The aim of this paper is to provide a new viewpoint of friction factor for contact stress calculations of gears. The idea of friction factor has been coined, for the calculation of contact stresses along the tooth contact for different helical gear pairs. Friction factors were developed by evaluating contact stresses with and without friction for different gear pairs. In this paper, 3D Finite Element Method (FEM) and Lagrange Multiplier algorithm has been used to evaluate the contact stresses. Initially, a spur gear FE model was validated with the theoretical analysis under frictionless condition, which is based on Hertz's contact theory. Then, similar FE models were constructed for 5, 15, 25 and 35 deg. helical gear pairs. The contact stresses of these models were evaluated for different coefficients of friction. These results were employed for the development of friction factor.