The Sustainable Development Goals (SDGs) adopted in 2015 integrate diverse issues such as addressing hunger, gender equality and clean energy and set a common agenda for all United Nations member states until 2030. The 17 SDGs interact and by working towards achieving one goal countries may further—or jeopardise—progress on others. However, the direction and strength of these interactions are still poorly understood and it remains an analytical challenge to capture the relationships between the multi-dimensional goals, comprising 169 targets and over 200 indicators. Here, we use principal component analysis (PCA), an in this context novel approach, to summarise each goal and interactions in the global SDG agenda. Applying PCA allows us to map trends, synergies and trade-offs at the level of goals for all SDGs while using all available information on indicators. While our approach does not allow us to investigate causal relationships, it provides important evidence of the degree of compatibility of goal attainment over time. Based on global data 2000–2016, our results indicate that synergies between and within the SDGs prevail, both in terms of levels and over time change. An exception is SDG 10 ‘Reducing inequalities’ which has not progressed in tandem with other goals.