Framing and carpentry
Stair calculator
The total rise is fixed by the building. Everything else follows from one integer — and the most comfortable stair and the one that fits the space are often not the same integer.
Written and edited by Pablo Ruiz Quintero
Last reviewed 2026-09-17 · Nothing you type leaves your browser
The opening
The total rise is fixed by the building. Everything else on this page follows from it and from one integer: how many risers you divide it into.
Finished floor to finished floor. If tile is going down at the top and not at the bottom, measure to where the floors will be, not where they are.
The walking surface, not counting the nosing. 10 in is the minimum under Residential (IRC).
Horizontal run you have. Leave blank if it is open.
Plumb from the nosing line to whatever is above. Blank to skip.
36 in clear is the minimum. It decides how many stringers go under it.
What a house is built to: 7 3/4 in of riser, 10 in of tread, and no more than 3/8 in between the tallest riser and the shortest.
The standard finished tread, glued up from strips and sanded. What most stairs on show are made of.
Closed is standard indoors. Open needs the 4 in sphere check.
Outdoor stairs are framed rather than finished, and cost about half as much a step.
Used only to pick a regional labour rate. It stays in your browser.
Risers
16
6.750 in each · 15 treads of 10.5 in · 157.5 in of run
Passes Residential (IRC) and 3 of the 3 comfort rules
191 in of stringer at 34.4°, with 5.57 in of 2 × 12 left behind the cuts.
The choice is an integer
The rise is fixed, so the only free variable is how many steps you cut it into.
| Risers | Each | Run | Verdict |
|---|---|---|---|
| 14 | 7.71" | 137" | Legal and fits, but fails every comfort rule — it will feel wrong underfoot |
| 15 | 7.20" | 147" | Legal and fits, passes 2 of the 3 comfort rules |
| 16 · | 6.75" | 158" | Legal, fits, and passes all three comfort rules |
| 17 | 6.35" | 168" | Legal and fits, but fails every comfort rule — it will feel wrong underfoot |
The stair, to scale
Against the code, and against the rules of thumb
- Riser under 7.75 in6.750 in each, all 16 identical
- Tread at least 10 in10.5 in, plus nosing over the riser below
- Width at least 36 in36 in clear
- Stringer throat at least 3.5 in5.57 in of 2 × 12 left behind the cuts
- 2R + T = 24wants 24–25 · ok
- R + T = 17.25wants 17–18 · ok
- R × T = 70.88wants 70–75 · ok
The comfort rules are not code. A stair can pass every legal check and still feel wrong, and these three are how a carpenter tells before building it.
Shopping list
- 2 × 12 stringers
191 in on the diagonal each, cut from stock with room for the plumb and level cuts at the ends3 stringers · 51 ft - Red oak tread
One to each of the 15 steps — the top step is the floor you are arriving at15 pieces - Risers
6.750 in each, and every one of them that height16 pieces
What it costs
National average. Stringers, treads, risers and carpentry. Handrail, balusters, newel posts and finishing are separate and on a finished stair they often cost more than this.
$253 a step. A stair is priced per step everywhere in the trade, because the work per step barely changes with the flight — deck stairs are the same carpentry at about half the rate, since nothing gets finished.
Worth knowing
- 16 risers of 6.750 in, and they all have to be that. The code allows 0.375 in between the tallest and the shortest across the whole flight, which sounds generous and is not: it is the tolerance for the entire stair, not for each step. Measure the total rise to the FINISHED floor at both ends — a layer of tile at the top and none at the bottom is how a flight ends up out of tolerance before anybody cuts anything.
- Drop the stringer by 1 in at the bottom — the thickness of one tread. Cut the triangles and set it down as it is and the first step is 1 in taller than every other one, which fails the variation rule on the step people trip on most.
- The lip of the tread projecting over the riser below. It adds walking depth without adding to the total run, and under an 11 in tread the code requires it. At 10.5 in of tread it is required, between 0.75 and 1.25 in, and it does not count towards the tread depth the code asks for.
- 3 stringers at 36 in wide: no more than 18 in apart, which is what a 1 in tread over a closed riser carries without flexing. Thinner stock — 5/4 decking on an outdoor flight — wants 16 in instead, and that is another stringer on a wide stair.
On this page — 8 sections
The whole problem is one integer
The short version
- The rise is fixed; the riser count is not. It is a whole number, and it is the only thing you choose.
- One fewer tread than risers. The top step is the floor you arrive at.
- Drop the stringer one tread thickness. Or the first step is taller than every other one.
- 0.375 in of variation across the whole flight. Not per step — per stair.
