The calculated distance (air line) between Shāhīn Dezh and Erbil is approximately 146 miles respectively 235 kilometers.
By car or train, the actual journey to Erbil is certainly longer, as only the direct route (as the crow flies) between Shāhīn Dezh and Erbil has been calculated here.
Air line (approximately)
235 kilometers
127 nautical miles