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Climate change is causing measurable harm globally1,2. Political and legal efforts seek to link these damages with specific emissions, including in discussions of loss and damage (L&D)3,4; however, no quantitative definition of L&D exists5,6, nor is there a framework to link past and future emissions from specific sources to monetized, location-specific damages. Here we develop such a framework, which is integrated with recent efforts to estimate the social cost of carbon7. Using empirical estimates of the non-linear relationship between temperature and aggregate economic output, we show that future damages from past emissions—one component of L&D—are at least an order of magnitude larger than historical damages from the same emissions. For instance, one tonne of CO2 emitted in 1990 caused US$180 in discounted global damages by 2020 ($40–530) and will cause an additional $1,840 through 2100 ($500–5,700). Thus, settling debts for past damages will not settle debts for past emissions. In other illustrative esti