Pedalium murex wastes comprising leaves, flowers, fruits, and seeds were used as precursors to synthesize biocarbon. The Brunauer-Emmett-Teller-specific surface area of 305 m2 g−1 with micro- and mesopores was identified using gas sorption analysis. The three-electrode configuration of a supercapacitor was used to identify the cathodic (−1.2 V) and anodic (0.9 V) limits of the carbon material vs Ag/AgCl(aq.) reference in 1.0 M Na2SO4(aq.). The reversible hydrogen sorption in micropores may be responsible for the extended cathodic potential limit of carbon electrodes. Symmetrical supercapacitors with three commercial-level mass-loaded electrodes were used to evaluate the electrochemical performance. EIS measurements were carried out with three different numbers of frequencies per decade to see their influence on the Warburg diffusion resistance and the relaxation time constant of the supercapacitor. The presence of significant quantities of microspores enables the aqueous supercapacitor with 1.0 M Na2SO4(aq.) to operate with a high cell potential of 1.6 V. The single-electrode-specific capacitances of 112 F g−1, 90 F g−1, and 54 F g−1 at 1.6 V were estimated for the supercapacitors with 10 mg cm−2, 20 mg cm−2, and 30 mg cm−2 areal active material mass loading, respectively, at 0.1 A g−1. Excellent coulombic efficiency of 99% and energy efficiency of 78% were obtained for 10 mg cm−2 mass loading. The specific energy and specific power of 9.7 Wh kg−1 and 2930 W kg−1 were estimated for the fabricated device. The stability of the supercapacitor was analyzed by conducting uninterrupted GCPL cycling up to 50,000 cycles.