In single-mode fiber based device anaysis expression of fundamental modal field appears within integrands. Therefore the approximation of the field by simple elementary function makes the compulation of propagation characteristics much simpler. Based on a simple novel and accurate near Gaussian function of the fundamental mode formulated recenty,we present analytical formula for the efficiency with which a uniform beam excites the fundamental mode of a single-mode fiber and fractional fundamental modal power guided in the core based on this function. Both the calculation for excitation efficiency and confinement factor are carried out for step and parabolic index profiles and are compared with the available exact numerical results. The prediction of the above two characteristics from our approximation is found to be excellent.