The Paris Agreement aims to constrain global warming to ‘well below 2 °C’ and to ‘pursue efforts’ to limit it to 1.5 °C above pre-industrial levels. We quantify global and regional risk-related metrics associated with these levels of warming that capture climate change–related changes in exposure to water scarcity and heat stress, vector-borne disease, coastal and fluvial flooding and projected impacts on agriculture and the economy, allowing for uncertainties in regional climate projection. Risk-related metrics associated with 2 °C warming, depending on sector, are reduced by 10–44% globally if warming is further reduced to 1.5 °C. Comparing with a baseline in which warming of 3.66 °C occurs by 2100, constraining warming to 1.5 °C reduces these risk indicators globally by 32–85%, and constraining warming to 2 °C reduces them by 26–74%. In percentage terms, avoided risk is highest for fluvial flooding, drought, and heat stress, but in absolute terms risk reduction is greatest for drought. Although water stress decreases in some regions, it is often accompanied by additional exposure to flooding. The magnitude of the percentage of damage avoided is similar to that calculated for avoided global economic risk associated with these same climate change scenarios. We also identify West Africa, India and North America as hotspots of climate change risk in the future.