Atrial fibrillation (AF) is a heart disease affecting millions of Americans. Clinicians evaluate AF-related risk by assessing the temporal pattern, variation, and severity of AF episodes through AF burden (AFB). However, existing prognostic tools based on these metrics are suboptimal, as they do not account for electrical complexity of AF signals. This study introduced Electrical Burden (EB) as a new marker to assess electrical instability and complexity of AF. We also developed a Complexity AF score that incorporates AFB, EB, and Poincaré analysis to assess the severity of AF. Electrocardiogram (ECG) from 50 AF patients in the Long-term AF database were analyzed. EB was calculated using four metrics and combined with AFB and Poincaré metrics to derive the Complexity AF score for each patient. Our results show that AFB, EB, and Poincaré metrics are independent markers, each describing different aspects of AF complexity. The Complexity AF score effectively distinguished between terminated (2.82 ± 1.29, 17 patients) and non-terminated AF groups (4 ± 1.46, 33 patients) (p-value < 0.05). This study emphasizes the importance of EB and Poincaré analysis as an indicator of electrical complexity of AF and highlights the utility of the Complexity AF score in accurately characterizing and stratifying AF to guide management.