Stair Calculator
15 risers at 7.2 in each.
| Dimension | Value |
|---|---|
| Risers all identical | 15 at 7.2 in |
| Treads | 14 at 10 in |
| Total run | 140 in (11.67 ft) |
| Stringer length corner to corner | 176.82 in (14.73 ft) |
| Stringer stock to buy | 2 × 12 at 16 ft, three of them |
| Stair angle | 37.6° |
| Rise + run 17–18 in is comfortable | 17.2 in — comfortable |
| Code check | Meets IRC riser and tread limits |
The total rise is divided by a whole number of risers, because every riser in a flight must be the same height — the IRC allows no more than 3/8 in of variation between the tallest and shortest, and an uneven riser at the top or bottom is the classic trip hazard. A flight always has one fewer tread than it has risers, since the top tread is the floor you step onto. Limits used are IRC R311.7: maximum 7.75 in riser, minimum 10 in tread, minimum 36 in width, and 6 ft 8 in headroom measured vertically from the tread nosing. Tread depth here excludes nosing overhang. Local codes and commercial stairs differ — check with your building department before cutting stringers.
Enter your total rise to get the riser count, exact riser height, total run, and stringer length — checked against the IRC code limits.
How to use this calculator
- Measure the total rise from finished floor to finished floor. If flooring is not down yet, add its thickness at both levels.
- Enter your preferred riser height. Seven inches is the comfortable target; the calculator lands on the nearest whole riser count and tells you the exact height.
- Set the tread depth — the horizontal run per step, not counting nosing overhang. Ten inches is the code minimum, eleven is more comfortable.
- Check the code line in the results. If either dimension is out of bounds you get a warning rather than a number that will fail inspection.
The formula
Risers = round(Total rise ÷ Preferred riser) · Riser height = Total rise ÷ Risers · Treads = Risers − 1
Total run = Treads × Tread depth · Stringer = √(Total rise² + Total run²)
Worked example — a 9 ft floor-to-floor rise
A standard storey with a 7 in target riser and 10 in treads.
- Total rise: 9 ft = 108 in
- Riser count: 108 ÷ 7 = 15.43 → 15 risers
- Exact riser height: 108 ÷ 15 = 7.2 in — inside the 7.75 in limit
- Treads: 15 − 1 = 14
- Total run: 14 × 10 = 140 in (11 ft 8 in)
- Stringer: √(108² + 140²) = 176.8 in (14 ft 9 in)
- Angle: 37.7° — comfortable; over 42° feels like a ladder
Note what happens if you take 7 inches literally and cut 15 risers at 7 inches: you climb 105 inches and are 3 inches short of the floor. That last step becomes 10 inches — a code violation and a genuine hazard. The rise divides evenly or it does not work.
Why every riser must be identical
People do not look at stairs while climbing them. Within two or three steps your body has learned the rhythm and is placing feet from memory. A riser that differs by even half an inch breaks that rhythm at exactly the moment you are least prepared — which is why uneven risers are among the most common causes of stair falls, and why the IRC allows no more than 3/8 inch of variation across a whole flight.
The practical consequence is the one people trip over when building: you cannot pick a riser height and use it. You pick a riser count, and the height falls out of the division. The most common way to get this wrong is measuring to the subfloor, cutting stringers, and then adding flooring — which changes the top or bottom riser by the flooring thickness and nothing else.
Code limits at a glance
| Dimension | IRC residential | Note |
|---|---|---|
| Maximum riser height | 7.75 in | Measured vertically, nosing to nosing |
| Minimum tread depth | 10 in | Excluding nosing overhang |
| Riser variation in a flight | 3/8 in maximum | Between the tallest and shortest |
| Minimum stair width | 36 in | Above the handrail height |
| Minimum headroom | 6 ft 8 in | Vertically from the nosing line |
| Nosing projection | 3/4 to 1¼ in | Required when treads are under 11 in |
| Handrail height | 34 to 38 in | Above the nosing line |
These are the IRC baseline figures. Commercial stairs under the IBC are stricter, and local amendments vary — confirm with your building department before cutting.
What makes a stair feel right
Passing code and feeling comfortable are not the same thing. A stair can be legal and still feel wrong. Three old rules, all of which give similar answers, describe what actually feels natural:
- Riser + tread = 17 to 18 in. The most-used rule. A 7 in riser with a 10.5 in tread is 17.5.
- Riser × tread ≈ 75. A 7 × 11 combination gives 77; 7.5 × 10 gives 75.
- 2 × riser + tread ≈ 25. Derived from the length of a natural stride.