A stair is the most constrained thing in a house. The floor is where it is and the floor above is where it is, so the total rise is given and cannot be argued with. Everything else follows from a single decision: how many steps you divide that height into.
And that decision is an integer. There is no 15.4-riser stair. With nine feet of rise you are choosing between fifteen steps of 7.2 in and sixteen of 6.75 in, and the gap between them is not a rounding error — it is ten and a half inches of floor space, which is frequently the difference between a stair that fits and one that lands in a doorway.
Every stair calculator returns one number. That hides the choice, which is the only interesting part.
risers = round(total rise ÷ 7) · riser = total rise ÷ risers
- total rise
- finished floor to finished floor, in inches
- 7 in
- a comfortable riser, used only to find the starting integer
- treads
- risers − 1, because the upper floor is the top step
- total run
- treads × tread depth
Worked through — 108 in of rise ÷ 7 = 15.4. Sixteen risers gives 108 ÷ 16 = 6.75 in each and 15 treads, so at 10 1/2 in of tread the stair needs 157.5 in of run. Fifteen risers gives 7.2 in each and 14 treads — 147 in of run, and 10.5 in of floor back.
Legal and comfortable are different questions
The code sets a ceiling on the riser and a floor under the tread and then stops. Inside that box are stairs that feel effortless and stairs that feel wrong, and carpenters have three rules for telling them apart — none of which appear in any code book.
| Rule | Wants | Where it comes from |
|---|---|---|
| 2R + T | 24–25 | The oldest of the three and the one most carpenters check. It comes from the length of an average pace on the level, about 25 in, and what climbing takes out of it. |
| R + T | 17–18 | The quick one, done in the head on site. |
| R × T | 70–75 | The least known and the most forgiving of unusual stairs, because it allows a tall riser to buy a deep tread. |
MaterialsEstimator, Stair layout practice and material survey · checked 2026-09-17
What an inspector actually measures
| Requirement | Residential | Commercial |
|---|---|---|
| Maximum riser | 7.75 in | 7 in |
| Minimum tread | 10 in | 11 in |
| Variation across the flight | 0.375 in | 0.375 in |
| Minimum headroom | 80 in | 80 in |
| Minimum width | 36 in | 44 in |
| Handrail height | 34–38 in | 34–38 in |
| Gap a sphere must not pass | 4 in | 4 in |
Adopted codes vary by jurisdiction and amendments are common. These are the model figures; the ones that apply are whatever your building department adopted.
International Code Council, International Residential Code, Sections R311.7 and R312, Stairways and guards · checked 2026-09-16
Cutting the stringers, and the two cuts people miss
A stringer is a 2 × 12 with triangles cut out of it, and the thing that carries the stair is not the triangles — it is what is left behind them. That leftover is called the throat, and a deep tread with a tall riser can cut so much away that there is barely a board left.
throat = 11.25 − (riser × tread) ÷ √(riser² + tread²)
- 11.25 in
- the real depth of a 2 × 12
- riser, tread
- the step being cut, in inches
- √(riser² + tread²)
- the diagonal of one step
Worked through — A 6.75 in riser with a 10.5 in tread: the step diagonal is 12.48 in, so the cut takes 6.75 × 10.5 ÷ 12.48 = 5.68 in, leaving 5.57 in of throat. Comfortably over the 3.5 in minimum. Push the riser to 7.75 and the tread to 11 and the throat falls to 4.94 in — still legal, and visibly less stair.
The two cuts that are not on the layout
- Drop the bottom by one tread thickness. There is no tread beneath the first step to make up the height, so the stringer has to come down by exactly that much.
- Take the riser board thickness off the top plumb cut where the stringer meets the header, or the top step gains it.
- Lay out with a framing square and stair gauges, marking every step from the same setup — stepping the square along by eye accumulates error down the board.
- Cut the triangles short with the circular saw and finish the corners by hand. Overcutting the inside corner is what actually breaks stringers.
- 18 in maximum between stringers, so a 36 in stair gets three.
- Hang the top on a ledger or hangers, not on toenails. The entire load of the stair arrives at that one connection.
- Check the throat before cutting anything, not after.
