The calculated distance (air line) between Hannover and Bad Homburg vor der Höhe is approximately 156 miles respectively 251 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 Hannover and Bad Homburg vor der Höhe has been calculated here.
Air line (approximately)
251 kilometers
135 nautical miles