EstimatorKitStringer layout
Stair calculator — rise, run and every mark on the stringer
A flight is laid out from one measurement — the total rise, finished floor to finished floor — and this divides it into risers, gives you the tread count, the run the flight eats and the stringer length, then issues the layout as cumulative marks from the floor, every one on a sixteenth. It reproduces the published IRC figures beside your numbers: a 7 3/4 inch maximum riser (R311.7.5.1), a 10 inch minimum tread (R311.7.5.2), and the 3/8 inch by which the tallest riser in a flight may exceed the shortest. Those are model-code figures for checking a layout — the code your jurisdiction adopted governs, and nothing here is a finding that a stair is safe.
- IRC R311.7.5 figures shown
- Marks to the nearest 1/16
- Throat and headroom
Code figures, headroom and stringer stock
These open on the residential figures, 7 3/4" and 10". A stair inside a commercial building answers to a different book — the IBC works to 7 in and 11 in — and plenty of jurisdictions amend either one. Set them to what yours adopted.
Floor above is the whole build-up at the header: joist, subfloor, finish and any ceiling hung under it. Twelve inches covers a 2 × 10 floor with 3/4 in sheathing and drywall below.
Tread thickness and floors laid after the stringers
These three are the whole reason a flight that measured right fails on uniformity. The tread sitting on the first notch adds its own thickness to the bottom riser unless the stringer is dropped by it, and tile or hardwood laid afterwards takes that much off the bottom riser or adds it to the top one.
9' 1" of rise, divided the fewest ways that stay under the limit
15 risers at 7 9/32"
- Treads
- 14 at 10"
- Total run
- 11' 8"
- Stringer, nosing to nosing
- 14' 9 7/16"
- Angle off level
- 36°
- Opening in the floor above
- 10' 6 5/8"
15 risers but 14 treads — the upper floor is the last tread, and buying 15 of them is the most common way this flight is ordered wrong.
Riser counts either side of this one
| Risers | Each | Run | 2R + T | Against 7 3/4" |
|---|---|---|---|---|
| 7 25/32" | 10' 10" | 25 9/16" · | over | |
| 7 9/32" | 11' 8" | 24 17/32" | under | |
| 6 13/16" | 12' 6" | 23 5/8" · | under | |
| 6 13/32" | 13' 4" | 22 13/16" · | under | |
| 6 1/16" | 14' 2" | 22 1/8" · | under |
A dot marks a 2R + T outside 24 to 25 in. That range is a proportioning rule out of practice rather than a published limit, and it moves with the stair's job: a basement utility flight is routinely built tighter than the main stair of the same house.
The published figures, next to yours
| Riser height | 7 3/4" maximum | 7 9/32" over 15 risers | within |
|---|---|---|---|
| Tread depth | 10" minimum, nosing to nosing | 10" over 14 treads | within |
| Uniformity across the flight | 3/8" between the tallest riser and the shortest | 1/16" as built, 1/16" on the marks alone | within |
| Rise in one flight | 151" between floors or landings | 9' 1" with no landing entered | within |
| Clear width | 36" minimum | 36" of stair, before a handrail intrudes | within |
| Nosing projection | 3/4 in to 1 1/4 in on solid risers | 3/4" | within |
| 2R + T | 24 in to 25 in — practice, not code | 24 17/32" | practice |
These are model-code figures reproduced so a layout can be checked against them, and nothing more. The code your jurisdiction adopted and the amendments on top of it are what govern, and the building official is the one who signs a stair off. No number on this page is a finding that a stair is safe.
