Non-technical abstract The world agreed to achieve 17 Sustainable Development Goals by 2030. Nine planetary boundaries set an upper limit to Earth system impacts of human activity in the long run. Conventional efforts to achieve the 14 socio-economic goals will raise pressure on planetary boundaries, moving the world away from the three environmental SDGs. We have created a simple model, Earth3, to measure how much environmental damage follows from achievement of the 14 socio-economic goals, and we propose an index to track effects on people's wellbeing. Extraordinary efforts will be needed to achieve all SDGs within planetary boundaries. Technical abstract Near-term gains on socio-economic goals under the 2030 Agenda could reduce the Earth system `safety margin' represented by the nine planetary boundaries. We built an intentionally simple global systems simulation model, Earth3, that combines a socio-economic model of human activity with a biophysical model of the global environment. Earth3 fills a key gap in the family of integrated models, by being capable of simulating the complex dynamic implementation challenge of the full 2030 Agenda. Earth3 generates consistent, transparent pathways from 1980 to 2050 for seven world regions. With these pathways, we assess the extent to which the 14 socio-economic SDGs are achieved and quantify the associated pressure on planetary boundaries to calculate endogenously the extent to which the three environmental SDGs are achieved. Sensitivity analysis indicates uncertainty of the order of +/- 20% in the number of SDGs achieved and in the biophysical safety margin. The Business-as-Usual scenario indicates that the social and environmental SDGs cannot be achieved together, nor within the planetary boundaries. Combined with an index tracking effects on people's wellbeing and with simple formulations that keep assumptions transparent, Earth3 can help identify and communicate policies that could improve the global sustainability situation.