Abstract This study aims to improve our understanding of the response of precipitation to forcings by proposing a physically-based equation that resolves simulated precipitation based on the atmospheric energy budget. The equation considers the balance between latent heat release by precipitation and the sum of the slow response by tropospheric temperature changes and the fast response by abrupt radiative forcing (RF) changes. The equation is tuned with three parameters for each climate model and then adequately reproduces time-varying precipitation. By decomposing the equation, we highlight the slow response as the largest contributor to forcing-driven responses and uncertainty sizes in simulations. The second largest one to uncertainty is the fast-RF response from aerosols or greenhouse gases (GHG), depending on the low or highest Coupled Model Intercomparison Projection 6 future scenarios. The likely range of precipitation change at specific warming levels under GHG removal (GGR) and solar radiation management (SRM) mitigation plans is evaluated by a simple model optimizing the relationship between temperature and decomposed contributions from multi-simulations under three scenarios. The results indicate that GGR has more severe effects from aerosols than GHG for a 1.5 K warming, resulting in 0.91%–1.62% increases in precipitation. In contrast, SRM pathways project much drier conditions than GGR results due to the tropospheric cooling and remaining anthropogenic radiative heating. Overall, the proposed physically-based equation, the decomposition analysis, and our simple model provide valuable insights into the uncertainties under different forcings and mitigation pathways, highlighting the importance of slow and fast responses to human-induced forcings in shaping future precipitation changes.