Most emission metrics have previously been inconsistently estimated by including the climate–carbon feedback for the reference gas (i.e. CO2) but not the other species (e.g. CH4). In the fifth assessment report of the IPCC, a first attempt was made to consistently account for the climate–carbon feedback in emission metrics. This attempt was based on only one study, and therefore the IPCC concluded that more research was needed. Here, we carry out this research. First, using the simple Earth system model OSCAR v2.2, we establish a new impulse response function for the climate–carbon feedback. Second, we use this impulse response function to provide new estimates for the two most common metrics: global warming potential (GWP) and global temperature-change potential (GTP). We find that, when the climate–carbon feedback is correctly accounted for, the emission metrics of non-CO2 species increase, but in most cases not as much as initially indicated by IPCC. We also find that, when the feedback is removed for both the reference and studied species, these relative metric values only have modest changes compared to when the feedback is included (absolute metrics change more markedly). Including or excluding the climate–carbon feedback ultimately depends on the user's goal, but consistency should be ensured in either case.