The calculated distance (air line) between Rottach-Egern and Karlsruhe is approximately 179 miles respectively 289 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Rottach-Egern and Karlsruhe has been calculated here.
Air line (approximately)
289 kilometers
156 nautical miles