How the headroom calculator works
The 80-inch line
Code requires 6 ft 8 in (80 in) of clearance measured vertically from every tread nosing. On stairs that pass through a floor opening, the critical point is where the stair passes the upper-floor edge: a person standing at the tread directly below needs 80 inches before the ceiling (the open floor) arrives.
The check, simplified
From the bottom, count treads until cumulative rise exceeds 80 inches — those treads must ALL fit within the opening's length (each consuming one tread depth). The calculator runs that arithmetic: required opening = tread × treads-to-clear. If your opening is shorter, options are: lengthen the opening (framing work), steepen toward the 7¾ cap (shortens tread depth), or accept the "duck" — which inspection will not.
Field verification
Before cutting: snap a plumb line at the opening's edge, measure up 80 inches, and picture the tallest user. After framing, re-measure — joists, headers, and ducts routinely claim an inch. After drywall is the expensive version of this test.