This paper presents an accurate model of a circular aperture with full parabolic-in-square aperture distribution that can be applied to reflectors, antenna arrays, microwave lenses, or other aperture antennas. The proposed aperture distribution is a weighted sum of the parabolic in square on a pedestal and parabolic tapered distributions. It permits the analysis and design of efficient aperture antennas with a low sidelobe level. The main far-field parameters of antenna radiation, aperture taper efficiency, directivity, radiated power, half-power beam width, and sidelobe level can be determined with simple formulas. Additionally, the applied aperture distribution permits accurate near-field estimation. Anew analytical solution of the Helmholtz equations for an on-axis near field is derived. A comparison of the obtained solution with known analytical results based on the Fresnel approximation is presented. Verification of the new near-field formula favorably coincides with near-field numerical simulations using electromagnetic software FEKO.