Where each figure comes from
- Riser height: IRC R311.7.5.1 (2021): riser height not more than 7 3/4 in, measured vertically between the leading edges of adjacent treads
- Tread depth: IRC R311.7.5.2 (2021): tread depth not less than 10 in, measured horizontally between the vertical planes of the foremost projection of adjacent treads
- Uniformity across the flight: IRC R311.7.5.1 and R311.7.5.2 (2021): within a flight, the greatest riser height may not exceed the smallest by more than 3/8 in, and the same limit applies to tread depth
- Rise in one flight: IRC R311.7.3 (2021): a flight may not rise more than 151 in between floor levels or landings
- Clear width: IRC R311.7.1 (2021): stairway clear width not less than 36 in above the permitted handrail height
- Nosing projection: IRC R311.7.5.3 (2021): a nosing of 3/4 in to 1 1/4 in where risers are solid and the tread is less than 11 in deep; no nosing required at a tread of 11 in or more
- 2R + T: two risers plus one tread landing between 24 and 25 in — the rule carpenters have used since Blondel put it at 63-65 cm, and a figure that appears nowhere in the IRC
- Headroom: IRC R311.7.2 (2021): 6 ft 8 in of headroom, measured vertically from the sloped line adjoining the tread nosings
Stringer marks, cumulative from the floor
109 in over 15 risers is 7 17/64" apiece, which no tape carries a line for. Marking every riser at 7 1/4" instead pushes the whole remainder onto the last one, and it finishes at 7 1/2" — 1/4" out of step, against the 3/8" the code allows across a flight.
The marks below spread that remainder instead: 4 risers at 7 5/16" and 11 at 7 1/4", a spread of 1/16". Take each mark from the floor rather than from the one below it — stepping off with a square carries the error in one setting into every riser above it, and a cumulative mark cannot.
| Riser | Height | Mark from the floor |
|---|---|---|
| 1 | 7 1/4" | 7 1/4" · 7 1/4" |
| 2 | 7 1/4" | 14 1/2" · 1' 2 1/2" |
| 3 | 7 1/4" | 21 3/4" · 1' 9 3/4" |
| 4 | 7 5/16" | 29 1/16" · 2' 5 1/16" |
| 5 | 7 1/4" | 36 5/16" · 3' 5/16" |
| 6 | 7 1/4" | 43 9/16" · 3' 7 9/16" |
| 7 | 7 1/4" | 50 13/16" · 4' 2 13/16" |
| 8 | 7 5/16" | 58 1/8" · 4' 10 1/8" |
| 9 | 7 1/4" | 65 3/8" · 5' 5 3/8" |
| 10 | 7 1/4" | 72 5/8" · 6' 5/8" |
| 11 | 7 1/4" | 79 7/8" · 6' 7 7/8" |
| 12 | 7 5/16" | 87 3/16" · 7' 3 3/16" |
| 13 | 7 1/4" | 94 7/16" · 7' 10 7/16" |
| 14 | 7 1/4" | 101 11/16" · 8' 5 11/16" |
| 15 | 7 5/16" | 109" · 9' 1" |
The bottom and the top are not equal yet
Cut every notch on its mark and the first tread sits 1" above the floor cut, so the bottom riser walks as 8 1/4" instead of 7 1/4". Take 1" off the foot of the stringer before the level cut and the tread puts that riser back on its mark.
With 0" of finish going down on the lower floor after the stringers are set and 0" on the upper one, the bottom riser ends at 7 1/4" and the top at 7 5/16". Across the whole flight that is a spread of 1/16", against the 3/8" the published figure allows — and those two risers are the ones that spend it.
Stringers, throat and boards
3 stringers at no more than 18" apart across 36" of stair. Each runs 14' 9 7/16" between the outer nosing points, so the shortest board that yields one whole is 16 ft, leaving 14 9/16".
Notching 7 9/32" by 10" out of 2 × 12 removes 5 7/8" measured square to the board — rise times run over the hypotenuse — which leaves a throat of 5 3/8" out of 11 1/4". The 5" people quote for this is not a model-code figure — the IRC sets no throat depth for a cut stringer, and 5 in is the number most building departments and stringer suppliers print, and it varies with the jurisdiction: local amendments name 3 1/2 in about as often as 5 in, and a manufactured or engineered stringer carries its own rating instead. This page prints the number; whether it is enough belongs to whoever wrote the code you build under.
Treads: 42 linear feet of stock at 10 3/4" wide — the 10" run plus the 3/4" nosing — or 14 ready-made treads cut to width, which come 11 1/2" wide (supplier — 11 1/4 in and 11 1/2 in are both stocked). Where treads butt behind the riser boards instead of running over them, deduct the riser thickness from that width.
