The calculated distance (air line) between Nizhniy Novgorod and Bogorodsk is approximately 25 miles respectively 40 kilometers.
By car or train, the actual journey to Bogorodsk is certainly longer, as only the direct route (as the crow flies) between Nizhniy Novgorod and Bogorodsk has been calculated here.
Air line (approximately)
40 kilometers
21 nautical miles