International climate change agreements typically specify global warming thresholds as policy targets, but the relative economic benefits of achieving these temperature targets remain poorly understood. Uncertainties include the spatial pattern of temperature change, how global and regional economic output will respond to these changes in temperature, and the willingness of societies to trade present for future consumption. Here we combine historical evidence with national-level climate and socioeconomic projections to quantify the economic damages associated with the United Nations (UN) targets of 1.5 °C and 2 °C global warming, and those associated with current UN national-level mitigation commitments (which together approach 3 °C warming). We find that by the end of this century, there is a more than 75% chance that limiting warming to 1.5 °C would reduce economic damages relative to 2 °C, and a more than 60% chance that the accumulated global benefits will exceed US$20 trillion under a 3% discount rate (2010 US dollars). We also estimate that 71% of countries—representing 90% of the global population—have a more than 75% chance of experiencing reduced economic damages at 1.5 °C, with poorer countries benefiting most. Our results could understate the benefits of limiting warming to 1.5 °C if unprecedented extreme outcomes, such as large-scale sea level rise, occur for warming of 2 °C but not for warming of 1.5 °C. Inclusion of other unquantified sources of uncertainty, such as uncertainty in secular growth rates beyond that contained in existing socioeconomic scenarios, could also result in less precise impact estimates. We find considerably greater reductions in global economic output beyond 2 °C. Relative to a world that did not warm beyond 2000–2010 levels, we project 15%–25% reductions in per capita output by 2100 for the 2.5–3 °C of global warming implied by current national commitments, and reductions of more than 30% for 4 °C warming. Our results therefore suggest that achieving the 1.5 °C target is likely to reduce aggregate damages and lessen global inequality, and that failing to meet the 2 °C target is likely to increase economic damages substantially.