A disconnect exists between theoretical conceptualizations of energy justice and the practical, policy-oriented approaches needed for real-world decision making and program implementation. Greater attention to quantifying energy justice will likely increase support for high-energy-burden households by facilitating the development of evidence-based, measurable, and targeted policy interventions to better address the needs of marginalized communities. To fill this gap, we develop a conceptual framework that integrates distributive, recognition, and procedural dimensions into quantifying energy justice using Washington, D.C. as a case study. The research employs a set of six metrics - energy burden, renewable energy access, service disconnections, system reliability, utility affordability programs, and public participation - to assess equity across socio-economic groups. Findings reveal that despite the presence of numerous affordability programs and the expansion of solar energy systems, energy affordability is still a significant challenge for low-income households, as evidenced by disproportionately high energy burdens and utility disconnections in vulnerable communities. Additionally, participation in energy forums lacks inclusivity, highlighting a procedural justice gap. Although measuring any form of justice can be challenging, this study's framework provides a simple yet practical model that can be extended to other cities to evaluate energy policy impacts.