To assess the progress towards a circular economy, numerous circularity metrics have been developed in recent years. However, there is a lack of alignment between circularity metric results and greenhouse gas emissions, as circularity metrics are mainly geared towards capturing material efficiency of circularity strategies and mostly disregard energy use. We target this gap by developing a new mass-based circularity metric that considers both material and energy resources (i.e., fuel and electricity). The circularity metric results are compared to the midpoint impact category Global Warming Potential in two case studies, where circularity strategies are applied to energy consuming products in several different scenarios. The results show that by including energy resources, the new metric is more aligned with GWP than purely material-based metrics. We discuss how this alignment changes in different systems and in which situations the circularity metric is a suitable proxy for GWP.