Abstract: Method of finding values of arcsines in data tables for an open loop single mode fiber optic gyroscope (FOG) is studied. Coefficients of fitting functions for arcsines are first solved under the least squares and least norm conditions based on measurement data in calibrating the FOG. A table of 2001 data against a large dynamic range of angular velocities (±300°/s) is then made. Theory and experiments demonstrated that, when combined with linear interpolation it can improve the linearity, symmetry and precision of FOG output in 0～±300°/s. In addition, it lowers the demands for performance of parts, simplifies operations, and increases the processing rate of DSP.