The calculated distance (air line) between Hofheim in Unterfranken and Dortmund is approximately 164 miles respectively 264 kilometers.
By car or train, the actual journey to Dortmund is certainly longer, as only the direct route (as the crow flies) between Hofheim in Unterfranken and Dortmund has been calculated here.
Air line (approximately)
264 kilometers
142 nautical miles