Separating how model-to-model differences in the forced response (UMD) and internal variability (UIV) contribute to the uncertainty in climate projections is important, but challenging. Reducing UMD increases confidence in projections, while UIV characterises the range of possible futures that might occur purely by chance. Separating these uncertainties is limited in traditional multi-model ensembles because most models have only a small number of realisations; furthermore, some models are not independent. Here, we use six largely independent single model initial-condition large ensembles to separate the contributions of UMD and UIV in projecting 21st-century changes of temperature, precipitation, and their temporal variability under strong forcing (RCP8.5). We provide a method that produces similar results using traditional multi-model archives. While UMD is larger than UIV for both temperature and precipitation changes, UIV is larger than UMD for the changes in temporal variability of both temperature and precipitation, between 20° and 80° latitude in both hemispheres. Over large regions and for all variables considered here except temporal temperature variability, models agree on the sign of the forced response whereas they disagree widely on the magnitude. Our separation method can readily be extended to other climate variables.