Stair Calculator

To lay out stairs, divide the total rise by your target riser height and round up to get the number of risers; treads are one fewer. For a 106 in rise and 7.5 in risers, 106 ÷ 7.5 ≈ 14.13, so 15 risers of about 7 1/16 in and 14 treads. This stair calculator adds total run, angle, stringer length, a diagram and a code check.

How to use the stair calculator

1. Measure the total rise: the vertical distance from the finished lower floor to the finished upper floor. Use finished surfaces, because flooring changes the first and last steps.
2. Choose From total rise if you have room to spare and want to pick the riser height and tread depth. Choose Fit a space if the horizontal space (total run) is fixed.
3. Enter the target or maximum riser height and, in the first mode, the tread depth. Add the tread thickness to get the bottom cut of the stringer, and the headroom to check it.
4. Read the number of risers, riser height, treads, total run, stair angle and stringer length. The diagram is drawn to scale, and Show steps explains each number.

Stair formulas

Rounding the riser count up, never down, keeps every riser at or below your target. There is one tread fewer than risers because the upper floor itself is the last step. The stair forms a right triangle with the total rise and total run as its legs, so the stringer’s sloped length is the hypotenuse from the Pythagorean theorem, and the angle comes from the tangent ratio, rise over run.

Worked example: a basement stair

The total rise is 8 ft 10 in, and you want risers of about 7 1/2 in with 10 1/2 in treads.

1. Total rise in inches: 8 × 12 + 10 = 106 in.
2. Risers: 106 ÷ 7.5 ≈ 14.13, rounded up to 15.
3. Riser height: 106 ÷ 15 ≈ 7.067 in, about 7 1/16 in.
4. Treads: 15 − 1 = 14, so the total run is 14 × 10.5 = 147 in (12 ft 3 in).
5. Angle: tan θ = 7.067 ÷ 10.5 ≈ 0.673, so θ ≈ 33.94°.
6. Stringer: √(106² + 147²) = √(11,236 + 21,609) ≈ 181.23 in, about 15 ft 1 1/4 in.

Worked example: fitting a fixed space

Same 106 in rise, but only 12 ft 6 in (150 in) of floor is available, and risers may be at most 7 3/4 in. Risers: 106 ÷ 7.75 ≈ 13.68, so 14 risers of 106 ÷ 14 ≈ 7.571 in (about 7 9/16 in). Treads: 13, each 150 ÷ 13 ≈ 11.54 in (about 11 9/16 in). The angle is arctan(7.571 ÷ 11.54) ≈ 33.27°, and the stringer is √(106² + 150²) ≈ 183.67 in.

Worked example: when the run is too short

A 96 in rise with only 9 ft (108 in) of run and 7 3/4 in maximum risers needs 13 risers of about 7 3/8 in (96 ÷ 7.75 ≈ 12.39, rounded up). The 12 treads would be 108 ÷ 12 = 9 in deep, under the 10 in minimum, and the stair would be about 39.4° steep. To get 10 in treads you need 12 × 10 = 120 in (10 ft) of run, which gives an angle of about 36.4°. The calculator flags this in the code check, so you can change the plan before you cut anything.

Stair code limits (IRC)

Most U.S. homes are built under a local version of the International Residential Code (IRC). Section R318.7 sets these limits for stairs in one- and two-family homes:

These are code minimums, not comfort targets, and they are not the whole code: landings, handrails, guards, winders and spiral stairs have their own rules. Your city or county may adopt a different edition or amend these numbers, so check your local building code, and your building department, before you build. Commercial buildings follow the International Building Code instead.

Riser height and stair angle

Because the angle depends only on riser ÷ tread, a small change in either moves it noticeably. At the code limits (7 3/4 in risers, 10 in treads) the angle is arctan(0.775) ≈ 37.78°, which is steep. The first example, at about 33.9°, climbs more gently. Lowering the riser adds a step, and every extra step adds one more tread depth to the total run, so a gentler stair always needs more floor space.

Common stair calculation mistakes

• Measuring to the subfloor. Measure finished floor to finished floor, or the top and bottom steps will differ from the rest.
• Counting treads as steps. A stair with 15 risers has 14 treads; the upper floor is the last step.
• Rounding the riser count down. 14.13 risers means 15; rounding to 14 makes every riser taller than planned.
• Forgetting the tread thickness. Cut the bottom of the stringer down by one tread thickness so the first step matches.
• Buying stringers at exactly the slope length. The calculated length runs floor to floor; stock must be longer to allow for the cuts.

Stair layout practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

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

108 in ÷ 7.75 ≈ 13.94, so at least 14 risers of about 7 11/16 in, with 13 treads. At a 7.5 in target, 108 ÷ 7.5 = 14.4 rounds up to 15 risers of 7.2 in.

What is the maximum riser height for stairs?

The IRC sets 7 3/4 in for homes, with a minimum tread depth of 10 in. Local codes can differ, so confirm with your building department.

How do you calculate the length of a stair stringer?

Use the Pythagorean theorem: stringer = √(total rise² + total run²). For 106 in of rise and 147 in of run that is about 181.23 in. Buy stock longer than this to allow for the end cuts.

What is a good stair angle?

The angle follows from riser ÷ tread. At the IRC limits, 7 3/4 in risers on 10 in treads, it is about 37.8°; 7 in risers on 11 in treads give about 32.5°. The lower the riser and the deeper the tread, the gentler the climb, at the cost of more floor space.

Is the number of steps the number of risers or treads?

Builders count risers, because each riser is one step up. The number of treads is one less.

Related calculators

• Pythagorean theorem calculator for the stringer length
• Trigonometry calculator for tangent and arctangent
• Roof pitch calculator for rise over run on a roof
• Board foot calculator for pricing stringer and tread lumber
• Slope calculator for slope as a ratio, percent and angle

Sources

• International Code Council, 2024 International Residential Code, section R318.7 Stairways (R318.7.1 width 36 in, R318.7.2 headroom 6 ft 8 in, R318.7.5.1 risers 7 3/4 in with 3/8 in variation, R318.7.5.2 treads 10 in, R318.7.5.3 nosing 3/4 to 1 1/4 in), checked November 2026. Earlier editions number this section R318.7.