The effective refractive index (or its inverse) of optical waveguides is found to be describable by an integral expression as a square-root of field-distribution-weighted-mean of squared refractive index distribution (or its inverse). This principle is utilized to find out the effective refractive index without solving the eigenvalue equation and a new fast numerical computation procedure is proposed. The proposed procedure can be applied to either linear or nonlinear waveguide, exhibiting a particular improvement in computational speed for the nonlinear case.