Greenhouse gases other than CO(2) make a significant contribution to human-induced climate change, and multi-gas mitigation strategies are cheaper to implement than those which limit CO(2) emissions alone. Most practical multi-gas mitigation strategies require metrics to relate the climate warming effects of CO(2) and other greenhouse gases. Global warming potential (GWP), defined as the ratio of time-integrated radiative forcing of a particular gas to that of CO(2) following a unit mass emission, is the metric used in the Kyoto Protocol, and we define mean global temperature change potential (MGTP) as an equivalent metric of the temperature response. Here we show that carbon-climate feedbacks inflate the GWPs and MGTPs of methane and nitrous oxide by similar to 20% in coupled carbon-climate model simulations of the response to a pulse of 50 x 1990 emissions, due to a warming-induced release of CO(2) from the land biosphere and ocean. The magnitude of this effect is expected to be dependent on the model, but it is not captured at all by the analytical models usually used to calculate metrics such as GWP. We argue that the omission of carbon cycle dynamics has led to a low bias of uncertain but potentially substantial magnitude in metrics of the global warming effect of other greenhouse gases, and we suggest that the carbon-climate feedback should be considered when greenhouse gas metrics are calculated and applied.