  The effective number of relativistic neutrino species is a fundamental probe
of the early Universe and its measurement represents a key constraint on many
scenarios beyond the Standard Model of Particle Physics. In light of this, an
accurate prediction of $N_{\rm eff}$ in the Standard Model is of pivotal
importance. In this work, we consider the last ingredient needed to accurately
calculate $N_{\rm eff}^{\rm SM}$: standard zero and finite temperature QED
corrections to $e^+e^- \leftrightarrow \nu\bar{\nu}$ interaction rates during
neutrino decoupling at temperatures around $T\sim {\rm MeV}$. We find that this
effect leads to a reduction of $-0.0007$ in $N_{\rm eff}^{\rm SM}$. This NLO
QED correction to the interaction rates, together with finite temperature QED
corrections to the electromagnetic density of the plasma, and the effect of
neutrino oscillations, implies that $N_{\rm eff}^{\rm SM} = 3.043$ with a
theoretical uncertainty that is much smaller than any projected observational
sensitivity.
