The calculated distance (air line) between Cologne and Bad Homburg vor der Höhe is approximately 88 miles respectively 142 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 Cologne and Bad Homburg vor der Höhe has been calculated here.
Air line (approximately)
142 kilometers
76 nautical miles