Risers: 27.3 sq ft over 15 boards. A 4 × 8 sheet rips into 6 strips at 7 9/32" with 4 3/8" left over for the kerfs, and each strip yields 2, so 2 sheets covers the flight.
The hole in the floor above
Headroom is measured straight up from the line joining the nosings, so the opening has to run (80" of headroom + 12" of floor) × 10" of run ÷ 7 9/32" of rise = 10' 6 5/8" back from the edge of the upper floor. Cut it shorter than that and you get the header everybody ducks under on the way down. A shallower riser lengthens the opening rather than shortening it, because the stair drops away from the header more slowly.
Laying out the flight
One measurement, one division, and the two adjustments that decide whether the risers come out equal.
Measure the total rise from finished floor to finished floor
Hook the tape on the upper floor and read down to the lower one, and make both of them the surface you will actually walk on. If the basement slab is getting an inch of tile, or the hall upstairs is waiting on 3/4 inch of oak, add it now — that thickness does not spread itself across fifteen risers, it lands entirely on the bottom or the top one, which is exactly the riser an inspector puts a level on. Feet and inches read fine here: 109, 9' 1" and 9ft 1in are the same climb.
Take the riser count the division gives you, then look either side of it
Total rise over the maximum riser, rounded up, is the fewest risers that stay under the limit — 109 inches gives 15, at a shade over 7 1/4 each. The table shows the counts one below and three above, with the run and the 2R + T each one produces, because the choice is a trade between a comfortable step and the floor it eats: every riser you add brings another tread with it, so 16 risers is nearly a foot more run than 15. Pick from that table rather than from the first number.
Mark the stringer cumulatively, and drop it by one tread thickness
Take every mark from the floor, not from the mark below it: a square set an ugly sixteenth out carries that error into all fifteen risers when you step off, and a cumulative list cannot. Cut the notches, then take the tread thickness off the bottom of the stringer before the level cut — otherwise the first tread sits on top of a full-height notch and the bottom riser is a tread thicker than every other one in the flight.
Risers, treads and headroom
Why does every riser in a flight have to be within 3/8 inch of the others?
Because the code says so and because your foot believes the first two steps. IRC R311.7.5.1 and R311.7.5.2 both put the limit at 3/8 inch: within one flight, the tallest riser may not exceed the shortest by more than that, and the same tolerance governs tread depth. Two or three steps in, a person stops looking and strides on the rhythm the flight has established, which is why an odd riser at the very top or the very bottom is the one that trips people rather than the one in the middle. It is also the easiest rule in the chapter to break by accident, since nothing about it shows up while you are cutting: the two ways it happens are a stringer that was not dropped by the tread thickness, and a floor finish laid after the stairs were framed.
Do I measure the total rise from the subfloor or the finished floor?
Finished floor to finished floor, every time. A stair framed off subfloor heights is correct in every riser except one, and that one absorbs the entire thickness of whatever goes down later — 3/4 inch of hardwood on the lower floor shortens the bottom riser by 3/4 inch, and the same on the upper floor lengthens the top riser by the same amount. Two out of the 3/8 inch you are allowed, gone, from a decision made by the flooring installer months later. If the finishes are not chosen yet, frame to the thickest one you might use and shim, or enter the intended thickness in the two fields on this page so the as-built bottom and top risers are printed before you cut anything.
How many treads do I get for 15 risers?
Fourteen. The top riser lands on the upper floor, and that floor is the last tread — so a flight always has one fewer tread than it has risers, and ordering fifteen treads for fifteen risers leaves you with a spare. The same off-by-one runs through the run: 14 treads at 10 inches is 11 feet 8 inches of floor, not 12 feet 6. It reverses only where the flight stops at a landing that is not the destination floor, in which case the landing is the tread and the counts are equal.
What is the maximum riser height and the minimum tread depth?
