The ionospheric radiance and electron density observed by the tiny ionospheric photometer (TIP) and GPS occultation experiment (GOX) payloads on FORMOSAT-3/COSMIC satellites are applied to determine the boundaries of the auroral oval and its width in the winter nighttime ionosphere for both hemispheres. The TIP collects ionospheric emission at 135.6 nm due to electron impact excitation, while the GOX offers ionospheric electron density profiles with radio occultation (RO) technique. Comparison between them shows similar patterns of the plasma structure in the polar caps. The mean width of the auroral bands ranges between about 2 and 11A degrees latitude in the winter nighttime and it varies with longitudes. The comparison by month suggests that the mean radius of the auroral ovals varies with the intensity of the auroral radiance.