The calculated distance (air line) between Königstein im Taunus and Karlsruhe is approximately 81 miles respectively 130 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Königstein im Taunus and Karlsruhe has been calculated here.
Air line (approximately)
130 kilometers
70 nautical miles