Atmospheric aerosols (acting as cloud condensation nuclei) can enhance the cloud droplet number concentration and reduce the cloud droplet size, and in turn affect the cloud optical depth, as well as the cloud albedo, and thereby exert a radiative influence on climate (the first indirect aerosol effect). In this paper, based on various relationships between cloud droplet spectral dispersion (E >) and cloud droplet number concentration (N (c)), we analytically derive the corresponding expressions of the cloud radiative forcing induced by changes in the cloud droplet number concentration. Further quantitative evaluation indicates that the cloud radiative forcing induced by aerosols for the different E >-N (c) relationships varies from -29.1% to 25.2%, compared to the case without considering spectral dispersion (E > = 0). Our results suggest that an accurate description of E > - N (c) relationships helps to reduce the uncertainty of the first indirect aerosol effect and advances our scientific understanding of aerosol-cloud-radiation interactions.