The calculated distance (air line) between Mannheim and Castrop-Rauxel is approximately 152 miles respectively 244 kilometers.
By car or train, the actual journey to Castrop-Rauxel is certainly longer, as only the direct route (as the crow flies) between Mannheim and Castrop-Rauxel has been calculated here.
Air line (approximately)
244 kilometers
132 nautical miles