The calculated distance (air line) between Mannheim and Bad Homburg vor der Höhe is approximately 51 miles respectively 83 kilometers.
By car or train, the actual journey to Bad Homburg vor der Höhe is certainly longer, as only the direct route (as the crow flies) between Mannheim and Bad Homburg vor der Höhe has been calculated here.
Air line (approximately)
83 kilometers
45 nautical miles