How this stair calculator works
Stairs are laid out backward from one number: the total rise, finished floor to finished floor. The calculator divides it into the largest set of equal risers near your target height, keeps them inside the IRC limit, and everything else follows:
riser = rise ÷ risers · run = treads × tread depth · stringer = √(rise² + run²)
At the defaults — 106 in of rise, 10 in treads, a 7 in target — that’s 15 risers of 7 1/16 in and a 16 ft stringer; the full chain is in the layout math section below.
The parts of a staircase
A stair is a short vocabulary, and knowing it turns the calculator’s outputs into a cut list:
Total rise and total run
Total rise is the vertical, finished floor to finished floor — the one measurement everything derives from. Total run is the horizontal the whole flight covers on the floor: treads × tread depth.
Riser and tread
The riser is the height of each step (the vertical face); the tread is the depth you step on. There is always one more riser than tread — the top riser lands you on the floor above, which has no tread of its own.
Stringer
The sawtooth-cut 2×12 that carries the treads — the structural spine of the stair. Its point-to-point length is the hypotenuse of rise and run, and the calculator names the shortest standard board that covers it.
Nosing
The ¾–1¼ in the tread overhangs the riser below. It buys foot room without adding run, and it’s required on treads under 11 in deep.
Landings and headroom
A landing at least as deep as the stair is wide top and bottom, and 6 ft 8 in of clear headroom over the nosing line — the two dimensions that shape the opening the stair drops through.
Stair rise and run: the code numbers
Stairs are one of the most-failed inspections in a house because the rules are exact and unforgiving. The residential IRC numbers:
- Riser height: 7¾ in maximum (IRC R311.7.5.1), and no more than 3/8 in variation across the finished stair.
- Tread depth: 10 in minimum, nose to nose; treads under 11 in need a ¾–1¼ in nosing.
- Width & headroom: 36 in clear width and 6 ft 8 in of headroom over the nosing line, minimum.
- Landings: a landing at least as deep as the stair is wide at top and bottom — a door can't swing over the top step.
- Handrail: 34–38 in above the nosing, graspable, on stairs of four or more risers.
These are the national IRC numbers — local amendments can be tighter, and commercial (IBC) stairs use 7 in / 11 in. The badges on the calculator flag the two limits that kill inspections most often.
Stair layouts by total rise
Table 1 runs common floor-to-floor rises through the engine at 10 in treads — riser count, even riser height, total run, and the board to buy.
| Total rise | Risers | Riser height | Total run | Stringer → board |
|---|---|---|---|---|
| 96 in | 14 | 6 7/8″ | 10′-10″ | 13′-5 5/8″ → 14 ft |
| 100 in | 14 | 7 1/8″ | 10′-10″ | 13′-8″ → 14 ft |
| 104 in | 15 | 6 15/16″ | 11′-8″ | 14′-6 3/8″ → 16 ft |
| 106 in | 15 | 7 1/16″ | 11′-8″ | 14′-7 5/8″ → 16 ft |
| 112 in | 16 | 7″ | 12′-6″ | 15′-7 3/16″ → 16 ft |
| 120 in | 17 | 7 1/16″ | 13′-4″ | 16′-8″ → 18 ft |
How to measure and cut a stair stringer
Get the total rise exactly right and the rest is layout. Measure floor-to-floor at the finished heights, not the framing.
- Measure the total rise from the finished lower floor to the finished upper floor — account for the flooring thickness top and bottom, because a ½ in of finish throws the riser count.
- Set your tread depth and target riser — 10 in and 7 in is the default; the calculator finds the even riser and flags any code miss.
- Lay out with a framing square: clamp stair gauges at the riser and tread numbers, step the square along the board, and mark every step before cutting.
- Drop the stringer: trim the bottom cut by one tread thickness, or the first step ends up tall and the top step short — the classic failed-inspection mistake.
- Cut one, copy the rest: test-fit the first stringer, then trace it. A 36 in stair wants three stringers, 16 in on center.
