The concept of a circular economy (CE) is gaining increasing attention from policy makers, industry, and academia. There is a rapidly evolving debate on definitions, limitations, the contribution to a wider sustainability agenda, and a need for indicators to assess the effectiveness of circular economy measures at larger scales. Herein, we present a framework for a comprehensive and economy-wide biophysical assessment of a CE, utilizing and systematically linking official statistics on resource extraction and use and waste flows in a mass-balanced approach. This framework builds on the widely applied framework of economy-wide material flow accounting and expands it by integrating waste flows, recycling, and downcycled materials. We propose a comprehensive set of indicators that measure the scale and circularity of total material and waste flows and their socioeconomic and ecological loop closing. We applied this framework in the context of monitoring efforts for a CE in the European Union (EU28) for the year 2014. We found that 7.4 gigatons (Gt) of materials were processed in the EU and only 0.71 Gt of them were secondary materials. The derived input socioeconomic cycling rate of materials was therefore 9.6%. Further, of the 4.8 Gt of interim output flows, 14.8% were recycled or downcycled. Based on these findings and our first efforts in assessing sensitivity of the framework, a number of improvements are deemed necessary: improved reporting of wastes, explicit modeling of societal in-use stocks, introduction of criteria for ecological cycling, and disaggregated mass-based indicators to evaluate environmental impacts of different materials and circularity initiatives.