3.5"
Minimum throat
left in the 2 × 12
18"
Stringer spacing
maximum, or treads flex
0.375"
Riser variation
across the whole flight
80"
Headroom
plumb from the nosings
When it does not fit
The commonest problem with a stair is not the geometry, it is the floor plan. A straight flight for nine feet of rise needs about thirteen feet of floor, plus landing space at both ends, and a great many houses do not have it.
| Straight flight | Turned, with a landing | |
|---|---|---|
| Floor space | The full run in one line | Splits it around a corner |
| Cost | The baseline | Landing framing and a second set of stringers |
| Moving furniture | Hard — nothing bends | Harder, and a sofa may not go at all |
| Falling | The whole flight | The landing stops it |
| Headroom | One continuous problem | Two smaller ones |
| Winders instead of a landing | — | Saves the most space, most restricted by code |
The temptation when space is short is a steeper stair, and within the code there is real room for it: pushing the riser from 6.75 to 7.75 in on a nine-foot rise saves over twenty inches of run. It is legal and it is noticeably harder to climb, every day, for as long as the house stands.
Same code and same geometry, at about half the labour — and the landing at the bottom needs a footing, which the deck calculator sizes along with everything else.
Is this a deck stair?Six ways this goes wrong
01Measuring the rise to the subfloor
Finish thicknesses differ at the two ends and the difference lands entirely on the first or last step, which blows the 0.375 in variation limit on its own.
Instead — Measure to where the finished floors will be. If they are not down yet, add their thicknesses on paper.
02Forgetting to drop the stringer
There is no tread under the first step to make up the height, so the whole stair sits one tread thickness high and the bottom step is that much taller than the rest.
Instead — Cut the triangles, then take exactly one tread thickness off the bottom edge.
03Cutting treads equal to risers
There is always one fewer tread, because the upper floor is the top step. Order by the riser count and one tread goes back.
Instead — Treads = risers − 1. Check it against the drawing before ordering.
04Leaving headroom until after the stringers are cut
Headroom is the one thing adjusting the risers cannot fix, and at 80 in it fails more basement stairs than every other requirement together.
Instead — Check it at layout, plumb from the nosing line. If it fails, the opening above has to change and that is a framing job.
05Chasing the steepest legal stair to save floor space
7.75 in is a limit, not a target. The saving is real — twenty inches of run on a nine-foot rise — and so is climbing it several times a day for thirty years.
Instead — Take the space from somewhere else if there is any, or turn the flight. Only go to the limit when there is genuinely nothing else.
06Ignoring the throat
A tall riser with a deep tread can cut a 2 × 12 down to less than 4 in of remaining board. The stair is legal, passes inspection and flexes underfoot from the first day.
Instead — Work it out before cutting. Under 3.5 in, use a deeper stringer or hang the treads on cleats instead of cutting the board away.
How the calculator works it out
- 01Measure the total rise to the finished floorsBoth ends, as they will be when the job is done. Tile at the top and bare deck at the bottom is how a stair ends up out of tolerance.
- 02Divide it into a whole number of risersTry the integers either side of total rise over 7. One of them is comfortable, one of them fits the space, and they are often not the same one.
- 03Check the riser against the code7.75 in maximum in a house, 7 in where the commercial code applies.
- 04Set the tread and get the total runOne fewer tread than risers, times the tread depth. That is the floor space the stair needs, and it is usually the surprise.
- 05Check headroom before cutting anything80 in plumb from the nosing line. It cannot be fixed by adjusting risers — it needs the opening above changed.
- 06Cut the stringers and drop them one tread thicknessLay out with a framing square and stair gauges, cut the triangles, then take the tread thickness off the bottom.
Riser, tread, variation, headroom, width and the four-inch sphere come from the residential code, and the tighter commercial figures from the building code. The three comfort rules, the stringer drop, nosing projection and the material and labour figures come from a survey of stair practice. All of it is on the sources page, dated.
Two things to be clear about. Adopted codes vary by jurisdiction and local amendments to the stair section are common — these are the model figures, not a permit. And the riser options are offered as a short list rather than a single answer on purpose: the stair that is most comfortable and the stair that fits the space are frequently different integers, and that is a decision, not a calculation.
Nothing you type is sent anywhere — the whole thing runs in your browser.
The words on a stair drawing
Two are worth knowing before cutting: the throat, because it decides whether the stringer can carry the stair, and dropping the stringer, because forgetting it ruins the first step.
- Rise
- The vertical of one step. Total rise is the whole flight, finished floor to finished floor, and it is the one number you cannot change.
- Run
- The horizontal of one step, which is the tread depth without the nosing. Total run is the floor space the flight eats, and it is what a stair runs out of.
- Tread
- The board you stand on. There is always one fewer tread than riser, because the last riser brings you up to the floor and the floor is the top step.
- Riser
- The vertical board between treads, and also the word for the height itself. Open-riser stairs have the height without the board.
- Stringer
- The sawtooth-cut 2 × 12 carrying the steps. Cut from nothing smaller, because what matters is how much board is left behind the cuts.
