Answer
The Calculate Geometry tool returns negative values due to incorrect geometry in the shapefile. Outer Lines that are digitized in a clockwise direction and inner rings that are digitized in a counter-clockwise direction produce an incorrect polygon arrangement. This arrangement, also known as 'incorrect ring order', creates negative values in the shapefile.
However, users can rectify the negative values by fixing the arrangement error.
1. Run the Check Geometry tool to determine the error in the shapefile.
2. Use the Feature Class To Feature Class tool to create a duplicate copy of the original shapefile.
3. Once the duplicate file is ready, run the Repair Geometry tool in the duplicate copy of the shapefile; this fixes the copy.