Carbon-based supercapacitors can provide high electrical power, but they do not have sufficient energy density to directly compete with batteries. We found that a nitrogen-doped ordered mesoporous few-layer carbon has a capacitance of 855 farads per gram in aqueous electrolytes and can be bipolarly charged or discharged at a fast, carbon-like speed. The improvement mostly stems from robust redox reactions at nitrogen-associated defects that transform inert graphene-like layered carbon into an electrochemically active substance without affecting its electric conductivity. These bipolar aqueous-electrolyte electrochemical cells offer power densities and lifetimes similar to those of carbon-based supercapacitors and can store a specific energy of 41 watt-hours per kilogram (19.5 watt-hours per liter).