The reason all three exist is that rise and run trade off against each other in a specific way: as steps get taller they need to get shallower, but not proportionally. Stairs that violate these rules feel either steep and tiring or stretched and stumbling, even when every dimension is within code.
Don't forget the floor space
The run is the number people underestimate. A 9 foot rise needs nearly 12 feet of horizontal run, and the IRC requires a landing at each end at least as deep as the stair is wide — 36 inches minimum. That is close to 15 feet of total floor length before you have added anything else.
If the space genuinely is not there, the answer is a landing and a turn, not steeper steps. A U-shaped or L-shaped stair with an intermediate landing fits a much smaller footprint, and the landing itself counts as a tread for rhythm purposes. What you must not do is shave the tread depth to fit — that is how the dangerously steep stairs in old houses came to exist.
Common mistakes to avoid
- Measuring to the subfloor. Finished floor to finished floor, always. Flooring thickness changes every riser.
- Using your target riser height literally. Divide the rise by a whole riser count instead; the height is the output, not the input.
- Counting treads and risers as the same number. A flight has one fewer tread than risers.
- Buying stringer stock exactly the calculated length. Notching cuts into the board's width, so you need the next size up — and at least three stringers for a 36 inch stair.
- Ignoring headroom. Easy to miss when a stair passes under a floor above. Check it before cutting, not after.
How we calculate this
The total rise is divided by the preferred riser height and rounded to the nearest whole number of risers, then the rise is divided by that count to get the exact riser height. Rounding rather than truncating is what keeps the result closest to the height you asked for. Treads are risers minus one, because the top tread is the floor you are stepping onto. Total run is treads × tread depth, and the stringer is the hypotenuse of rise and run: √(rise² + run²). Compliance is checked against IRC R311.7 — a maximum 7.75 in riser and a minimum 10 in tread. Tread depth here excludes nosing overhang.
Sources
Frequently asked questions
How do I calculate stair stringers?
Measure the total rise from finished floor to finished floor, divide by your preferred riser height to get a whole number of risers, then divide the total rise by that number to get the exact riser height. Treads are always one fewer than risers. Total run is treads times tread depth, and the stringer length is the diagonal: the square root of rise squared plus run squared.
How many steps for a 9 foot rise?
A 9 foot rise is 108 inches. Dividing by a comfortable 7 inches gives 15.4, so you use 15 risers at exactly 7.2 inches each. That gives 14 treads, and at 10 inches per tread the stair consumes 140 inches — 11 feet 8 inches — of floor space. The stringer works out at about 176.8 inches, or 14 feet 9 inches, so you need 16 foot stock.
What is the maximum riser height allowed by code?
7.75 inches for residential stairs under the International Residential Code (R311.7.5). The minimum tread depth is 10 inches, the minimum stair width is 36 inches, and headroom must be at least 6 feet 8 inches measured vertically from the tread nosings. Commercial stairs under the IBC are stricter — typically a 7 inch maximum riser and 11 inch minimum tread.
Why must all risers be the same height?
Because people climb stairs without looking at them. After two or three steps your body has learned the rhythm, and a riser that differs by even half an inch breaks it — which is why uneven risers are one of the most common causes of falls on stairs. The IRC allows no more than 3/8 inch of variation between the tallest and shortest riser in a flight. This is also why you divide the rise by a whole number rather than using your target height literally.
What is the ideal riser and tread combination?
A long-standing carpenter's rule is that riser plus tread should add up to 17 to 18 inches. A 7 inch riser with a 10 or 11 inch tread lands in that range and feels natural. Two related rules give similar answers: riser times tread should be near 75, and two risers plus one tread should be around 25. If your numbers fall outside these, the stair will feel steep or stretched even when it passes code.
How much space does a staircase need?
More than most people expect. A standard 9 foot rise needs about 11 feet 8 inches of horizontal run, plus landing space at both ends — the IRC requires a landing at least as deep as the stair is wide, so 36 inches minimum. That means budgeting roughly 15 feet of total floor length. Running short is the reason so many older houses have stairs that are too steep.
Do I measure the total rise to the subfloor or the finished floor?
Finished floor to finished floor, always. If the upper floor will get 3/4 inch hardwood and the lower gets tile over backer, both thicknesses change the total rise and therefore every riser. Cutting stringers to subfloor heights and then adding flooring is exactly how you end up with a first or last step that differs from the rest — the single most common stair-building error.
How long a board do I need for a stair stringer?
Take the stringer length this calculator gives you and buy the next stock length up, because you cut into the board's width when you notch it. For the 9 foot rise example the stringer is about 14 feet 9 inches, so 16 foot 2x12 stock. You will need at least three stringers for a 36 inch wide stair — one at each side and one in the middle.