Historical evidence shows that atmospheric greenhouse gas (GhG) concentrations increase during periods of warming, implying a positive feedback to future climate change. We quantified this feedback for CO₂ and CH₄ by combining the mathematics of feedback with empirical ice-core information and general circulation model (GCM) climate sensitivity, finding that the warming of 1.5–4.5°C associated with anthropogenic doubling of CO₂ is amplified to 1.6–6.0°C warming, with the uncertainty range deriving from GCM simulations and paleo temperature records. Thus, anthropogenic emissions result in higher final GhG concentrations, and therefore more warming, than would be predicted in the absence of this feedback. Moreover, a symmetrical uncertainty in any component of feedback, whether positive or negative, produces an asymmetrical distribution of expected temperatures skewed toward higher temperature. For both reasons, the omission of key positive feedbacks and asymmetrical uncertainty from feedbacks, it is likely that the future will be hotter than we think.