What rise and run mean on a stair, and why the rise decides everything
A stair is not designed from the tread down; it is designed from the total rise up. The total rise is the vertical distance between the two finished surfaces the stair connects — finished floor to finished floor, or grade to the top of the deck boards. That single measurement is fixed by the building, and every other dimension follows from it.
The reason is that all risers in a flight must be equal. You cannot fudge a leftover half inch into the bottom step, because the human gait locks onto a rhythm after two or three treads and a riser that differs by even half an inch is the single most reliable way to make someone fall. Codes say this explicitly: the IRC allows a maximum of 3/8 in between the tallest and shortest riser in a flight, and the IBC allows the same. So the total rise must divide into a whole number of equal parts, and the only free choice you have is how many parts.
Pick a target riser — 7 in is the traditional starting point in American residential work — divide the total rise by it, and round to the nearest whole number. That gives your riser count. Dividing the total rise by that count gives the exact riser height, which will almost never be a round fraction. A 112 in rise divides cleanly into sixteen 7 in risers; a 113 in rise gives sixteen risers of 7.0625 in, and you cut every one of them to 7 1/16 in.
The unit run (British and Australian practice calls it the going) is the horizontal distance from one nosing to the next. It is the dimension the code calls tread depth, and it is not the width of the board you buy: a tread board is the unit run plus the nosing overhang, so a 10.5 in unit run with a 1 in nosing wants an 11.5 in board. Multiply the unit run by the number of treads and you have the total run, which is how much floor the stair eats.
The arithmetic, and why the tread count is one fewer than the riser count
Three lines of arithmetic produce a stair layout. First, n = round(H ÷ Rtarget), where H is the total rise. Second, the exact riser R = H ÷ n. Third, the total run = (n − 1) × G, where G is the unit run.
That subtraction catches almost every first-time stair builder. Walk up a flight and count: you step up onto tread 1, tread 2, and so on, and the last step up lands you on the upper floor itself. The upper floor is the last tread. So a flight with sixteen risers has fifteen treads, and it occupies fifteen unit runs of floor, not sixteen. Getting this wrong adds a full tread depth to your run and puts the stair through a wall.
The exception is a stair that lands on a separate landing platform whose surface sits below the upper floor — for instance a deck stair that stops on a concrete pad. There the count of physical treads equals the number of risers minus one still, because the pad is the bottom, not the top. But if you build a stair that terminates on a landing at the top rather than at the floor surface, you get n treads and a run of n × G. Decide which case you have before you cut.
The angle falls out of the same two numbers: θ = arctan(R ÷ G). A 7 in riser over a 10.5 in run is 33.69°, which is a comfortable domestic stair. The steepest flight the IRC permits — a 7.75 in riser over a 10 in tread — is 37.78°. Anything past about 42° stops being a stair and becomes a ship's ladder, with its own separate rules.
Finally there is the rule of thumb that separates a legal stair from a good one. 2R + G should land between 24 in and 25 in. It is an empirical relationship, not a code requirement, and it encodes the fact that a person's stride shortens as they climb: taller risers need shallower treads and vice versa. A 7 in riser with a 10.5 in run gives 24.5 in and walks beautifully. A 7.75 in riser with a 10 in tread gives 25.5 in — legal, but noticeably steep.
Worked example: 112 in from a basement slab to a first floor
You measure 112 in from the finished basement slab to the top of the finished first-floor flooring. You want a 7 in riser, a 10.5 in unit run, a 1 in nosing, and a 36 in clear width, built to the IRC.
- Trial riser count. 112 ÷ 7 = 16.00 exactly, so n = 16 risers.
- Exact riser height. 112 ÷ 16 = 7.000 in. Every riser is cut to 7 in.
- Tread count. 16 − 1 = 15 treads. The first-floor surface is the sixteenth step up.
- Total run. 15 × 10.5 = 157.5 in, or 13 ft 1.5 in of floor.
- Angle. arctan(7 ÷ 10.5) = arctan(0.66667) = 33.69°.
- Comfort check. 2 × 7 + 10.5 = 24.5 in, right in the middle of the 24–25 in band.
- Code check. 7.000 in ≤ 7.75 in maximum riser, and 10.5 in ≥ 10 in minimum tread. The flight is legal, with 0.75 in of riser height in hand.
- Tread board width. 10.5 + 1 = 11.5 in, so a pair of 2×6 treads at 5.5 in each with a 0.5 in gap, or one solid 11.5 in tread.
Now suppose the framer gets it wrong and you actually measure 113.5 in because the finish flooring went in thicker than planned. 113.5 ÷ 7 = 16.21, still rounding to 16 risers, so the riser becomes 113.5 ÷ 16 = 7.09375 in — 7 3/32 in. Still legal, still uniform, and the run is unchanged at 157.5 in. That is why you measure to finished surfaces: a 1.5 in flooring surprise discovered after the stringers are cut leaves you with one bottom riser 1.5 in taller than the rest, which no inspector will pass.
How to read the result against the code you are building to
Check three numbers in this order: riser height, tread depth, then the run you actually have.
Riser height is the hard limit. Under the IRC (one- and two-family dwellings and townhouses) the maximum riser is 7.75 in. Under the IBC (commercial buildings, and most multifamily common stairs) it drops to 7 in. That difference of three-quarters of an inch changes the riser count on nearly every flight: a 120 in rise takes 16 risers residentially and 18 commercially. If your riser margin comes back negative, add one riser and recalculate — never shave the bottom one.
