The calculated distance (air line) between Ḩayy al Bunayyāt and Karak City is approximately 51 miles respectively 82 kilometers.
By car or train, the actual journey to Karak City is certainly longer, as only the direct route (as the crow flies) between Ḩayy al Bunayyāt and Karak City has been calculated here.
Air line (approximately)
82 kilometers
44 nautical miles