The calculated distance (air line) between Buckingham and Stoke-on-Trent is approximately 86 miles respectively 138 kilometers.
By car or train, the actual journey to Stoke-on-Trent is certainly longer, as only the direct route (as the crow flies) between Buckingham and Stoke-on-Trent has been calculated here.
Air line (approximately)
138 kilometers
74 nautical miles