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Arrive on June 10 and leave on June 13. Is that four days or three nights? It is both.
Calendar dates are inclusive: June 10, 11, 12 and 13. That makes four days on the calendar.
Hotel nights are the gaps between dates: after June 10, 11 and 12. That makes three nights.
Check-out day is still a calendar date, but it is not another hotel night when you leave that day.
Use the free Trip Days and Nights Calculator at Map Your Days. No signup, and your dates are not uploaded or saved.