Spherical motion is a special case of camera motion where the camera moves on the imaginary surface of a sphere with the optical axis normal to the surface. Common sources of spherical motion are a person capturing a stereo panorama with a phone held in an outstretched hand, or a hemi-spherical camera rig used for multi-view scene capture. However, traditional structure-from-motion pipelines tend to fail on spherical camera motion sequences, especially when the camera is facing outward. Building upon prior work addressing the calibrated case, we explore uncalibrated reconstruction from spherical motion, assuming a fixed but unknown focal length parameter. We show that, although two-view spherical motion is always a critical case, self-calibration is possible from three or more views. Through analysis of the relationship between focal length and spherical relative pose, we devise a global structure-from-motion approach for uncalibrated reconstruction. We demonstrate the effectiveness of our approach on real-world captures in various settings, even when the camera motion deviates from perfect spherical motion.