Using the symbolic calculation program Mathematica, based on the power series expansions of common latitude with geodetic latitude as a variable, power series expansions of common latitude with geocentric latitude as variable are derived. The coefficients of the two groups of formulas are based on the ellipsoid eccentricity e and the ellipsoid third flattening n, which make the expansions more uniform. Taking CGCS2000 as an example, numerical analysis is applied to verify the accuracy and reliability of the derived power series expansions. By analyzing and calculating the truncation error of common latitude based on ellipsoidal eccentricity e and the third flattening n expansion to different orders, we obtain simplified practical formulas for common latitude that satisfy the requirement of geodesic accuracy. Moreover, we show that the practical formula derived has higher calculation efficiency and easier dissemination, enriches the theory of map projection, and provides a basis for better display of remote sensing images.
