The calculated distance (air line) between Qom and Shahr-e Kord is approximately 160 miles respectively 257 kilometers.
By car or train, the actual journey to Shahr-e Kord is certainly longer, as only the direct route (as the crow flies) between Qom and Shahr-e Kord has been calculated here.
Air line (approximately)
257 kilometers
139 nautical miles