This article traces how the notion of finite limits to emissions based on 2°C carbon budgets was applied to increase the credibility of a carbon-constrained future in two very separate realms, social movements contesting fossil-fuel development and the financial sector—a process yet to be described in the relevant political and financial literature. For each realm and sub-areas within them, we apply a three-wave taxonomy to trace the application of 2°C carbon budget based concepts—including stranded assets, the carbon bubble, divestment and anti-pipeline campaigns—from the fringe to the mainstream in under ten years. We do so by drawing on relevant primary documents and peer-reviewed literature, complemented by a quantitative textual analysis of relevant discourse from news sources. The article establishes how, in efforts to shift expectations, climate proponents used 2°C carbon budgets to frame a stark choice between a safe climate with strict carbon constraints and growth-oriented fossil-fuel interests. The article also demonstrates that these concepts, and efforts inspired by them, contributed to constraints on fossil-fuel developments and interests, arguably further enhancing the credibility of a carbon-constrained future. We conclude with a discussion of the potentially self-reinforcing nature of such expectation dynamics and by highlighting overlapping implications for actors across finance, where investors reorient risk assessment around climate, and social movements, where activists disrupt states’ entrenched commitment to fossil-fuel expansion.