The calculated distance (air line) between Frankfurt am Main and Bad Homburg vor der Höhe is approximately 8 miles respectively 13 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 Frankfurt am Main and Bad Homburg vor der Höhe has been calculated here.
Air line (approximately)
13 kilometers
7 nautical miles