The United Nation’s 17 Sustainable Development Goals (SDGs) offer an extensive framework for coordinating and shaping government policies, and for engaging the public with sustainability. Public understanding of the SDGs and sustainability can influence this engagement, as people are more likely to accept and share information consistent with their own understanding. We identify public understandings of SDGs through mental maps of how people relate the SDGs to environmental, social and economic sustainability. Using responses from 12 developed/developing countries (n = 2,134), we identified four mental maps that varied mainly on two dimensions, which diverged from some expert models. Some people’s mental maps identified tension between achieving environmental versus social sustainability, whereas for others the tension was between economic sustainability and the other two sustainability elements. Some people related different SDGs to each element of sustainability, whereas others saw all SDGs as targeting the same sustainability element(s). These findings highlight opportunities and challenges to engage the public with sustainability more effectively, especially with wide-ranging initiatives such as a Green New Deal. We observed cultural differences but we also identified a dominant mental map across countries that could serve as a default model for communicating sustainability internationally.