The capacitance of conducting polymers represents one of the most important material parameters that in many cases determines the device and material performances. Despite a vast number of experimental studies, the theoretical understanding of the origin of the capacitance in conducting polymers remains unsatisfactory and appears even controversial. Here, we present a theoretical method, based on first principle capacitance calculations using density functional theory (DFT), and apply it to calculate the volumetric capacitance of two archetypical conducting polymers: poly(3,4-ethylene dioxythiophene) (PEDOT) and polypyrrole (PPy). Our aim is to achieve a quantitate description of the volumetric capacitance and to provide a qualitative understanding of its nature at the atomistic level. We find that the volumetric capacitance of PEDOT and PPy is approximate to 100 F cm(-3) and approximate to 300 F cm(-3), respectively, which is within the range of the corresponding reported experimental results. We demonstrate that the capacitance of conducting polymers originates from charges stored in atomistic Stern layers formed by counterions and doped polymeric chains. The Stern layers have a purely electrostatic origin, since the counterions do not form any bonds with the atoms of the polymeric chains, and no charge transfer between the counterions and conducting polymer takes place. This classifies the conducting polymers as double-layer supercapacitors rather than pseudo-capacitors. Further, we analyze contributions to the total capacitance originating from the classical capacitance C-C and the quantum capacitance C-Q, respectively, and find that the latter provides a dominant contribution. The method of calculations of the capacitance developed in the present paper is rather general and opens up the way for engineering and optimizing the capacitive response of the conducting polymers.