The chemical potential and the capacitance of a 2D circular model quantum dot have been investigated for GaAs, InSb, and Si material parameters, covering a range from a few nanometers to micrometer dimensions. The Schro¨dinger equation has been solved self‐consistently, with the inclusion of many‐body effects, using a local density approximation as well as the optimized Krieger‐Li‐Iafrate exchange potential. Gate structures are included by use of the method of images. We have focused on quantum deviations from classical electrostatic capacitive behavior and found such deviations to be significant even for the material parameters of silicon for feature sizes smaller than 30 nm. The most striking features of quantum dot capacitance are signatures of the dot symmetry analogous to the orbital grouping in atoms: we find structure in the dot capacitance arising from quantum effects in correspondence with the filling of each group of energy‐degenerate orbitals. We also cover the influence of a magnetic field perpendicular to the dot plane and we report some results for the chemical potential vs magnetic field and electron number, assuming an effectiveg‐factor corresponding to the one of bulk gallium arsenide. ©1995 American Institute of Physics.