An upcoming NASA mission, the Carruthers Geocorona Observatory, will provide better measurement coverage of the Earth's outermost atmospheric layer than is available in existing data. The Carruthers mission will use a technique called tomography to create 3D maps of this part of the atmosphere, similar to a medical CT scan. A major goal of the mission is not just to create a single 'best-fit' map, but also to show the level of confidence in the data at every part of that map. This uncertainty quantification is important for distinguishing real atmospheric structures from glitches caused by the mapping process itself. However, standard methods for calculating this uncertainty are too slow and computationally expensive for tomography. This research presents a faster method to solve this problem, utilizing a mathematical shortcut to efficiently calculate the uncertainty for the entire 3D map.