Electron backscattering diffraction (EBSD) patterns reveal information about the phase component, crystal structure, grain orientation, grain size and grain boundaries of the material. EBSD patterns are very complex and usually require special computing software to analyze. A systematic study of the mathematical characteristics of EBSD patterns is carried out in this paper. A mathematical relationship between arbitrary crystal orientation and EBSD pattern is established, mathematical characteristics of EBSD patterns at pattern center of the basal zone axes of face-centered cubic, body-centered cubic, and close-packed hexagonal crystals are derived, as well as the theoretical Kikuchi patterns of (001)<110> orientation and (001)<100> orientation of face-centered cubic crystals. The theoretical EBSD pattern characteristics of the basic crystal zone axes of each lattice are compared in the analysis of the measured EBSD patterns, that is, by comparing the image features, the crystal system, lattice and the crystal zone axes ［uvw］ corresponding to the intersection points of some Kikuchi lines of the measured patterns can be directly determined. The crystal orientation or texture can be calculated from the coordinates of the basic crystal zone axes, and the spatial distribution of the basic crystal plane can also be provided, such as atomic close-packed plane in the sample, which is beneficial to the study on the deformation or growth mechanism of the crystal. EBSD provides new methods for single-crystal chip quality inspection.