Accurate estimation of effective camera focal length is crucial to the success of panoramic image stitching. Fast techniques for estimating the focal length exist, but are dependent upon a close initial approximation or the existence of a full circle panoramic image sequence. Numerical solutions of the focal length demonstrate strong coupling between the focal length and the angles used to position each component image about the common spherical center. This paper demonstrates that parameterizing panoramic image positions using spherical arc length instead of angles effectively decouples the focal length from the image position. This new parameterization does not require an initial focal length estimate for quick convergence, nor does it require a full circle panorama in order to refine the focal length. Experiments with synthetic and real image sets demonstrate the robustness of the method and a speedup of 5 to 20 times over angle based positioning.