The calculated distance (air line) between Murnau am Staffelsee and Karlsruhe is approximately 158 miles respectively 254 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Murnau am Staffelsee and Karlsruhe has been calculated here.
Air line (approximately)
254 kilometers
137 nautical miles