The jet energy calibration and its uncertainties are derived from measurements of the calorimeter response to single particles in both data and Monte Carlo simulation using proton-proton collisions at $\sqrt{s} = 13$ TeV collected with the ATLAS detector during Run 2 at the Large Hadron Collider. The jet calibration uncertainty for anti-k$_t$ jets with a jet radius parameter of $R = 0.4$ and in the central jet rapidity region is about 2.5% for transverse momenta ($p_T$) of 20 GeV, about 0.5% for $p_T = 300$ GeV and 0.7% for $p_T = 4$ TeV. Excellent agreement is found with earlier determinations obtained from $p_T$-balance based in situ methods ($Z/γ$+jets). The combination of these two independent methods results in the most precise jet energy measurement achieved so far with the ATLAS detector with a relative uncertainty of 0.3% at $p_T = 300$ GeV and 0.6% at $4$ TeV. The jet energy calibration is also derived with the single-particle calorimeter response measurements separately for quark- and gluon-induced jets and furthermore for jets with $R$ varying from 0.2 to 1.0 retaining the correlations between these measurements. Differences between inclusive jets and jets from boosted top-quark decays, with and without grooming the soft jet constituents, are also studied.