The calculated distance (air line) between Yazd and Shahr-e Bābak is approximately 131 miles respectively 211 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 Yazd and Shahr-e Bābak has been calculated here.
Air line (approximately)
211 kilometers
114 nautical miles