Sinkholes are the most common karst feature and their extent can be a good indicator of overall karst development. Previous methods of measuring sinkhole extent include sinkhole density, defined as the number of sinkholes per unit area, and sinkhole area ratio, the ratio of sinkhole area per unit area. Sinkhole density is easily measured, but is a poor indication of sinkhole extent because it does not reflect sinkhole area or depth. Sinkhole area ratio more closely reflects the extent of sinkholes (although it does not reflect depth), but is very time consuming to execute. We here present a new method of measuring sinkhole extent that reflects both sinkhole area and depth, and is very rapidly measured. The method consists of placing a grid over a given map area and counting the number of intersections between grid lines and closed (hachured) contour lines. This “sinkhole index” is defined as the total length of the grid lines divided by the total number of intersections, which is equivalent to the mean spacing of closed contour lines in the area. We applied this method to 5056 blocks with dimensions of 2.5' latitude by 2.5' longitude, covering most of the state of Tennessee. A map showing the sinkhole index for all blocks is similar to a previously published map of karst development, although the present map expresses the variations in surface karst more accurately. The sinkhole index map was also compared with analogous maps of cave distribution, using data from the Tennessee Cave Survey. Maps showing the number of caves and total length of caves in each 2.5' block are grossly similar to the sinkhole index map, although there are some interesting exceptions. At a more detailed scale, however, the correlation is relatively weak, with r values between block values ranging from 0.41 for the Cumberland Plateau to 0.11 for the Central Basin. Thus, whereas sinkhole and cave development are promoted by similar conditions, their formation at a particular location does not appear to be closely linked.