The calculated distance (air line) between Garmisch-Partenkirchen and Karlsruhe is approximately 162 miles respectively 261 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Garmisch-Partenkirchen and Karlsruhe has been calculated here.
Air line (approximately)
261 kilometers
141 nautical miles