Will the drain carry it?
Fixture units add up plainly here — no curve. The catch is that a branch and a stack of the same size are different pipes, so this checks them separately.
Drainage fixture units, branch and stack kept apart
The DFU values and the capacities come from your book. What this insists on is that a branch and a stack of the same nominal size are not the same pipe.
A fixture's drainage fixture unit value follows the trap it is on, so check the trap you are actually installing rather than the fixture's name. Then read the maximum DFU for your candidate pipe size twice — once from the horizontal branch column and once from the stack column. They are different numbers, and the branch is the smaller one.
The fixtures
The pipe you are considering
Where the load comes from
How this is calculated
total DFU = Σ (count × DFU per fixture)
That is the whole calculation. Unlike water supply there is no probability curve here — drainage fixture units add up directly, because the design case is different: supply worries about simultaneous demand, drainage worries about the pipe's ability to carry solids and to keep its own air column stable.
The comparison against branch and stack capacities is done separately and reported separately, because the same nominal size carries different loads in the two orientations.
What this does not do. It does not size vents, which have their own tables and their own distance-to-trap rules; it does not handle offsets in a stack, which can require the offset to be sized as a branch; and it does not check developed length or fixture-to-vent distance. Those are separate requirements a DFU total says nothing about.
Why the branch is smaller than the stack
A vertical stack and a horizontal branch of the same nominal diameter do not carry the same fixture load, and the stack carries more. The reason is how the water travels.
In a stack, water clings to the wall and falls as an annular sheet with an air core down the middle. That air core is the point: it is what keeps the pressure in the system stable, and what stops traps being siphoned or blown. A stack works well because gravity is pulling along the whole length of the pipe.
A horizontal drain has only its slope. It is designed to run part-full — commonly around half — because the empty space above the flow is the vent path, and because a horizontal pipe running full loses the ability to carry solids at the velocity it needs. Same diameter, less usable capacity, which is why the two columns exist.
The trap size decides the fixture unit value
This catches people because fixture tables are usually listed by fixture name, and it is natural to read down the name column and stop. But the same appliance on a larger trap contributes a larger DFU value, and on a remodel the trap you inherit may not be the one the table assumed. Check the trap.
Passing on fixture units is not the whole job
A DFU total tells you the pipe can carry the flow. It says nothing about whether the system will hold its water seals, and that is the failure people actually notice — a trap that gurgles or empties and lets sewer gas into the room. That is a venting question: vent sizing, the distance from each trap to its vent, and how the stack is vented at the top. A drain sized correctly and vented badly is a system that smells.