The neutrino energy density of the Universe can be conveniently parametrized in terms of the so-called effective number of neutrinos , N _ { \nu } ^ { eff } .
This parameter enters in several cosmological observables .
In particular it is an important input in those numerical codes , like CMBFAST , which are used to study the Cosmic Microwave Background anisotropy spectrum .
By studying the neutrino decoupling with Boltzmann equations , one can show that this quantity differs from the number of massless neutrino species for an additional contribution due to a partial heating of neutrinos during the e ^ { \pm } annihilations , leading to non thermal features in their final distributions .
In this paper we review the different results obtained in the literature and perform a new analysis which takes into account , in a fully consistent way , the QED corrections at finite temperature to the photon and e ^ { { \pm } } plasma equation of state .
The value found for three massless active neutrinos is N _ { \nu } ^ { eff } = 3.0395 , in perfect agreement with the recommended value used in CMBFAST , N _ { \nu } ^ { eff } = 3.04 .
We also discuss the case of additional relativistic relics and massive active neutrinos .