In this letter, we report a new analytical technique for estimating the peak reflectivity of lossless dielectric stacks with combinations of quarter and/or half-wave thicknesses. A simple variable substitution is used to transform the standard formula for the reflectivity of a Fabry-Perot resonator into a remarkably simplified form. The resulting expressions for reflectivity are intuitively appealing, allowing one to use additive algebra to calculate the peak reflectivity of a multilayer dielectric stack. The ability to treat graded interface dielectric stacks is also made possible with the present formalism.