The program presented in this paper is intended to provide a valuable aid for teaching antennas to electrical engineers, and to provide fast and accurate pre-designs for professionals. This paper covers the theory and numerical techniques used in SABOR. In summary, this program computes the radiated field of an aperture antenna (horn or reflector), using a common engine based on the Gauss-Legendre quadrature method for evaluating the radiation integrals. For horn, the aperture fields are the usual dominant modes of the feed waveguide, with a quadratic phase correction. For reflectors, the aperture fields are computed using geometrical optics ray tracing from the feed horn. Also, equivalent-reflector concepts are applied for dual-reflector antennas. The paper includes some examples to demonstrate the most important features of the program.