The calculated distance (air line) between Bad Königshofen im Grabfeld and Dortmund is approximately 155 miles respectively 250 kilometers.
By car or train, the actual journey to Dortmund is certainly longer, as only the direct route (as the crow flies) between Bad Königshofen im Grabfeld and Dortmund has been calculated here.
Air line (approximately)
250 kilometers
135 nautical miles