To calculate stairs, measure the total rise, divide by the maximum riser height and round up to get the number of risers; then divide the rise by that number for the exact riser height. With a total rise of 101½ inches and the International Residential Code’s 7¾-inch limit, 101.5 ÷ 7.75 = 13.1, so you need 14 risers of 7¼ inches, 13 treads, and, with 10½-inch treads, a total run of 136½ inches.
Step 1: Measure the total rise
The total rise is the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor. If flooring is not yet installed, add its thickness to your measurement. A ¾-inch hardwood floor at the top and bare concrete at the bottom changes the rise by ¾ inch, enough to make the top or bottom step noticeably different.
For decks, measure from the deck surface to the ground or landing pad where the stairs will end. If the ground slopes, measure at the actual landing point, not at the house.
Step 2: Find the number of risers and riser height
The ⌈ ⌉ brackets mean round up. Dividing evenly matters: the IRC allows riser heights in a flight to vary by no more than ⅜ inch, because people expect every step to be the same and trip on one that is not.
Total rise = 101.5 in
101.5 ÷ 7.75 = 13.1 → round up → 14 risers
101.5 ÷ 14 = 7.25 in (7¼ in) per riser
Step 3: Treads and total run
Treads = 14 − 1 = 13
With 10½-in treads: total run = 13 × 10.5 = 136.5 in (11 ft 4½ in)
Make sure that horizontal distance is actually available, plus a landing at the bottom. The IRC requires a floor or landing at the top and bottom of each stairway, at least as wide as the stairs and at least 36 inches deep in the direction of travel. Running out of floor space is the most common reason a stair plan has to change.
The ratio of rise to run is also the stair’s slope, 101.5 ÷ 136.5 ≈ 0.74, far steeper than a ramp. Slope, grade and angle conversions are covered in how to find the slope of a line.
Step 4: Stringer length and angle
The stringer, the notched board that carries the treads, is the hypotenuse of a right triangle with the rise and run as legs:
Stringer = √(101.5² + 136.5²) = √28,935 ≈ 170.1 in (about 14 ft 2 in)
Angle = arctan(7.25 ÷ 10.5) ≈ 34.6°
Buy a board longer than the calculated length to allow for the plumb and level cuts at each end; here a 16-foot 2×12 is the practical choice. The math comes straight from how to use the Pythagorean theorem.
Comparing options
You can usually choose between two or three riser counts. For the same 101½-inch rise with 10½-inch treads:
| Risers | Riser height | Treads | Total run | Angle | 2R + T |
|---|---|---|---|---|---|
| 13 | 7.81 in | 12 | 126 in | 36.6° | 26.1 in |
| 14 | 7.25 in | 13 | 136.5 in | 34.6° | 25.0 in |
| 15 | 6.77 in | 14 | 147 in | 32.8° | 24.0 in |
Thirteen risers exceed the 7¾-inch limit, so they are not allowed. Fifteen risers make a gentler stair but need almost a foot more run. Fourteen hits the classic comfort target.
Comfort rules of thumb
| Rule | Target | 7¼ × 10½ result |
|---|---|---|
| 2 × riser + tread | 24–25 in | 25 in ✓ |
| Riser + tread | 17–18 in | 17.75 in ✓ |
| Riser × tread | 70–75 in² | 76.1 in² (close) |
These rules date back centuries and reflect average stride length. Stairs that satisfy them feel natural to walk.
IRC stair requirements at a glance
| Item | IRC requirement (one- and two-family homes) |
|---|---|
| Maximum riser height | 7¾ in |
| Minimum tread depth | 10 in, measured nosing to nosing |
| Nosing | ¾ to 1¼ in where treads are under 11 in |
| Variation within a flight | ⅜ in maximum for risers and for treads |
| Minimum width | 36 in |
| Minimum headroom | 6 ft 8 in |
| Handrail | Required with four or more risers, 34–38 in high |
| Maximum rise of one flight | 151 in (12 ft 7 in) between floors or landings |
These figures come from Section R311.7 of the IRC. Commercial buildings under the International Building Code are stricter, with risers of 4 to 7 inches and treads of at least 11 inches. Local amendments are common, so check with your building department before building.
Cutting stringers: practical notes
- Convert to fractions. Framing squares and tapes use sixteenths. 7.25 in is 7¼; a riser of 7.571 in would round to 7 9/16. The decimal to fraction calculator helps.
- Drop the stringer. The bottom cut must be shortened by the thickness of one tread, or the first step will be taller than the rest by that amount.
- Check the top. The top riser is measured to the finished upper floor, so allow for any flooring there too.
- Use enough stringers. Many builders space stringers no more than about 16 inches apart for 1-inch-thick treads; follow your tread material’s span rating.
A deck stair example
A deck 30 inches above a patio: 30 ÷ 7.75 = 3.87 → 4 risers of 7½ inches and 3 treads. With four risers, the IRC requires a handrail. The deck calculator helps with the deck itself, and the board foot calculator prices hardwood treads.
Common mistakes
- Measuring to the subfloor instead of the finished floor.
- Counting treads equal to risers, which adds one extra tread of run.
- Rounding risers down below the code limit instead of up.
- Forgetting headroom under a floor or beam above the stairs.
The stair calculator runs all of these steps, compares riser counts and flags code issues automatically. For adding up rise and run measurements in feet and inches, the feet and inches calculator keeps the fractions straight.
Frequently asked questions
How do I calculate the number of stairs I need?
Measure the total rise from finished floor to finished floor, divide by the maximum riser height (7¾ inches under the IRC), and round up. That is the number of risers. For a 101½-inch rise, 101.5 ÷ 7.75 = 13.1, so you need 14 risers of 101.5 ÷ 14 = 7¼ inches each.
Why are there fewer treads than risers?
The top riser brings you up to the upper floor, which acts as the last step, so it needs no separate tread. A staircase with 14 risers has 13 treads.
What are the code requirements for residential stairs?
The International Residential Code (IRC) limits risers to 7¾ inches and requires treads of at least 10 inches, a minimum width of 36 inches, headroom of at least 6 feet 8 inches, and riser and tread variations of no more than ⅜ inch within a flight. Local codes may differ, so confirm with your building department.
How long should a stair stringer be?
Use the Pythagorean theorem with the total rise and total run as the two legs. For a 101½-inch rise and 136½-inch run, the diagonal is √(101.5² + 136.5²) ≈ 170.1 inches, about 14.2 feet, so buy at least a 16-foot board.
What is the most comfortable stair angle?
Most residential stairs fall between about 30 and 37 degrees. A common comfort rule is that two risers plus one tread should equal about 24 to 25 inches; a 7¼-inch riser with a 10½-inch tread gives exactly 25 and an angle of about 34.6 degrees.