Quantum capacitance of graphene plays a significant role for graphene's applications in electrochemical devices and sensors, while the determination of these basic characters of Dirac point, Fermi energy, quantum capacitance, etc is still a subject of considerable debate in both experiments and simulations. Here, we report joint first-principles/continuum calculations (JFPCCs) on a monolayer graphene electrode immersed in an electrolyte coupled with a reference electrode under an applied potential. The JFPCCs gave the Fermi level, charge density on graphene, Dirac point energy, electrostatic potential, electric double layer etc as a function of the applied potential with respect to the reference electrode. These results revealed the strongly coupled relationship between Fermi level change and Dirac point shift in electrochemical cell. The total capacitance of the electrochemical cell was dissected into the quantum capacitance of the graphene electrode and the capacitance of the electric double layer. Furthermore, simple and analytic formulas were proposed for the three capacitances, which predicted, in sufficient accuracy, the behavior of capacitance versus potential. These findings deepen the understanding of quantum capacitance of graphene, which will stimulate novel experimental and theoretical studies and boost the applications of graphene in electrochemical and energy areas. (C) 2015 Elsevier Ltd. All rights reserved.