The calculated distance (air line) between Bad Soden am Taunus and Karlsruhe is approximately 78 miles respectively 126 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Bad Soden am Taunus and Karlsruhe has been calculated here.
Air line (approximately)
126 kilometers
68 nautical miles