Where the width comes from
Draw two parallel lines up the flight. One runs through the front corners of the steps, where each tread meets the riser below it. The other runs through the inside corners, where each tread meets the riser above it. Those two lines are parallel to the rake and the skirt has to reach from one to the other, plus whatever reveal you want beyond each.
The gap between them is rise times run divided by the step hypotenuse. On a 7-1/2 by 10 stair that is 7.5 times 10 divided by 12.5, which is exactly 6 inches. Add an inch and a half of reveal above and the same below and the board has to be 9 inches wide, which a 1x10 covers with a quarter inch to spare and a 1x8 does not cover at all.
The bottom cut nobody can make on a mitre saw
The two end cuts are complements. The plumb cut at the top is the rake angle off square and the level cut at the bottom is whatever is left of 90. On the default stair the rake is 36.87 degrees, so the top cut is 36.87 off square and the bottom is 53.13.
Most mitre saws do not swing that far, and the page compares it against the number you read off your own saw rather than assuming one. This is why the bottom of a skirtboard gets marked with a square and cut freehand or with a circular saw, and it is why a shallower stair is harder to trim than a steep one — as the flight flattens, the top cut gets easier and the bottom cut gets worse.
Marking the board
Every step corner sits one step hypotenuse further along the top edge than the last, which is 12-1/2 in on the default stair. The page lists them as running measurements from the first mark, so you can pull one tape up the board instead of stepping a square fourteen times and accumulating the error. Twenty-four steps get listed individually and anything past that gets the spacing instead.
What the nosing does and does not do
Nothing, for this calculation, as long as the skirt runs behind the treads. The treads pass over the top of the skirt, the nosing projects past it, and the rake line is set by the step corners. That is the usual detail and it is the one this page assumes.
Run the skirt over the treads and everything changes: the board gets cut to the actual step profile, the width has to allow for the nosing projection, and the number here becomes a starting point rather than an answer. That version is also far less forgiving of risers that are not all the same height, because every step is cut individually and the errors do not average out.
A joint in the rake
Anything over about 15 ft of rake needs a joint in 16 ft stock once you have added the end allowances, so the default flight at 13 ft 11 in scrapes in. A joint in a skirt shows more than a joint in a baseboard because the rake turns it into a diagonal across the face of the board. Land it over a stringer so both halves can be nailed, and put it high in the flight where it is read at a glancing angle rather than square on.
What this page does not settle
Nothing here is a code figure. Riser heights, tread depths, the tolerance between the tallest and shortest riser in a flight, handrails and guards are all set by the authority that inspects the work, and this page states none of them. It takes the rise and run you measured and does geometry on them. If the rise you measured is not the rise you want, that decision happens on the stair stringer calculator before the skirt is cut.
Questions people ask
How wide does a stair skirtboard need to be?
On a 7-1/2 by 10 stair, 6 inches to cover the steps and nothing more. Add the reveal you want above the treads and below the step corners and it becomes the board width — an inch and a half each way gives 9 in, which a 1x10 covers. Steeper or deeper stairs change the 6 in figure, which is rise times run over the step hypotenuse.
What angle do I cut the top and bottom of a skirt board?
They are complements of each other. On the default 7-1/2 by 10 stair the plumb cut at the top is 36.87 degrees off square and the level cut at the bottom is 53.13. The bottom one is past the swing of many mitre saws, which is why it is normally marked with a square and cut by hand. The page compares both against whatever swing you read off your own saw.
Will a 1x10 work as a skirt board?
It depends on the stair and the reveals, which is what the calculator is for. A 1x10 measures about 9.25 in actual, so on the default stair it covers the 6 in step depth with 3.25 in of reveal to distribute. A steeper stair eats that quickly: at 8 by 9 the step depth goes to 5.98, at 8 by 11 it is 6.47.
Does the nosing change the skirt width?
Not when the skirt runs behind the treads, which is the usual detail and the one assumed here. The treads pass over the skirt and the nosing projects past it, so the rake is set by the step corners. Running the skirt over the treads is a different job with a different cut, and this width becomes a starting figure rather than the answer.
How long a board do I need for the skirt?
The rake length plus an allowance at each end. Fourteen risers at 7-1/2 with 13 treads at 10 gives 105 by 130 in, which is 167-1/8 in along the rake, or just under 14 ft. Add six inches at each end for the cuts and it is 179-1/8 in — over a 14 ft stick, under a 16 ft one.