Over the last 10 years, the concept of a global ‘carbon budget’ of allowable CO2 emissions has become ubiquitous in climate science and policy. Since it was brought to prominence by the Fifth Assessment Report of the IPCC, the carbon budget has changed how climate change is enacted as an issue of public concern, from determining the optimal rate of future emissions to establishing a fixed limit for how much emissions should be allowed before they must be stopped altogether. Exploring the emergence of the carbon budget concept, this article shows how the assessment process of the IPCC has offered scientific experts the means to modify how the climate issue is problematized, and discusses the implications of this ‘modifying-work’ for the politics of climate change. It finds that the ‘modified climate issue’ must be seen as an outcome of the ordinary work within established scientific and political institutions, and the agency these institutions afford scientists to enact the issue differently. On this basis, it argues that the case of the carbon budget holds important insights not only for the relationship between climate science and policy, but also for the pragmatist literature on ‘issue formation’ in STS.