Stair Calculator
One measurement — finished floor to finished floor — becomes a riser count, an exact riser height, a total run, and a stringer length. Every riser count is checked against the code limits, and the table of options is the part worth reading.
One straight flight of stairs
Measure from the finished floor below to the finished floor above — including any flooring not yet laid. Nine feet is 108 inches. Every riser in the flight comes out of this one measurement, so an error here is an error in all of them.
This is the choice you actually make. Riser height is not an input anywhere on this page, because it cannot be: it is the rise divided by this number. The table below shows every count worth considering.
Measured nosing to nosing, which is what the code measures — not the width of the board. Ten inches is the residential minimum; eleven walks noticeably better if the floor space is there.
15 equal risers of 7 3/16 in on the tape, and 14 treads taking up 11 ft 8 in of floor. This flight is inside the IRC limits for riser height, tread depth, and rise between landings.
- Risers
- 15
- Riser height (every one the same)
- 7.20 in — 7 3/16 in on a tape
- Treads (risers − 1)
- 14
- Total run
- 140.00 in (11 ft 8 in)
- Stringer length
- 176.816 in (14 ft 8.8 in)
- Rise + run (17–18 in is comfortable)
- 17.20 in — in the band
- 2 × rise + run (24–25 in)
- 24.40 in — in the band
- Headroom required
- 80 in (6 ft 8 in), measured plumb from the nosings
- Riser variance allowed
- 3/8 in across the whole flight
- Code check
- Inside the IRC limits
| Risers | Riser height | On a tape | Total run | Meets code |
|---|---|---|---|---|
| 12 | 9.00 in | 9 in | 110.00 in | No — riser too tall |
| 13 | 8.308 in | 8 5/16 in | 120.00 in | No — riser too tall |
| 14 | 7.714 in | 7 11/16 in | 130.00 in | Yes |
| 15 (chosen) | 7.20 in | 7 3/16 in | 140.00 in | Yes |
| 16 | 6.75 in | 6 3/4 in | 150.00 in | Yes |
| 17 | 6.353 in | 6 3/8 in | 160.00 in | Yes |
| 18 | 6.00 in | 6 in | 170.00 in | Yes |
- Every riser must be equal. The IRC allows the tallest and the shortest riser in a flight to differ by no more than 3/8 in. An uneven riser is not seen, is not expected, and is the leading cause of falls on stairs.
- The way that rule gets broken is finish flooring. Cut the stringer to a rise measured off the subfloor, lay 3/4 in of hardwood at the top only, and the bottom riser is now 3/4 in out on its own — twice the tolerance. Measure finished floor to finished floor, and cut the bottom of the stringer short by the thickness of one tread.
- Building codes are local. These figures follow the International Residential Code, which most US jurisdictions adopt and many amend. Confirm riser, tread, headroom, and handrail requirements with your building department before you cut anything.
- A tread shallower than 11 in must carry a nosing that projects 3/4 to 1 1/4 in. Tread depth here is measured nosing to nosing, so the run above is unaffected by it — but the board you buy is that much wider.
Why the riser count is the input and the height is the output
Every riser in a flight must be the same height. That single constraint decides the shape of this calculator: you cannot pick a riser height and see how many fit, because the last one would come out short. You pick how many risers, and the height follows — the total rise divided by that count, to as many decimal places as the division produces.
riser = R ÷ n • treads = n − 1 • run = (n − 1) × T • stringer = √(R² + run²)- R
- Total rise, finished floor to finished floor, in inches
- n
- Risers — the number you choose, and the only real design decision on this page
- n − 1
- Treads. There is always one fewer tread than riser, because the top riser lands on the floor above rather than on a tread of its own
- T
- Tread depth, measured nosing to nosing — the walking surface, not the width of the board
The options table applies that division across every riser count worth considering, from two below the steepest legal flight to four above it, and marks which rows satisfy the two dimensional limits: a riser no taller than 7¾ inches and a tread no shallower than 10 inches. Picking a row from that table is the design. The calculator also checks the flight rise against the 12 ft 7 in maximum allowed between floors or landings, because a tall flight can have perfectly legal risers and still need a landing partway up.
A 108 inch rise, laid out three ways
A nine-foot floor-to-floor rise is 108 inches. Start at the code line: 108 ÷ 7.75 = 13.9, so 14 risers is the fewest that stays legal, at 108 ÷ 14 = 7.714 inches each — under the limit by about a sixteenth. Thirteen risers would be 8.308 inches, which fails, and fails by enough that no amount of careful cutting saves it.
Take 15 risers instead and each one is exactly 7.2 inches — 7 3/16 on a tape measure. Fourteen treads at 10 inches make a total run of 140 inches, or 11 ft 8 in of floor space, and the stringer is √(108² + 140²) = 176.8 inches, about 14 ft 9 in of 2×12.
