The UN's 17 Sustainable Development Goals (SDGs) aim to improve the lives of people, increase prosperity, and protect the planet. Given the large number of goals, interactions are inevitable. We analyse the interaction between two social goals (related to SDG1 Poverty and SDG10 Inequality) and three environmental goals (related to SDG13 Carbon, SDG15 Land, and SDG6 Water). We use a trade-linked, consumption-based approach to assess interactions in 166 nations, each subdivided into four income groups. We find that pursuing social goals is, generally, associated with higher environmental impacts. However, interactions differ greatly among countries and depend on the specific goals. In both interactions, carbon experiences smaller changes than land and water. Although efforts by high- and low-income groups are needed, the rich have a greater leverage to reduce humanity’s footprints. Given the importance of both social and environmental sustainability, it is crucial that quantitative interactions between SDGs be well understood so that, where needed, integrative policies can be developed.