In this paper, an approximate closed-form solution of the impedance coefficient for a small dipole using the method of moments is developed from the reduced or approximate Pocklington equation. As an application, the close-form self-impedance coefficient using the piecewise constant and linear basis functions are found, with well-defined rounding error functions. The authors found that the self-impedance using the piecewise constant basis function is inconsistent with the physics of the problem for segments close to wavelength tenths and arbitrary small wire diameters, independent of the reduced kernel approximation and the printed source model used.