The zero-bias anomaly at low temperatures, originated by the Kondo effect when an electric current flows through a system formed by a spin-$1/2$ quantum dot and two metallic contacts is theoretically investigated. In particular, we compare the width of this anomaly $2T_{\rm NE}$ with that of the Kondo resonance in the spectral density of states $2T_{K}^{\rho}$, obtained from a Fano fit of the corresponding curves and also with the Kondo temperature, $T_K^G$, defined from the temperature evolution of the equilibrium conductance $G(T)$. In contrast to $T_K^G$ and $2T_{K}^{\rho}$, we found that the scale $2T_{\rm NE}$ strongly depends on the asymmetry between the couplings of the quantum dot to the leads while the total hybridization is kept constant. While the three scales are of the same order of magnitude, $2T_{\rm NE}$ and $T_{K}^{\rho}$ agree only in the case of large asymmetry between the different tunneling couplings of the contacts and the quantum dot. On the other hand, for similar couplings, $T_{\rm NE}$ becomes larger than $T_{K}^{\rho}$, reaching the maximum deviation, of the order of $30\%$, for identical couplings. The fact that an additional parameter to $T_{\rm NE}$ is needed to characterize the Kondo effect, weakenig the universality properties, points that some caution should be taken in the usual identification in experiments of the low temperature width of the zero-bias anomaly with the Kondo scale. Furthermore, our results indicate that the ratios $T_{\rm NE}/T_K^G$ and $T_{K}^{\rho}/T_K^G$ depend on the range used for the fitting.