Summary: We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos, \(N_{\mathrm{eff}}^{\mathrm{SM}}\), that quantifies the cosmological neutrino-to-photon energy densities. The calculation takes into account neutrino flavour oscillations, finite-temperature effects in the quantum electrodynamics plasma to \(\mathcal{O}(e^3)\), where \(e\) is the elementary electric charge, and a full evaluation of the neutrino-neutrino collision integral. We provide furthermore a detailed assessment of the uncertainties in the benchmark \(N_{\mathrm{eff}}^{\mathrm{SM}}\) value, through testing the value’s dependence on (i) optional approximate modelling of the weak collision integrals, (ii) measurement errors in the physical parameters of the weak sector, and (iii) numerical convergence, particularly in relation to momentum discretisation. Our new, recommended standard-model benchmark is \(N_{\mathrm{eff}}^{\mathrm{SM}}= 3.0440 \pm 0.0002\), where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure (\(|\delta N_{\mathrm{eff}}| \sim 10^{-4}\)), augmented by measurement errors in the solar mixing angle \(\sin^2\theta_{12}\) (\(|\delta N_{\mathrm{eff}}| \sim 10^{-4}\)).
For Part I, see the [first author et al., ibid. 2021, No. 3, Paper No. A01, 2 p. (2021; Zbl 1500.83005)].