The calculated distance (air line) between Karbala and Sarpol-e Z̄ahāb is approximately 166 miles respectively 267 kilometers.
By car or train, the actual journey to Sarpol-e Z̄ahāb is certainly longer, as only the direct route (as the crow flies) between Karbala and Sarpol-e Z̄ahāb has been calculated here.
Air line (approximately)
267 kilometers
144 nautical miles