. The calibration of forward jets (vertical bar eta vertical bar > 0.8) is derived from dijet p(T) balance measurements. For jets of p(T) = 80 GeV, the additional uncertainty for the forward jet calibration reaches its largest value of about 2% in the range vertical bar eta vertical bar > 3.5 and in a narrow slice of 2.2 < vertical bar eta vertical bar < 2.4.