- Overcut nothing: finish inside corners with a handsaw or jigsaw — circular-saw overcuts weaken the stringer exactly where it carries load.
Worked example: stairs for an 8 ft floor
The default, worked line by line — 106 in of total rise, 10 in treads, 7 in target riser:
riser = 106 ÷ 15 = 7 1/16″
treads = 15 − 1 = 14
run = 14 × 10 = 140″ = 11′-8″
stringer = √(106² + 140²) = 175.6″ = 14′-7 5/8″ → 16 ft 2×12
angle = atan(106 ÷ 140) = 37.1°
Watch the rounding both ways. A 7 in target over 106 in wants 15.1 risers — round to 15 and the riser lands at 7 1/16, comfortably legal. Round down to 14 and it’s 7.57 in, still under 7¾ but a steeper climb. The engine takes the nearest whole count, then adds risers only if the height would break code — so it never hands you an illegal stair.
What this stair calculator doesn’t cover
The engine gives you the rise-run-stringer layout. A finished stair needs more:
- Treads and risers as material. The boards that land on the stringers — 5/4 or 2× treads, riser stock — priced separately by the board foot calculator.
- Landings and framing. The platform framing and the opening the stair drops through.
- Handrail and guards. Rail, balusters and newels to code — a real line on a finished stair.
- Winders and curves. This is a straight-flight layout; winders and spirals are their own geometry.
- Hardware. Stringer hangers, tread screws, construction adhesive.
- Finish. Skirt boards, paint or stain, and any carpet or tread caps.
Stair calculator FAQ
How many steps do I need for an 8 ft ceiling?
Usually 15 risers. An 8 ft ceiling plus joists and subfloor gives a total rise around 106 in, and 106 ÷ 15 = a comfortable 7 1/16 in riser with 14 treads. Always work from the measured floor-to-floor rise, not the ceiling height.
What is the maximum stair riser height?
The IRC (R311.7.5.1) caps risers at 7¾ in, and the difference between the tallest and shortest riser on a finished stair can be no more than 3/8 in. Commercial stairs under IBC are stricter — 7 in max riser, 11 in min tread.
What is the minimum tread depth?
10 in under the IRC, measured nose to nose — and treads under 11 in must have a nosing of ¾ to 1¼ in. 10½–11 in treads feel noticeably safer walking down; use the chips above to compare the run they cost you.
What is the 7-11 rule for stairs?
The comfortable-stair rule of thumb: a 7 in riser paired with an 11 in tread. It sits just inside the IRC limits (7¾ max riser, 10 min tread) and satisfies the old riser-plus-tread ≈ 17–18 in check. Many builders aim for it as the target, then let the total rise nudge the riser to an even number.
How long a 2×12 do I need for a stair stringer?
The stringer for the default 106 in rise runs 14 ft 7 5/8 in point to point, so you buy a 16 ft 2×12 — the calculator names the shortest standard board for your layout. Pick straight, tight-knot stock; the stringer is the structure.
How many stringers does a staircase need?
Three for a standard 36 in stair — the two outer plus one in the middle, spaced about 16 in on center — so the treads do not bounce. Wider stairs add stringers to keep the spacing under ~18 in; 2× treads on a narrow stair can sometimes run on two.
What is a comfortable stair angle?
Residential stairs land between about 30° and 38°; the default layout is 37.1°. Shallower needs more run, steeper gets harder to descend — the old carpenter check is riser + tread ≈ 17–18 in, which 7 1/16 + 10 satisfies.
Sources and standards
- IRC R311.7: stairways — riser (7¾ max), tread (10 min), width, headroom, landing and nosing requirements.
- IRC R311.7.8: handrail height and graspability.
- IBC 1011: the stricter 7 in / 11 in commercial limits referenced for contrast.
- Right-triangle trigonometry: the stringer length and angle are computed exactly from rise and run — the table is the same math printed out.
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