Now check the comfort rules on both. At 15 risers, rise + run = 7.2 + 10 = 17.2, inside the 17-to-18 band, and 2 × rise + run = 24.4, inside the 24-to-25 band. At 14 risers, rise + run = 17.71 — still fine — but 2 × rise + run = 25.43, outside it. Both flights are legal; the second is measurably steeper, and the stride rule is what catches it. The 10 inches of extra hallway is what you pay for the difference.
One more comparison worth running: keep 15 risers and take the tread to 11 inches. The run grows to 154 inches, rise + run becomes 18.2 and steps outside the band the other way — a stair can be too shallow as well as too steep, and a tread much over 11 inches starts to break stride rather than help it.
Three eighths of an inch, across the whole flight
The IRC limits the difference between the greatest riser height and the smallest riser height in a flight to ⅜ of an inch. Not between adjacent risers — between the tallest and the shortest anywhere in the run. It is the tightest dimensional tolerance in ordinary residential carpentry, tighter than anything demanded of a wall, a floor, or a roof.
The reason is how people climb. The first two steps calibrate an automatic gait, and everything after that is run open-loop: the foot is placed where the pattern predicts the step will be, not where it is. A riser half an inch taller than its neighbours catches the toe on the way up. A riser half an inch shorter drops the foot through empty air on the way down, which is the worse of the two. An uneven riser is a trip hazard and is the leading cause of stair falls — not steepness, not the absence of a handrail, but the one step that is not like the others.
Since the risers must be equal, the arithmetic is forced: riser height = total rise ÷ riser count, and the count is what you choose. The danger is never in the division. It is in what happens between cutting the stringer and finishing the job:
- The bottom riser. A stringer sits on the lower floor and the first tread sits on the stringer, so the bottom of the stringer must be cut short by exactly the thickness of one tread. Miss it and the bottom riser is an inch or more taller than the rest — three times the tolerance, in the single most dangerous position in the flight.
- Finish flooring added later. Cut to a rise measured off the subfloor, then lay ¾ inch of hardwood at the top and nothing at the bottom, and every riser but the first grew by ¾ inch. Measure between finished floor levels, or account for what is going down at each end before you cut.
- Site-built adjustments. Shimming a stringer to fix a fit problem changes one riser and one riser only. If it needs shimming, it needs recutting.
Run, headroom, and the landing rule
A staircase takes up as much floor as a small room, at both levels. The total run is the tread count times the tread depth — 140 inches for the worked example above — and that space has to exist at the bottom, with somewhere to arrive that is not a doorway opening across the flight.
Above the flight, the requirement is 6 ft 8 in of headroom minimum, measured vertically from a line drawn along the tread nosings to whatever is overhead, all the way from the bottom nosing to the top. This is the number that usually decides how long the floor opening upstairs has to be, and it is the one people discover last, after the framing is in.
Finally, a single flight may not rise more than 12 ft 7 in between floors or landings. A tall flight can have perfectly legal risers and still be illegal for this reason alone, and the calculator flags it — a landing is not an optional courtesy at that height, it is the thing that stops a fall from becoming a very long fall.
What this calculator assumes
- One straight flight, with every riser equal and the top riser landing on the floor above. Winders, landings partway up, turns, and spiral stairs are not modelled.
- The total rise is measured between finished floor levels. Flooring added after a stringer is cut is the most common way a compliant layout becomes a non-compliant staircase.
- Tread depth is nosing to nosing, which is how the code measures it, so the total run is unaffected by nosing projection. A tread shallower than 11 inches must carry a nosing projecting ¾ to 1¼ inches, and the board you buy is that much wider than the depth entered here.
- Stringer length is the plain diagonal, √(rise² + run²), before any notches are cut and before the bearing cuts at either end. Buy stock longer than it, and cut stringers from 2×12 so enough material remains behind the notches.
- The limits applied are the International Residential Code’s: 7¾ in maximum riser, 10 in minimum tread, ⅜ in maximum variation within a flight, 6 ft 8 in minimum headroom, and 12 ft 7 in maximum rise between landings. Building codes are local; this reflects the IRC as a common baseline and is not a substitute for your jurisdiction.
- The IRC sets no minimum riser height for dwellings, so a very shallow flight is marked as meeting code even where it walks badly. That is what the two comfort rules are shown for.
- Nothing here covers handrails, guards, baluster spacing, structural sizing of the stringers, fire separation, or the stricter IBC and ADA requirements that apply to commercial and public stairs.
Stair calculator FAQ
How many stairs do I need for a 9 foot floor-to-floor rise?
Fourteen risers at the very steepest, and fifteen is the better answer. Nine feet is 108 inches, and the residential limit on riser height is 7¾ inches, so 108 ÷ 7.75 = 13.9 — you cannot have 13.9 risers, so 14 is the fewest that stays legal, at 7.714 inches each. Fifteen risers gives 7.2 inches, which is easier to climb and lands squarely inside both of the old comfort rules. The trade is floor space: 14 risers means 13 treads and a 130 inch run, while 15 means 14 treads and 140 inches. Ten more inches of hallway buys a noticeably better staircase.
