Using a tunneling approach for the field emission from a single carbon nanotube, expressions for the emission current as a function of the anode voltage and of the emitted electron energy spectrum are obtained. The low dimensionality of the electronic system of a carbon nanotube is taken into account. The extraction field on the nanotube's tip is evaluated using numerical computations. For nanotubes of practical interest, having large enough diameters, it is demonstrated that the influence of the detailed form of the electron energy dispersion relations is not of major importance. This influence could be generally embedded in a numerical factor entering the expression of the emission current. The influence of the various tube parameters on the characteristics is also identified and analyzed. An approximate formula for use in practical analysis in field emission is deduced and its validity for different nanotube sizes is verified.