Jet energy scale and resolution measurements with their associated uncertainties are reported for jets using 36-81 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ of proton-proton collision data with a centre-of-mass energy of $s=13$ TeV collected by the ATLAS detector at the LHC. Jets are reconstructed using two different input types: topo-clusters formed from energy deposits in calorimeter cells, as well as an algorithmic combination of charged-particle tracks with those topo-clusters, referred to as the ATLAS particle-flow reconstruction method. The anti-$kt$ jet algorithm with radius parameter $R=0.4$ is the primary jet definition used for both jet types. Jets are initially calibrated using a sequence of simulation-based corrections. Next, several $in\; situ$ techniques are employed to correct for differences between data and simulation and to measure the resolution of jets. The systematic uncertainties in the jet energy scale for central jets () vary from 1% for a wide range of high-$pT$ jets ( GeV), to 5% at very low $pT$ (20 GeV) and 3.5% at very high $pT$ ($>2.5$ TeV). The relative jet energy resolution is measured and ranges from ($24\pm 1.5$)% at 20 GeV to ($6\pm 0.5$)% at 300 GeV.