The calculated distance (air line) between Erbil and As Sulaymānīyah is approximately 90 miles respectively 145 kilometers.
By car or train, the actual journey to As Sulaymānīyah is certainly longer, as only the direct route (as the crow flies) between Erbil and As Sulaymānīyah has been calculated here.
Air line (approximately)
145 kilometers
78 nautical miles