The analytical expression for effective core area of single mode graded index fiber is prescribed and formulated using power series expression of the fundamental mode developed by Chebyshev technique. The step and parabolic index fibers are used as typical examples. Using the said formulation, we estimate the effective core areas for different values of normalized frequency V. We also evaluate the indices of refraction for the said fibers. The concerned evaluations require little computation. We also show the accuracy of our simple formalism by comparing our results with the available exact results. Thus the formalism will prove beneficial to the technologists in the field of optical technology. © 2018 National Institute of Optoelectronics. All rights reserved.