The calculated distance (air line) between Mainz and Bad Soden am Taunus is approximately 15 miles respectively 24 kilometers.
By car or train, the actual journey to Bad Soden am Taunus is certainly longer, as only the direct route (as the crow flies) between Mainz and Bad Soden am Taunus has been calculated here.
Air line (approximately)
24 kilometers
13 nautical miles