Empirical research on barriers to a circular plastics economy has predominantly relied on case study approaches. While research has provided insights into the conceptual and anecdotal aspects of these barriers, a gap remains in the application of formalized methodologies to systematically understand and address them. This paper seeks to bridge this gap by developing an equation system tailored to the plastics industry, bringing clarity to the complex interplay of factors that constitute barriers to a circular economy. The study identifies four primary barriers to the circular economy, as documented in the literature between 2017 and 2024: economic, institutional and regulatory, technological, and social. The results include 24 equations, synthesized into four master equations. A mathematical case study demonstrates how numerical weights, and the relative importance of variables can differ between countries, offering a practical guide for applying the framework across diverse contexts. The study concludes that reducing regulatory ambiguity, scaling recycling infrastructure, and fostering consumer trust in recycled materials are critical steps. However, each country will face unique challenges, requiring policymakers to adopt tailored approaches and variable weighting.