The calculated distance (air line) between Röthenbach an der Pegnitz and Mannheim is approximately 125 miles respectively 200 kilometers.
By car or train, the actual journey to Mannheim is certainly longer, as only the direct route (as the crow flies) between Röthenbach an der Pegnitz and Mannheim has been calculated here.
Air line (approximately)
200 kilometers
108 nautical miles