Earth system models simplify complex terrestrial respiration processes assuming a first-order chemical reaction or assuming a Michaelis-Menten kinetics. The epistemic uncertainty related to the respective mathematical representations is unclear. Using a simplified model of biogeochemical feedbacks to climate, we show that the terrestrial carbon-climate feedback is more than 35 % higher, and hence the remaining carbon budget to keep global warming below 2 °C is 89–158 Pg C higher, when assuming Michaelis-Menten kinetics instead of first-order kinetics, but these differences depend on the underlying emission scenario. These results show the importance of an increased understanding of the mathematical model structure of respiration processes in Earth System Models for more reliably projecting future carbon dynamics and climate, related feedback mechanisms, and hence to estimate a valid remaining anthropogenic carbon budget.