Tread depth is the other hard limit: 10 in minimum under the IRC, 11 in under the IBC. Below 11 in the IRC also requires a nosing that projects between 0.75 in and 1.25 in, which recovers some of the foot area the shallower tread gives up. A solid riser with no nosing and a 10 in tread is a common failure on DIY deck stairs.
Width and headroom come next. The IRC wants 36 in of clear stairway width above the handrail height, and 6 ft 8 in of headroom measured vertically from the nosing line. The IBC generally wants 44 in of width for occupant loads over 49. Headroom is not calculated here because it depends on the floor opening above, but it is the second most common reason a stair gets torn out: check it by measuring vertically from a line drawn through the nosings to the nearest framing overhead.
Then look at the run. If the stair does not fit the opening, you have three moves, in ascending order of cost: reduce the unit run toward the code minimum (which buys you a fraction of an inch per tread and makes the stair steeper), add a landing and turn the flight 90° or 180°, or open up the floor above. Reducing the unit run from 11 in to 10 in on a fifteen-tread stair saves 15 in of run — often exactly enough.
Riser height and total run for common total rises
| Total rise | Risers | Riser height | Treads | Total run | Angle |
|---|---|---|---|---|---|
| 36 in (3 ft) | 5 | 7.200 in | 4 | 42.0 in | 34.44° |
| 45 in | 6 | 7.500 in | 5 | 52.5 in | 35.54° |
| 54 in | 8 | 6.750 in | 7 | 73.5 in | 32.73° |
| 72 in (6 ft) | 10 | 7.200 in | 9 | 94.5 in | 34.44° |
| 84 in (7 ft) | 12 | 7.000 in | 11 | 115.5 in | 33.69° |
| 96 in (8 ft) | 14 | 6.857 in | 13 | 136.5 in | 33.15° |
| 105 in | 15 | 7.000 in | 14 | 147.0 in | 33.69° |
| 112 in | 16 | 7.000 in | 15 | 157.5 in | 33.69° |
| 120 in (10 ft) | 17 | 7.059 in | 16 | 168.0 in | 33.91° |
Under the IBC the 7 in riser cap forces a higher count: a 120 in rise needs 18 risers of 6.667 in, not 17.
Which code applies to your stair
This calculator checks against the International Residential Code, section R311.7 for dwellings, and the International Building Code, section 1011 for commercial and most multifamily work. Both are model codes: your jurisdiction adopts a specific edition and may amend it. Some states are notably stricter — several New England jurisdictions have historically enforced tighter riser limits than the model IRC — and spiral stairs, winders, alternating-tread devices and ship's ladders all have separate provisions that these limits do not cover.
Confirm the adopted edition with your building department before you cut stringers. The riser and tread numbers used here are those of the 2021 IRC and 2021 IBC, which are unchanged from the 2018 editions.
Mistakes that make a stair fail inspection
- Measuring to subfloor instead of finished floor. Tile, hardwood or a deck board added later changes the total rise and leaves one riser out of tolerance. Measure finished-to-finished, or add the flooring thickness yourself.
- Forgetting that the top floor is a tread. Using n unit runs instead of n − 1 adds a full tread depth to the run and puts the bottom of the stair somewhere it cannot go.
- Not dropping the bottom riser by the tread thickness. When a stringer is notched, the bottom cut must be shortened by the thickness of the tread material or the first riser ends up that much taller than the rest. The stair stringer calculator handles that adjustment.
- Confusing tread depth with tread board width. Code measures nosing to nosing; the board you buy is that plus the nosing projection.
- Ignoring headroom. A perfectly legal rise and run still fails if the floor opening above gives less than 6 ft 8 in measured from the nosing line.
- Designing to the maximum riser. A 7.75 in riser is legal and uncomfortable. If the run allows it, take the extra riser.
- Assuming the same numbers apply commercially. The IBC's 7 in riser and 11 in tread will change the riser count on nearly every flight you have already drawn.
Where this fits with the rest of the stair build
Rise and run is the first of four calculations. Once you have the riser height and unit run fixed, you lay out the stringers — the diagonal length, the notch marks and the throat left after notching are all derived from these two numbers, and the stringer layout calculator takes them directly. Then comes the guard: the IRC requires a 36 in guard on any deck or landing more than 30 in above grade, with balusters spaced so a 4 in sphere cannot pass, and a 6 in sphere at the triangular opening formed by the tread, riser and bottom rail. The baluster spacing calculator divides a rail evenly to meet that.
If the stair is exterior, the footing under the bottom of the stringers is a real structural element, not a paver — size it the same way you size a deck post footing with the deck footing calculator. If you are decking the landing or the treads, the deck board calculator gives the board count.
When the rise is small and the run is generous, ask whether a ramp serves better than a stair. The ADA and the IRC both cap accessible ramp slope at 1:12, which needs 12 in of run for every inch of rise — the wheelchair ramp slope calculator works that out. And if you are cutting concrete steps rather than framing wood ones, the same rise and run feeds the volume takeoff in the concrete stairs calculator.
Key terms
- Total rise
- The vertical distance between the two finished surfaces the stair connects. Fixed by the building; everything else is derived from it.
- Riser
- One vertical step. Also the board that closes the vertical face of the step, on a closed-riser stair.
- Unit run (going)
- The horizontal distance from the nosing of one tread to the nosing of the next. This is what code calls tread depth.
- Nosing
- The part of the tread that projects past the riser below it. Required at 0.75–1.25 in by the IRC wherever tread depth is under 11 in.
- Total run
- The horizontal floor space the flight occupies: the number of treads times the unit run.
- 2R + T
- Twice the riser plus the tread depth. A stair-builder's comfort rule, not a code requirement; 24–25 in walks well.