We fabricated high performance supercapacitors by using all carbon electrodes, with volume energy in the order of 10−3 Whcm−3, comparable to Li-ion batteries, and power densities in the range of 10 Wcm−3, better than laser-scribed-graphene supercapacitors. All-carbon supercapacitor electrodes are made by solution processing and filtering electrochemically-exfoliated graphene sheets mixed with clusters of spontaneously entangled multiwall carbon nanotubes. We maximize the capacitance by using a 1:1 weight ratio of graphene to multi-wall carbon nanotubes and by controlling their packing in the electrode film so as to maximize accessible surface and further enhance the charge collection. This electrode is transferred onto a plastic-paper-supported double-wall carbon nanotube film used as current collector. These all-carbon thin films are combined with plastic paper and gelled electrolyte to produce solid-state bendable thin film supercapacitors. We assembled supercapacitor cells in series in a planar configuration to increase the operating voltage and find that the shape of our supercapacitor film strongly affects its capacitance. An in-line superposition of rectangular sheets is superior to a cross superposition in maintaining high capacitance when subject to fast charge/discharge cycles. The effect is explained by addressing the mechanism of ion diffusion into stacked graphene sheets.