What is the maximum riser height for residential stairs?
7¾ inches under the International Residential Code, with a minimum tread depth of 10 inches measured nosing to nosing. Those two numbers together define the steepest stair a dwelling may legally have. Commercial and public stairs are held to tighter limits — the ADA Standards call for risers of 4 to 7 inches and treads of at least 11 inches — so a stair that is legal in a house is often not legal in a shop. Codes are adopted and amended locally, so treat 7¾ and 10 as the common baseline and confirm with your building department.
Why do all the risers in a staircase have to be the same height?
Because after the first two steps, nobody is looking. Climbing a stair is handed off to an automatic gait calibrated by those first risers, and the foot is then placed where the pattern says the step will be rather than where it is. A riser that is half an inch out is not seen, is not expected, and catches the toe or drops the foot into empty air — which is why uneven risers are the leading cause of stair falls, and why the IRC allows the tallest and shortest riser in a flight to differ by no more than ⅜ inch. That tolerance is the tightest dimensional requirement in ordinary residential carpentry, and it is tight for a reason.
How do I calculate stair stringer length?
It is the hypotenuse of the rise and the run: √(rise² + run²). A 108 inch rise with a 140 inch run gives √(11,664 + 19,600) = √31,264 = 176.8 inches, or about 14 ft 9 in. Two practical caveats. First, that is the length of the line the notches are cut along, so buy stock longer than it and allow extra at both ends for the bearing cuts. Second, a notched stringer loses depth wherever a tread is cut in, which is why stringers are cut from 2×12 stock rather than 2×10 — the uncut material left behind the notches is what carries the load, and most jurisdictions expect several inches of it.
What is the 17-18 rule for stairs?
One riser plus one tread should come to somewhere between 17 and 18 inches — a rule of thumb about as old as carpentry, and a decent proxy for a stair that walks naturally. Its companion is 2 × rise + run landing between 24 and 25 inches, which tracks the stride of a person moving on the level and adjusts for the extra effort of climbing. The pair are useful because they disagree in the interesting cases: 7.714 inch risers with a 10 inch tread give 17.71 — comfortably inside the first rule — but 25.43 on the second, which is the stride rule catching a steepness the first one let through. Neither rule is code. Both are worth satisfying if the space allows.
How much space do stairs need?
More than people expect. The horizontal run is the tread count times the tread depth, and the tread count is one less than the riser count — so a 15-riser flight at a 10 inch tread eats 140 inches, or 11 ft 8 in, of floor at both levels. You also need 6 ft 8 in of headroom measured plumb from the nosing line all the way down the flight, which is what governs where the floor opening above has to end, and a landing at least as deep as the stair is wide at any door. Add a riser and the run grows by one tread; add tread depth for comfort and it grows faster still.
Why is the bottom of a stair stringer cut short?
Because the first tread sits on top of the stringer and adds its own thickness to the first step. If the stringer is not shortened at the bottom by exactly the thickness of one tread, the bottom riser ends up that much taller than every other riser in the flight — typically an inch or more, which is nearly three times the ⅜ inch the code allows. The same trap operates through finish flooring: cut a stringer to a rise measured off the subfloor, then lay ¾ inch of hardwood at the top only, and the bottom riser is ¾ inch out on its own. Measure finished floor to finished floor, and subtract the tread thickness at the bottom.
Do these numbers apply everywhere?
No. This calculator reflects the International Residential Code, which most US jurisdictions adopt as a baseline and many amend. Some older housing stock is legal only because it predates the current limits; some states apply different riser and tread figures; commercial work in the same building may fall under the IBC and the ADA Standards instead, which are stricter. Nothing here covers winders, landings, spiral stairs, handrail height and graspability, guard spacing, or the fire-rating rules that apply to a stair in an enclosed shaft. Check with the authority having jurisdiction before you cut a stringer.
Sources and review notes
- ICC Digital Codes — the International Residential Code, section R311.7, which sets the 7¾ in riser, 10 in tread, ⅜ in variation, 6 ft 8 in headroom, and 12 ft 7 in flight-rise limits used here
- U.S. Access Board — the ADA Standards for Accessible Design, section 504, whose stricter stair geometry (4 to 7 in risers, 11 in treads) governs public and commercial stairs
- U.S. Consumer Product Safety Commission — NEISS injury data, in which stairs, ramps, and landings are consistently among the highest-frequency products in emergency department records
The arithmetic on this page is exact. The limits it checks against are not universal: the IRC is a model code, adopted and amended jurisdiction by jurisdiction, and commercial work usually falls under the IBC and the ADA Standards instead. Verify riser, tread, headroom, handrail, and guard requirements with your building department before cutting anything, and treat the ⅜ inch variation limit as the number that matters most on site.