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Stair Calculator

Lay out a straight stair from its total rise: number of risers and treads, riser height, tread depth, total run, stringer length and angle.

Level: Grades 9–10

Printable worksheet

Stair Calculator

Inputs
What do you know?

Measure vertically between finished floor surfaces. 9 ft = 108 in.

7.75 in is a common limit for homes. Use what your local code allows.

Measured flat from riser to riser, not counting the nosing (the front edge that sticks out).

Result

Number of risers

14

14 risers of 7.714 in and 13 treads of 10 in, at about 37.6°.

Riser height
7.714 in
Number of treads
13
Tread depth
10 in
Total run
130 in
Stringer length (rise–run diagonal)
169.01 in
Stringer length in feet
14.08 ft
Stair angle
37.6 °
2 × riser + tread
25.43 in
Guideline check (verify with your local code)
Within common residential guidelinesCommon residential guidelines, as in the IRC: riser ≤ 7.75 in, tread ≥ 10 in.

See the step-by-step solution ↓

Step-by-step solution

  1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

    1087.75=13.9355=rounded up:14

  2. Divide the rise evenly across the risers, so every step is the same height

    10814=7.7143 in

  3. You need one fewer tread than risers, because the upper floor serves as the top step

    14−1=13

  4. Multiply the number of treads by the tread depth to see how far the stair reaches

    13×10=130 in

  5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

    1082+1302=169.0089 in

  6. Find how steep the stair is: the angle whose slope is riser height over tread depth

    arctan7.714310=37.65 °

  7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

    2×7.7143+10=25.43 in

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Work out how many steps your stair needs, how tall and deep each one is, and how long the side boards must be. A comfortable, safe stair has risers (the upright part of each step) that are all the same height. Its treads (the part you step on) are all the same depth too. You start from the total rise, the height from one finished floor to the next. Split it into equal risers no taller than your limit, and you know how many steps you need. The tread depth then sets how far the stair reaches across the floor.

This calculator splits the total rise into the fewest equal risers that stay at or under your maximum. Then it either uses the tread depth you want or spreads a known total run across the treads. (The run is how far the stair reaches across the floor.) It gives the stringer length, the board that runs along the side and holds the steps. It also gives the stair's angle. It checks the result against common home guidelines found in the International Residential Code: risers no taller than 7¾ in and treads at least 10 in deep. Check these locally, though. The code adopted where you live, and any changes to it, decide what's allowed.

Where it's used

Why this math matters outside the classroom:

  • Riser count. A 108 in total rise with a 7¾ in maximum riser needs 108 ÷ 7.75 ≈ 13.9, so 14 risers.
  • Equal risers. Those 14 risers split the rise evenly at 108 ÷ 14 ≈ 7.71 in each.
  • Stringer length. With 13 treads of 10 in the run is 130 in, and the stringer is √(108² + 130²) ≈ 169 in long.
  • Stair angle. The same stair climbs at arctan(108 ÷ 130) ≈ 39.7°.
  • Deck steps. Deck builders lay out a short stair from the deck surface to the ground so every step is the same height.

Grade level and standards: Grades 9–10; Common Core State Standards for Mathematics HSG.SRT.C.8. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether you know the tread depth you want or the total run you have room for.
  2. Enter the total rise between finished floors and the tallest riser you're allowed.
  3. Enter the tread depth or the total run, in inches.
  4. Read the number of risers and treads, their sizes, the stringer length, the angle and the guideline check.

What the inputs mean

Total rise (finished floor to finished floor)
Measure between the finished surfaces, including flooring not yet installed on either level. A mistake here spreads across every step, and uneven risers make people trip.
Maximum riser height
The calculator picks the fewest risers that keep each one at or below this height. Lowering it adds steps and makes a gentler stair.
Tread depth (run per step)
The depth of each step, measured flat from the face of one riser to the next. The nosing (the front edge that sticks out) overhangs this and isn't added in.
Total run available
Use this when a wall or landing limits how far the stair can reach. The calculator works out the tread depth that fits.

Formula and method

risers = total rise ÷ max riser, rounded up
riser height = total rise ÷ risers
treads = risers − 1
total run = treads × tread depth   (or tread depth = total run ÷ treads)
stringer length ≈ √(total rise² + total run²)
angle = arctan(riser height ÷ tread depth)

In the formulas, √ is the square root, and arctan turns a slope into an angle (it's the "tan⁻¹" key on a calculator).

Rounding the number of risers up makes sure no riser is taller than your limit. Dividing the rise evenly makes them all the same. A straight stair has one fewer tread than risers, because the top riser brings you up to the upper floor.

The stringer figure is the diagonal across the total rise and total run. It's a good guide to the board length you need. The board you cut from must be longer, to allow for the top and bottom cuts and any overhang.

The 2 × riser + tread figure is an old rule of thumb for comfort, and about 24 to 25 in is often quoted. It's shown for your information and is not a code requirement.

Worked example

A basement stair has a total rise of 108 in. You want risers no taller than 7.75 in and 10 in treads.

  1. Risers: 108 ÷ 7.75 = 13.94, rounded up to 14.
  2. Riser height: 108 ÷ 14 = 7.714 in.
  3. Treads: 14 − 1 = 13, so the total run is 13 × 10 = 130 in.
  4. Stringer: √(108² + 130²) = 169.01 in, about 14.08 ft.
  5. Angle: arctan(7.714 ÷ 10) = 37.7°.

Result: 14 risers of 7.714 in and 13 treads of 10 in. That makes a 130 in run, a stringer of about 169 in and an angle of 37.7°, within the common guidelines.

Understanding the result

Most building codes limit more than the tallest riser and shallowest tread. They also limit how much any riser or tread may differ from the others, often by no more than about 3/8 in. Dividing evenly, as here, avoids that problem on paper. Careful cutting keeps it true when you build.

Angles of roughly 30 to 37 degrees feel natural for most people. Steeper stairs save floor space, but they're harder to climb up and down.

Assumptions and limitations

  • A straight stair in one flight, with no landings or winders (wedge-shaped steps that turn a corner).
  • Every riser and every tread is the same size.
  • The top of the stair is the upper floor, not an extra tread.
  • It doesn't check headroom, stair width, handrails, guards, how far the nosing sticks out, or landing sizes. Codes regulate all of them.
  • The stringer length is the rise–run diagonal. A cut list needs extra length, and must allow for the thickness of the treads and risers.
  • This is an estimate. It doesn't replace your local building code or a building official's approval.

Frequently asked questions

Why is there one fewer tread than risers?

The last riser brings you up to the upper floor, which acts as the top step. So a stair with 14 risers has 13 separate treads. If your design adds a top tread below the floor level, count it in the run separately.

What is the maximum riser height for a house?

Many places in the US follow the International Residential Code. It commonly allows risers up to 7¾ in and requires treads of at least 10 in. Local codes can differ and change over time, so check with your building department.

How long should the stringer board be?

Start from the diagonal shown here. Add enough for the plumb (straight up) and level cuts at the top and bottom. Many builders buy the next standard length up. For a 169 in diagonal, a 16 ft board leaves plenty extra.

Can I make the stair less steep?

Lower the maximum riser to add risers, or make the treads deeper. Both make the total run longer, so check there's still room for a landing at the bottom of the stair.

How this calculator is checked

Method: Equal division of total rise with ceiling rounding; Pythagorean diagonal for stringer; arctangent of riser over tread for angle; IRC-style residential guideline values (7¾ in riser, 10 in tread) labeled as guidelines. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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