The calculated distance (air line) between Karak City and Wādī Mūsá is approximately 61 miles respectively 98 kilometers.
By car or train, the actual journey to Wādī Mūsá is certainly longer, as only the direct route (as the crow flies) between Karak City and Wādī Mūsá has been calculated here.
Air line (approximately)
98 kilometers
53 nautical miles