The far end is not usually the problem
Run the defaults and the arithmetic looks straightforward: 42 feet at a quarter inch per foot is 10-1/2 inches of fall, plus an inch and a half of fitting drop at the kitchen wye, in an 11 inch cavity. It does not fit, and it does not fit by a long way once the 4-1/2 inch pipe and the inch and a half under it are counted.
What the point by point walk shows is where it stopped fitting, which is not at 42 feet. The pipe bottom reaches the 11 inch line at about 18 feet along, a foot short of the beam crossing, on slope alone. By the beam at 19 feet it is a quarter inch short. The kitchen wye at 27 feet then takes another inch and a half in a single step, and everything downstream of it inherits that inch and a half on top of the slope, so the run finishes 7-1/2 inches short rather than the 6 it would have been without the fitting.
What the depth actually is
The commonest mistake on this form is entering the joist depth. The joist depth is what you have if the pipe can sit tight to the subfloor with nothing below it, which is never the case. What goes in the field is the distance from the underside of the structure down to the lowest point the whole assembly may reach: the finished ceiling if there is one, the head height you have to keep in a basement, the top of a door opening the run crosses.
Then the pipe eats it from both directions. The outside diameter is 4-1/2 inches on 4 inch DWV, more at a hub. The hanger, the insulation and the ceiling assembly take their own thickness underneath. And the pipe cannot start hard against the deck, so a little goes at the top before the run has begun. On the defaults, 6-1/2 inches of the 11 is gone before a single foot of slope is taken.
The steepest slope that fits
The page gives that back as a number, and it is worth reading before deciding anything else. It is the grade at which the tightest point along the run sits at exactly zero room, computed at every point you entered plus both ends. If it comes back below what you need for the size of line you are running, no amount of care with the grade will make the route work, and the answer lies in the route, the depth or a pump instead.
It is a maximum, not a recommendation. Whether a flatter grade is permitted on the size of pipe you are running is a question for the adopted code and the inspector, and this page has no opinion on it.
Fitting drops are the invisible half
A slope is easy to picture. A fitting that offsets the invert down by an inch and a half is easy to forget, and there are usually several of them: a wye plus an eighth bend to bring a branch in flat, a change of direction that costs depth, a transition between materials. Each one is a step in the profile rather than a ramp, and each one is paid for by every foot of run below it.
They belong in the list with the distance they occur at, because where they occur changes the answer. The same inch and a half taken at 5 feet and taken at 35 feet are two different jobs.
Questions people ask
Why does my drain not fit when the fall is less than the joist depth?
Because the fall is only part of what has to fit. On the default run, 10-1/2 inches of fall in an 11 inch cavity sounds like it clears, but the pipe itself is 4-1/2 inches of that cavity, the hangers and ceiling below take another inch and a half, and a fitting drop takes an inch and a half more. The fall gets whatever is left after the pipe and the assembly have taken their share, which here is about four and a half inches.
What depth should I enter, the joist depth or something else?
The distance from the underside of the structure to the lowest point the whole assembly is allowed to reach. If there is a finished ceiling below, that is the ceiling. If it is an open basement with a head height you have to keep, it is that height. The joist depth flatters the answer because it assumes the pipe can sit hard against the subfloor with nothing beneath it.
Where does a run usually run out of room?
Earlier than the far end, which is where people check. On the default run the pipe bottom reaches the line at about 18 feet on slope alone, before any fitting drop has been taken. A drop taken early makes it worse still, because it is paid for by every remaining foot of the run. The page prints the distance at which the room actually goes, and the point on your list that is tightest, for exactly this reason.
Can I just flatten the grade to make it fit?
Sometimes, and it is not this page that decides. Larger lines are commonly run at gentler grades than small ones, and what is permitted for your size comes out of the code your jurisdiction has adopted. The calculator gives the steepest grade that fits so you can see whether the gap between what fits and what you need is small or hopeless, but the permission question is not arithmetic.
Does this account for hubs, couplings and sag?
No, and it says so. The pipe is treated as a straight barrel at a constant grade. A hub or a coupling stands proud of the barrel, a hanger has its own thickness, and a long run not properly carried will sag between supports and put the low point somewhere the arithmetic does not. Treat the numbers as an upper bound on the room you have.