- Throat
- The width of board remaining behind the cut-outs, measured square to the stringer. Under 3.5 in it has no section left to carry anything, and it is the check nobody does until the stair flexes.
- Dropping the stringer
- Cutting the bottom of the stringer down by one tread thickness. Skip it and the first step is that much taller than every other one — on the step people trip on most.
- Nosing
- The lip of the tread projecting over the riser below, 0.75 to 1.25 in. It adds walking room without adding to the total run, and under an 11 in tread it is required.
- Headroom
- Clear height measured plumb from the nosing line to whatever is above it. 80 in minimum, and it is the requirement that stops more basement stairs than any other.
- Variation
- The difference between the tallest riser in a flight and the shortest. The code allows 0.375 in across the whole stair — not per step — because an uneven step is what a foot finds by falling through it.
- Four-inch sphere
- The test for any gap in a guard or an open riser: a 4 in sphere must not pass through. It is the size of a small child's head, which is exactly why the number is what it is.
- Winder
- A tapered tread that turns a corner instead of a landing. It saves space and it is the most restricted thing in the stair section of the code, because the narrow end is where people fall.
Common questions
- How do you calculate stairs?
- Take the total rise, floor to floor, and divide it by about 7 in to get a starting number of risers. Round it to a whole number — that is the only choice in the whole exercise — and divide the total rise by it to get the exact riser height. Treads are one fewer than risers, and the total run is that count times the tread depth.
- How many stairs for 9 feet?
- 108 in divided by 7 is 15.4, so it is 15 or 16 risers. Sixteen gives 6.75 in each, which with a 10 1/2 in tread passes all three comfort rules; fifteen gives 7.2 in and needs 10 1/2 in of run less. Both are legal. Which one is right depends entirely on whether you have the floor space.
- What is the maximum riser height?
- 7.75 in under the residential code, 7 in under the commercial one — and the second number is why a stair in a converted shop is noticeably longer than the same rise in a house. The limit that catches people is not the maximum, though: it is the 0.375 in allowed between the tallest and shortest riser across the whole flight.
- Why is there one more riser than treads?
- Because the last riser lifts you onto the upper floor, and the upper floor is the top step. A 16-riser stair has 15 treads. It is the off-by-one that costs a tread, and getting it wrong means ordering one too many or cutting the run 10 in short.
- What is the 2R + T rule?
- The oldest of the three and the one most carpenters check. It comes from the length of an average pace on the level, about 25 in, and what climbing takes out of it. Two risers plus a tread should land between 24 and 25 in. It is not code and no inspector checks it — it is how you know a stair will feel right before you build it.
- How long does a stringer need to be?
- The hypotenuse: the square root of the total rise squared plus the total run squared. A 9 ft rise over 157 in of run gives about 191 in, so it comes out of a 18 ft board once you allow for the plumb cut at the top and the level cut at the bottom.
- How many stringers do I need?
- One every 18 in of width, so a 36 in stair takes three and a 48 in stair takes four. Spacing them further apart makes the treads flex underfoot, which is the first thing anybody notices about a cheap stair.
- What does dropping the stringer mean?
- Cutting the bottom of the stringer down by the thickness of one tread, because at the bottom there is no tread below to make up the height. Forget it and the first step is a tread thickness taller than all the others — an inch or an inch and a half — which both fails the variation rule and is the step people catch a toe on.
- What is the minimum headroom for stairs?
- 80 in — 6 ft 8 in — measured plumb from a line along the nosings to whatever is above. It is the requirement that kills more basement stairs than anything else, and unlike the riser height it cannot be solved by changing the stair: the opening above has to get longer.
- Can stair treads be too deep?
- Yes, and it is the least intuitive thing about stairs. Past about 12 in of tread there is no riser height that satisfies all three comfort rules at once — the stride stops matching the climb, and people either shuffle or take two paces per step. The long shallow flight everyone pictures as gentle is not, by the measures carpenters use.
- How much does a staircase cost?
- Roughly $160 a step for interior carpentry in oak, so a 16-step flight is around $2,600 for the stair itself. The handrail, balusters and newel posts on a finished stair frequently cost more than that again, and they are quoted separately everywhere.
- Do deck stairs follow the same rules?
- The same code and the same geometry, at about half the labour, because nothing gets finished. The differences are practical: treads are two boards with a gap so they shed water, risers are usually left open, and the bottom lands on a footing rather than a floor.
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About the author
Pablo Ruiz Quintero — Editor
Editor of MaterialsEstimator. Decides which documents count as a source, what every default value is, and where the line sits between what the reader parses and what the engines compute.
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