The calculated distance (air line) between Port-au-Prince and Cap-Haïtien is approximately 85 miles respectively 136 kilometers.
By car or train, the actual journey to Cap-Haïtien is certainly longer, as only the direct route (as the crow flies) between Port-au-Prince and Cap-Haïtien has been calculated here.
Air line (approximately)
136 kilometers
73 nautical miles