A rise too tall for one flight
Thirteen feet from floor to floor is 156 inches, and a single flight may not climb more than 151 (IRC R311.7.3, renumbered R318.7.3 in the 2024 edition). So it becomes two flights with a landing between them: 78 inches each, 11 risers of 7 1/16 inches, 10 treads — and 8 feet 4 inches of run per flight instead of the 16 feet 8 inches one straight flight would have needed. That run is usually the real reason for a landing. Few houses have seventeen feet of floor to give a staircase.
Splitting costs material rather than saving it. One illegal 156 inch flight would take 21 risers and 3 stringers, about $772 at the reference prices here; two flights take 22 risers and 6 stringers, about $983. Each flight carries its own stringers, and that is where the money goes.
The landing is not halfway by default
Nothing says the two flights have to be equal. Type each one's own rise and the page works them out separately — which is worth doing, because the rounding falls differently. Split 156 inches as 90 and 66 and you get 21 risers, not 22, and about $927: each flight rounds its riser count up on its own, and an even split happens to round badly. The risers are then 7 1/2 inches in the lower flight of twelve and 7 5/16 in the upper flight of nine.
The code's 3/8 inch uniformity rule is about the risers within one flight; it does not join two flights together. Your building department is the one to ask before you lean on that.
What the landing itself has to be
At least 36 inches in the direction of travel (R311.7.6), and at least as wide as the stairs it serves. A straight run through a landing and an L that turns 90 degrees on it are the same arithmetic: two flights, one landing, stringers per flight. The turn changes the framing, not the step count.
This page does not count the landing's own framing — the joists, the posts, the decking across it. That is a small platform rather than a stair, and the material belongs to a different list. The stringers, treads and risers for both flights are here, and the landing is the gap between them.
Reading the panel
Every line that describes one flight says which one: "Each riser, Stair 1", "Total run, Stair 1". The counts that add up say so too — "22 risers in all". With two flights those are different numbers and the page will not let them blur.
Add a flight for a three-storey run, or delete one to see the single flight fail its check. The nine code checks run on the flights as typed, with the edition you pick at the top of the assumptions.