The calculated distance (air line) between Shiraz and Shahr-e Bābak is approximately 159 miles respectively 256 kilometers.
By car or train, the actual journey to Shahr-e Bābak is certainly longer, as only the direct route (as the crow flies) between Shiraz and Shahr-e Bābak has been calculated here.
Air line (approximately)
256 kilometers
138 nautical miles