Stairs are quoted separately from the rooms they connect, and they are the job people most often under-order. The reason is almost always the nosing, or the winders.
Tread depth, front to back, the part you stand on. Measure to the front edge, not to where the nosing starts curving.
Riser height, the vertical face between one tread and the next.
Width, wall to wall or wall to the base of the balusters, depending on whether the carpet runs full width or as a runner.
The carpet run for a single step is tread plus riser, plus an allowance for the nosing, which is the rounded front edge the carpet has to wrap around. That nosing allowance is commonly around an inch and a half per step and it is the number people leave out.
A common working figure for a standard step is about 18 inches of carpet run, covering tread, riser and nosing. Useful for a quick estimate. Not a substitute for measuring, because tread depths vary considerably between older and newer houses and the error multiplies by every step in the flight.
A staircase is typically 13 to 16 steps. An error of an inch per step is over a foot across the flight, and an error of two inches is nearly three feet.
That is the mechanism behind almost every stair carpet shortfall. The per-step figure looks small enough to estimate, and the flight turns a small estimate into a real shortage.
Measure two or three steps rather than one. Stairs are usually uniform, but the bottom and top steps frequently are not, and a bullnose bottom step is both wider and deeper than the rest.
Winders are the wedge-shaped steps on a turn, and they are the single biggest source of under-ordering.
Each winder is a different shape, and each one has to be measured individually at its widest point, because the carpet piece has to cover the whole tread even though most of it is narrower. There is no averaging here. A set of three winders needs three separate measurements, each taken at the wide end.
The offcuts from winders are wedges, and a wedge does not fit anywhere else. So winders waste heavily as well as needing more material, and a staircase with a winding turn can need considerably more carpet than its step count suggests.
A quarter-turn landing is easier: it is a small rectangular floor area, measured as a rectangle and added.
A full-width fit runs wall to wall and needs the full stair width for every step.
A runner sits centred with finished floor showing at each side, and the runner width is your choice. What you measure is the same tread and riser dimensions, but the width comes from the runner specification rather than the staircase, and you also need the length for the whole flight in one continuous piece if the runner is being fitted unbroken.
Runners are usually fitted with the pattern running true up the flight, which means the pattern repeat becomes a factor exactly as it does with wallpaper. Check the repeat before calculating length.
These are the two fitting styles and they use different amounts.
Waterfall runs the carpet straight over the nosing and down the riser, which is faster and uses slightly less. Capped, sometimes called upholstered, wraps the carpet tightly around and under the nosing before continuing, which looks more tailored and uses more.
Decide which you want before ordering, because the difference is real across a full flight. Your fitter will have a preference and it is worth asking.
Stairs are the worst place on a job to be short. The carpet has to be one continuous piece down the flight for appearance, so you cannot patch in a second batch, and a colour or pile-direction mismatch on a staircase is visible from every part of the house.
Measure every step, measure every winder individually, add the nosing allowance, then add the waste factor on top. Measuring a room for carpet works on completely different logic, because there the roll width governs rather than the step count.
For what we recommend overall across every use case, the front page is the place to look.