The calculated distance (air line) between Giv'at Shmuel and Modiin Ilit is approximately 15 miles respectively 25 kilometers.
By car or train, the actual journey to Modiin Ilit is certainly longer, as only the direct route (as the crow flies) between Giv'at Shmuel and Modiin Ilit has been calculated here.
Air line (approximately)
25 kilometers
13 nautical miles