The calculated distance (air line) between Ingelheim am Rhein and Karlsruhe is approximately 68 miles respectively 110 kilometers.
By car or train, the actual journey to Karlsruhe is certainly longer, as only the direct route (as the crow flies) between Ingelheim am Rhein and Karlsruhe has been calculated here.
Air line (approximately)
110 kilometers
59 nautical miles