The calculated distance (air line) between Rothenburg ob der Tauber and Karlsruhe is approximately 84 miles respectively 136 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Rothenburg ob der Tauber and Karlsruhe has been calculated here.
Air line (approximately)
136 kilometers
73 nautical miles