Getting furniture up the stairs
On a straight run the item travels along the slope. What has to fit is its cross-section, set against the stair width and the headroom measured square to the slope, which is less than the vertical headroom.
Headroom shrinks with the pitch
With vertical headroom H (from the line of nosings to the ceiling) and pitch angle α, the clearance square to the slope is H × cos α. A stair with 7½ in risers and 10 in treads has a pitch of about 36.9°, so cos α = 0.8, and 80 in of vertical headroom gives only 64 in square to the slope. For reference, the U.S. International Residential Code generally requires at least 36 in of width and 6 ft 8 in of headroom for stairs in new homes. Older and other buildings vary.
The hard parts aren't modelled
The difficult moments are at the top and bottom, where the item changes from level to sloped under a ceiling edge, and at landings and winders. These are 3D problems that depend on details such as the bulkhead and the balustrade. Carry Clearance checks only the straight run (and flat landing turns) and never reports a route with stairs as "probably fits". The best it will say is that the straight run clears.
Safety
Stairs are where moving injuries and damage happen. Heavy or awkward items need enough people, the right straps or dollies, and often professionals.
Sources
- International Code Council, International Residential Code (2021) §R311.7.1 (width) and §R311.7.2 (headroom).