According to the International Code Council 404.3 Minimum ceiling heights: “Basement rooms in one- and two-family dwellings occupied exclusively for laundry, study or recreation purposes, having a ceiling height of not less than 6 feet 8 inches (2033 mm) with not less than 6 feet 4 inches (1932 mm) of clear height under beams, girders, ducts and similar obstructions.”
Minimum ceiling height clearance for a basement is 6’-8”,
One more important height to finish basement, will be the height between stairs nosing to ceiling beam, which is 7’-2”