To ensure the accuracy of harmonic compensation value for the turntable positioning error, a calculating method for the harmonic error function is proposed. The harmonic compensation method for turntable positioning is described and the feasibility of the CORDIC algorithm for harmonic error function calculation is introduced in detail. Based on the principle of the CORDIC, the quantitative models of the iteration number n and the data width b are established, respectively. The overall quantization error of calculating harmonic function is deduced. The calculating method is implemented by using the laboratory-made field-programmable gate array circuit. The value of n and b are determined to satisfy the calculation accuracy. Finally, a series of evaluation tests are performed to demonstrate the effectiveness of the method by comparing theoretical and computational values. The data of experiment performed on the test turntable platform confirm that the proposed method can calculate the value of harmonic function effectively. The positioning accuracy of turntable is improved from 29. 0" to 5. 3" with this method.