In 2015, the UN adopted a new set of Sustainable Development Goals (SDGs) to eradicate poverty, establish socioeconomic inclusion and protect the environment. Critical voices such as the International Council for Science (ICSU), however, have expressed concerns about the potential incompatibility of the SDGs, specifically the incompatibility of socio-economic development and environmental sustainability. In this paper, we test, quantify and model the alleged inconsistency of SDGs. Our analyses show which SDGs are consistent and which are conflicting. We measure the extent of inconsistency and conclude that the SDG agenda will fail as a whole if we continue with business as usual. We further explore the nature of the inconsistencies using dynamical systems models, which reveal that the focus on economic growth and consumption as a means for development underlies the inconsistency. Our models also show that there are factors which can contribute to development (health programmes, government investment) on the one hand and ecological sustainability (renewable energy) on the other, without triggering the conflict between incompatible SDGs. © 2016 The Author(s).