Stair Calculator: Steps, Risers & Stringer Length

Step	Height of step top above lower floor	Distance from the first step’s front edge
1	7 11/16 in	0 in
2	15 7/16 in	10 in
3	23 1/8 in	20 in
4	30 7/8 in	30 in
5	38 9/16 in	40 in
6	46 5/16 in	50 in
7	54 in	60 in
8	61 11/16 in	70 in
9	69 7/16 in	80 in
10	77 1/8 in	90 in
11	84 7/8 in	100 in
12	92 9/16 in	110 in
13	100 5/16 in	120 in
14 (upper floor)	108 in	130 in

How to use this calculator

Measure the total rise: the vertical distance from the finished floor at the bottom to the finished floor at the top. Include flooring you haven’t laid yet, such as hardwood or tile, or the first and last steps will come out different heights.
Enter your maximum riser height. The calculator uses the IRC limit of 7¾ inches by default; enter 7 to 7½ inches for gentler stairs.
Enter the tread depth (the run of each step, nosing to nosing). The IRC minimum is 10 inches.
Choose whether the upper floor is the top step, which is how most stairs are built, or whether there’s a full tread at the top, as on some deck stairs.
Optionally set the nosing overhang under Tread boards to see how deep each tread board must be.

The result gives the number of steps, the exact riser height to the nearest sixteenth of an inch, the total run, the stringer length and angle, and a pass/fail check against the main IRC stair rules. The layout table lists where each step lands, which is handy for marking out a stringer.

The formulas

First the calculator finds the fewest risers that keep every one at or below your maximum, then divides the rise evenly between them:

n = ⌈ \frac{total rise}{max riser} ⌉ riser = \frac{total rise}{n}

With the upper floor as the last step there’s one fewer tread than risers, so the total run is (n − 1) × tread depth. The stringer length is the hypotenuse of the rise and run, √(rise² + run²), and the angle is arctan(riser ÷ tread).

Worked example

A typical floor-to-floor height with 8-foot ceilings is about 9 feet, the default:

Total rise: 9 ft × 12 = 108 in.
Risers: 108 ÷ 7.75 = 13.94, rounded up to 14 risers.
Riser height: 108 ÷ 14 = 7.714 in, about 7 11/16 in.
Treads: 14 − 1 = 13, because the upper floor is the last step.
Total run: 13 × 10 in = 130 in (10 ft 10 in).
Stringer: √(108² + 130²) = 169 in, about 14 ft 1 in, so buy 16-foot 2×12s.
Angle: arctan(7.714 ÷ 10) = 37.6°, just under the IRC’s implied maximum of 37.8°.

These stairs pass every check, but they’re as steep as the code allows. Lower the maximum riser to 7.5 inches and you get 15 risers of 7 3/16 inches, 14 treads, an 11 ft 8 in run and a 35.8° angle.

Steps for common floor-to-floor heights

The first set uses the IRC limits (7¾ in risers, 10 in treads); the second is a more comfortable layout (7¼ in maximum risers, 11 in treads). Both have the upper floor as the last step.

Total rise	Risers at code max	Riser height	Total run	Comfortable risers	Riser height	Total run
7 ft (84 in)	11	7 5/8 in	8 ft 4 in	12	7 in	10 ft 1 in
8 ft (96 in)	13	7 3/8 in	10 ft	14	6 7/8 in	11 ft 11 in
8 ft 6 in (102 in)	14	7 5/16 in	10 ft 10 in	15	6 13/16 in	12 ft 10 in
9 ft (108 in)	14	7 11/16 in	10 ft 10 in	15	7 3/16 in	12 ft 10 in
10 ft (120 in)	16	7 1/2 in	12 ft 6 in	17	7 1/16 in	14 ft 8 in
11 ft (132 in)	18	7 5/16 in	14 ft 2 in	19	6 15/16 in	16 ft 6 in
12 ft (144 in)	19	7 9/16 in	15 ft	20	7 3/16 in	17 ft 5 in

The comfortable layout needs 2 to 2½ feet more floor space. If space is tight, that’s where the trade-off lives. Rises over 151 inches (12 ft 7 in) need a landing partway up.

