The calculated distance (air line) between Katav-Ivanovsk and Chelyabinsk is approximately 131 miles respectively 211 kilometers.
By car or train, the actual journey to Chelyabinsk is certainly longer, as only the direct route (as the crow flies) between Katav-Ivanovsk and Chelyabinsk has been calculated here.
Air line (approximately)
211 kilometers
114 nautical miles