The roll width is the whole problem
Carpet is made on a loom of a set width and sold off the roll. Everything about laying it in a room follows from that: a room narrower than the roll takes one piece and has no seams, a room wider than the roll takes two or more drops, and every joint between them is a seam somebody has to cut straight and hold together. The yardage is not the floor area — it is the roll length used, times the full roll width, whether or not you needed all of that width.
That last point is where the sticker shock comes from. A 14 ft wide room off a 12 ft roll takes two drops: one full 12 ft width and one strip 2 ft wide, and the strip is cut off a full 12 ft width. You buy 24 ft of width to cover 14, and the ten feet left over is offcut unless another room in the same job can use it.
Turning the layout does two things at once
Run the drops the other way and the number of drops changes, and so does the length of each. Sometimes that saves material and adds a seam; sometimes it saves both. The two do not move together, which is why the page prints them separately rather than picking a winner on yardage alone. A room that comes out a yard cheaper the other way round but puts a seam straight down the middle of the walking line is not cheaper.
Pile direction removes the usual trick
On almost every other rolled good, an awkward offcut gets turned end for end and used somewhere. Carpet has a nap: the fibres lean, and a drop laid the other way up reflects light differently enough that the seam between them reads as a colour change across the room. Every drop runs the same direction, so the offcuts stay offcuts. It is also the reason a patch cut from a leftover piece years later has to be oriented the same way as the floor it goes into.
A repeat costs in both directions
A patterned carpet has to line up across the seam, so every drop gets cut at a whole number of repeats, which rounds each cut length up. A half-drop pattern adds to that: alternate drops start half a repeat along the roll, so the roll length grows again. The page shows both parts separately, because the first one is a few inches per drop and the second can be a whole extra repeat on the job.
Questions people ask
How many yards of carpet do I need for a 14 by 20 room?
Off a 12 ft roll with drops running the length, that is two drops of about 20 ft 6 in each, so roughly 41 ft of roll and about 55 sq yd, against 31 sq yd of actual floor. Run the drops the other way and it becomes two drops of 14 ft 6 in, about 29 ft of roll and 39 sq yd, with a seam that now runs across the room rather than along it. The page prints both so the trade is visible.
Where should a carpet seam go?
That is the installer decision this page deliberately does not make. What the arithmetic settles is that the seams fall at multiples of the roll width from whichever wall the first drop starts against, so the way to move a seam is to change which wall you start from or which way the drops run. Away from the main light, out of the traffic line and not through a doorway are the usual considerations, and they beat saving a yard.
Why is the yardage so much more than the room area?
Because you buy roll width, not the width you use. A 2 ft fill strip is cut from a full width of carpet and the rest of that width is offcut unless something else on the job takes it. Add the trim on both ends of every drop and any pattern repeat rounding and the gap widens further. On a small awkward room the purchased area can be half again the floor area and nothing has gone wrong.
Can I turn a drop around to make it fit?
No, and this is the one rule that catches people who are used to sheet goods. Carpet pile leans one way and a drop laid the other way up looks like a different dye lot under the same light. Every drop runs the same direction, which is why the offcuts on a carpet job stay offcuts and why a patch has to be oriented to match the floor around it.
Does a wider roll always use less carpet?
Not always. A 13 ft 1 in roll into a 14 ft room still needs a second drop, and now the fill strip is 11 in instead of 2 ft, cut off a wider and more expensive width. Whether the wider roll wins depends on how the room divides into it, which is what the drop count and the fill strip width on this page are showing. Change the roll width field and watch both move.