The calculated distance (air line) between Eggenstein-Leopoldshafen and Dortmund is approximately 173 miles respectively 278 kilometers.
By car or train, the actual journey to Dortmund is certainly longer, as only the direct route (as the crow flies) between Eggenstein-Leopoldshafen and Dortmund has been calculated here.
Air line (approximately)
278 kilometers
150 nautical miles