A formulation for predicting the Helmholtz-Kohlrausch (H-K) effect is given to the new VCC (variable chromatic color) method, which can derive the luminance factors of various chromatic object colors that match in perceived lightness with a fixed achromatic color. By using the formulation, the H-K effect by the VCC method is predicted within the whole chromaticity gamut including spectral colors. The magnitude of the effect in logarithmic scale by the VCC method is estimated to be twice as large as that by the VAC (variable achromatic color) method previously used. It is also stated that the VCC method is practically more important than the VAC method. The effectiveness of the new formulation is confirmed by comparing its predictions with the observations in two kinds of experiments.