7 3/4 inches and 10 inches for a house, from IRC R311.7.5.1 and R311.7.5.2 in the 2021 edition. The riser is measured vertically between the leading edges of adjacent treads and the tread horizontally between the vertical planes of the foremost projections, which is to say nosing to nosing rather than across the board. Those are residential figures: a stair inside a commercial building answers to the IBC instead, where the numbers are 7 inches and 11 inches, and plenty of jurisdictions amend either book. Both limits are editable fields on this page for that reason, and the code your building department adopted is the one that governs, not the one quoted here.
How long does the floor opening have to be for headroom?
Headroom plus the thickness of the floor above, multiplied by the run and divided by the rise. With 80 inches of headroom, a 12-inch floor build-up, a 10-inch tread and a 7 1/4-inch riser, that is (80 + 12) × 10 ÷ 7.25 = 126.9 inches, so the opening runs just under 10 feet 7 inches back from the edge of the upper floor. IRC R311.7.2 sets the 80 inches, measured vertically from the sloped line joining the nosings rather than from any one tread. The counter-intuitive half is that a gentler stair needs a longer hole: drop to a 7-inch riser and the opening grows to nearly 11 feet, because the flight descends away from the header more slowly.
Dividing a rise into equal risers
A stair is one division carrying a great many consequences. Total rise over riser count gives the riser height, and from that single number falls the tread that keeps the flight walkable, the run it eats on the floor, the angle, the length of the stringer, the depth left under the notch and the length of the hole in the floor above. What makes it awkward is that the division almost never comes out on a mark: 109 inches over 15 risers is 7.2667 inches, and there is no line on any tape for 7 and seventeen sixty-fourths. Most calculators print that decimal and stop, which is the point at which their answer becomes somebody else’s problem. Round it to 7 1/4 and mark fourteen of them and the fifteenth has to make up the whole remainder — it comes out at 7 1/2, a quarter inch taller than every other riser in the flight and two thirds of the way through the tolerance on its own. This page distributes the remainder instead — four risers at 7 5/16 and eleven at 7 1/4, a spread of one sixteenth — and gives the marks cumulatively from the floor, because a mark measured from the mark below it inherits every error underneath it.
The published figures are worth stating precisely, because half of what circulates about them is a paraphrase. IRC R311.7.5.1 puts the maximum riser at 7 3/4 inches, measured vertically between the leading edges of adjacent treads, and R311.7.5.2 puts the minimum tread at 10 inches, measured horizontally between the vertical planes of the foremost projection of adjacent treads — nosing to nosing, not the width of the board you buy, which is the run plus the nosing overhang. Both sections carry the same 3/8 inch uniformity limit within a flight. R311.7.2 asks for 6 feet 8 inches of headroom measured from the sloped line joining the nosings, R311.7.1 for 36 inches of clear width, R311.7.3 caps a single flight at 151 inches of rise, and R311.7.5.3 sets the nosing at 3/4 to 1 1/4 inches where risers are solid and the tread is under 11 inches. Those are 2021 residential figures; the IBC works to 7 and 11 for a commercial stair, section numbers move between editions, and jurisdictions amend both. They are reproduced here so a layout can be checked against them, and the limits are editable fields for exactly that reason. Whether a stair passes is decided by the building official, not by this page.
The two things that actually fail inspections are not in the arithmetic at all. The first is the bottom of the stringer: cut all the notches on their marks and the first tread sits on top of a full-height notch, so the bottom riser is a tread thicker than every other one — you take the tread thickness off the foot of the stringer before the level cut, and the tread puts that riser back where it belongs. The second is finish flooring laid after the stairs are framed, which shortens the bottom riser or lengthens the top one by its whole thickness and spends most of the 3/8 inch you were allowed. Both are printed on this page before you cut. The rest is boards: the stringer wants a single length longer than the nosing-to-nosing run of the flight, which is the same “shortest stock that yields one whole piece” question a rafter asks, and the notch takes rise × run ÷ hypotenuse out of it. That diagonal is the same triangle a rafter length is stepped off from, with rise and run swapped for total rise and total run. Treads and riser boards are a take-off: run the tread stock through the linear feet calculator for whole sticks, and the ripped riser strips through the plywood calculator for the sheet count. An exterior flight off a deck is the same layout with the total rise measured to grade and the stringers hung off a rim board.