To estimate the apex field enhancement factor associated with an array of carbon nanotubes (CNTs) on a planar cathode surface, the model of floating spheres between parallel anode and cathode plates is proposed. An approximate formula for the enhancement factor is derived, showing that the intertube distance of a CNT array critically affects the field emission. When the intertube distance is less than the height of the tube, the enhancement factor decreases rapidly with decreasing distance, qualitatively in agreement with the numerical simulation. Considering the field emission current density, the field emission can be optimized when the intertube distance is comparable with the tube height, in accordance with the results from experiments. Finally, the influence of the anode-cathode distance on the enhancement factor is also discussed, showing that the anode-cathode distance has little effect on the field emission from CNT array. Thus, we can reduce the threshold voltage to some extent by decreasing the anode-cathode distance.