The prescribed anthropogenic aerosol forcing recommended by Coupled Model Intercomparison Project Phase 6 (CMIP6) was implemented in an atmospheric model. With the reduced complexity of anthropogenic aerosol forcing, each component of anthropogenic aerosol effective radiative forcing (ERF) can be estimated by one or more calculation methods, especially for instantaneous radiative forcing (RF) from aerosol–radiation interactions (RFari) and aerosol–cloud interactions (RFaci). Simulation results show that the choice of calculation method might impact the magnitude and reliability of RFari. The RFaci—calculated by double radiation calls—is the definition-based Twomey effect, which previously was impossible to diagnose using the default model with physically based aerosol–cloud interactions. The RFari and RFaci determined from present-day simulations are very robust and can be used as offline simulation results. The robust RFari, RFaci, and corresponding radiative forcing efficiencies (i.e., the impact of environmental properties) are very useful for analyzing anthropogenic aerosol radiative effects. For instance, from 1975 to 2000, both RFari and RFaci showed a clear response to the spatial change of anthropogenic aerosol. The global average RF (RFari + RFaci) has enhanced (more negative) by ~6%, even with a slight decrease in the global average anthropogenic aerosol, and this can be explained by the spatial pattern of radiative forcing efficiency.