IRC stair rules at a glance

The International Residential Code, section R311.7, sets these limits for stairs in one- and two-family homes:

Rule	Limit	IRC section
Riser height	7¾ in maximum	R311.7.5.1
Tread depth	10 in minimum, nosing to nosing	R311.7.5.2
Riser and tread variation	⅜ in maximum within a flight	R311.7.5.1, R311.7.5.2
Nosing	¾–1¼ in where treads are under 11 in deep (solid risers)	R311.7.5.3
Headroom	6 ft 8 in minimum	R311.7.2
Width	36 in minimum clear above the handrail	R311.7.1
Height of one flight	151 in maximum between floors or landings	R311.7.3

Commercial buildings follow the International Building Code instead, with 7-inch maximum risers and 11-inch minimum treads, and some cities amend the IRC. Your building department has the final word.

Tips for building

Measure the rise in more than one place. Floors aren’t perfectly level. Measure where the bottom of the stringer will actually land.
Account for flooring. If you’ll add ¾ inch hardwood upstairs but not down, the rise grows by ¾ inch. The ⅜ inch tolerance is easy to blow with a forgotten floor finish.
Drop the stringer. When you cut a stringer, the bottom riser is cut shorter by the thickness of one tread so that, once treads go on, every step is the same height.
Building deck or porch steps? The concrete calculator sizes the landing pad, and the fence calculator counts posts and concrete for a fence or railing. Tiling the treads? See the tile calculator.

Assumptions and limitations

The calculator assumes a single straight flight with equal risers. Winders, spiral stairs and landings aren’t modeled.
Stringer length is measured along the slope from the total rise and run. Cuts at the top and bottom need a few extra inches, which the suggested board length allows for.
Headroom and width depend on the opening above and the walls beside the stairs, so they’re listed as checks to measure, not calculated.
This is a planning tool, not a permit drawing. Confirm the requirements with your local building department before you build.

Sources

Frequently asked questions

What is the maximum riser height for residential stairs?

The International Residential Code limits risers to 7¾ inches (section R311.7.5.1), measured vertically between the leading edges of adjacent treads. Most US states and cities adopt the IRC, sometimes with amendments, so check with your local building department. Within one flight, the tallest and shortest risers may differ by no more than ⅜ inch.

What is the minimum tread depth?

The IRC requires treads at least 10 inches deep, measured horizontally from nosing to nosing (R311.7.5.2). Treads under 11 inches deep with solid risers also need a nosing that projects ¾ to 1¼ inches. Deeper treads, around 11 inches, make stairs noticeably easier to walk.

How many steps do I need for a 9 foot rise?

A 9 foot (108 inch) rise needs 14 risers of 7 11/16 inches each at the IRC maximum. With the upper floor as the last step, that's 13 treads and a total run of 10 feet 10 inches with 10 inch treads. For gentler stairs, a 7¼ inch maximum gives 15 risers of 7 3/16 inches.

How do I calculate stair stringer length?

The stringer runs along the slope, so its length is the hypotenuse of the total rise and the total run, from the Pythagorean theorem. For a 108 inch rise and 130 inch run that's about 169 inches, or 14 feet 1 inch. Buy the next standard 2×12 length with a little extra for the cuts, here 16 feet.

What is the best angle for stairs?

Code-maximum residential stairs, 7¾ inch risers with 10 inch treads, come out at about 37.8 degrees. Many people find stairs around 30 to 35 degrees more comfortable. A classic rule of thumb is that twice the riser plus the tread should be about 24 to 25 inches.

How much headroom do stairs need?

The IRC requires at least 6 feet 8 inches of headroom, measured vertically from a sloped line along the tread nosings to the ceiling or anything above (R311.7.2). On basement stairs, the beam or floor opening above is the usual problem, so measure it before you cut stringers.

Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.

Your stairs

Layout: where each step lands