Stair Calculator

To find your number of stairs, divide the total rise in inches by a target riser height and round up. A 9 foot rise at a 7 1/2 inch target takes 15 risers of 7.20 inches and 14 treads.

Find Your Stair Layout

Enter the total rise from finished floor to finished floor, then your target riser and tread run.

15 risers

each 7.20 in tall, about 7 3/16 in, with 14 treads between the floors.

Total run 11 ft 8 in, stair angle 35.8 degrees

Check Local CodeThis result is stair geometry, not code approval. Confirm riser, tread, headroom, and handrail rules with your local building department before you cut anything.

Material List

These figures lay out the stair. Measure on site before you cut a stringer.

Risers: 15
Treads: 14
Riser Height: 7.20 in, about 7 3/16 in
Total Run: 140 in, about 11 ft 8 in
Stair Angle: 35.8 degrees
Rise Plus Run: 17.20 in
Stringer Diagonal: 176.82 in, about 14 ft 9 in
Stringer Stock With Waste: 15 ft 9 in to 16 ft 3 in
First Riser on Stringer: 5.70 in, about 5 11/16 in

How It Works

Measure the total rise from the finished floor at the bottom to the finished floor at the top. The calculator divides that by your target riser and rounds up, since you cannot build part of a step and rounding down makes every riser taller. It then divides the total rise by that whole number, so all the risers come out equal.

Risers = total rise / target riser, rounded upRiser height = total rise / risersTreads = risers minus 1Total run = treads x tread runStringer diagonal = square root of (total rise x total rise + total run x total run)First riser on stringer = riser height minus tread thicknessStair angle = arctangent of (riser height / tread run)

The top floor acts as the last tread, so there is always one fewer tread than risers. Fine Homebuilding says to deduct one tread thickness from the first riser, or that step will end up higher than the rest. It also says to add the thickness of the finished floor to the riser if the flooring is not installed yet.

See Methods and Sources

Worked Example

Here is the math for a stair with a 9 foot total rise, a 7 1/2 inch target riser, a 10 inch tread run, and 1 1/2 inch treads.

  1. 9 ft x 12 = 108 in of total rise
  2. 108 in / 7.5 in = 14.4, rounded up to 15 risers
  3. 108 in / 15 = 7.20 in per riser
  4. 15 risers minus 1 = 14 treads
  5. 14 x 10 in = 140 in of total run, or 11 ft 8 in
  6. Square root of (108 x 108 + 140 x 140) = 176.82 in of diagonal, about 14 ft 9 in
  7. 7.20 in minus 1.5 in = 5.70 in for the first riser on the stringer

The calculator shows a stair angle of 35.8 degrees for this layout. With 12 to 18 inches added for waste, the stringer stock comes to about 15 ft 9 in to 16 ft 3 in.

Stair Counts by Total Rise

These counts use a 7 1/2 inch target riser, so a different target changes them. A 10 foot rise is the one row here that lands exactly on the target.

Total RiseRisersRiser HeightTreadsTotal Run at 10 inTotal Run at 11 in
3 ft57.20 in43 ft 4 in3 ft 8 in
4 ft76.86 in65 ft 0 in5 ft 6 in
6 ft107.20 in97 ft 6 in8 ft 3 in
8 ft137.38 in1210 ft 0 in11 ft 0 in
9 ft157.20 in1411 ft 8 in12 ft 10 in
10 ft167.50 in1512 ft 6 in13 ft 9 in
11 ft187.33 in1714 ft 2 in15 ft 7 in
12 ft207.20 in1915 ft 10 in17 ft 5 in

Rise and Run Rules of Thumb

The Journal of Light Construction says a safe and comfortable rise is between 7 and 8 inches. Swanson Tool gives three quick checks: rise plus run of 17 to 18 inches, two risers plus one run of 24 to 25 inches, and rise times run of 72 to 76 inches. The worked example comes to 17.2, 24.4, and 72.0, so it falls inside all three.

This table shows the stair angle for common pairs, in degrees. A taller riser or a shorter run makes the stair steeper.

Riser Height10 in Run10 1/2 in Run11 in Run12 in Run
7 in35.033.732.530.3
7 1/4 in35.934.633.431.1
7 1/2 in36.935.534.332.0
7 3/4 in37.836.435.232.9

Model Code Limits to Compare

These figures come from Section R311.7 of the 2021 International Residential Code, or IRC. They are model code values and not your local rules, and this calculator does not approve a stair.

Item2021 IRCSection
Maximum riser height7 3/4 inR311.7.5.1
Largest riser difference in a flight3/8 inR311.7.5.1
Minimum tread depth10 inR311.7.5.2
Nosing projection3/4 to 1 1/4 inR311.7.5.3
Minimum clear width36 in above the handrail; at and below it, 31 1/2 in with one handrail or 27 in with twoR311.7.1
Minimum headroom6 ft 8 inR311.7.2
Maximum rise of one flight12 ft 7 inR311.7.3
Minimum landing depth, straight run36 inR311.7.6
Handrail height34 to 38 inR311.7.8.1

The code calls for a handrail on at least one side of a flight with four or more risers, and the nosing is not required where the tread depth is at least 11 inches. The 2024 IRC keeps the same riser, tread, width, headroom, and flight rise limits in Section R318.7.

Local rules can differ. The Journal of Light Construction notes that the riser limit can vary by state, and the National Association of Home Builders recommends that state and local governments set residential stair limits at a riser of no more than 8 1/4 inches and a tread of no less than 9 inches, or keep the limits in their legacy codes. Workplaces follow other rules, and OSHA allows standard stairs a riser up to 9.5 inches, a tread of at least 9.5 inches, and an angle of 30 to 50 degrees.

Cutting the Stringers

The Journal of Light Construction says most open stringers are cut from 2×12 stock. Fine Homebuilding says to leave at least 5 inches of stock behind the notches, and the Journal of Light Construction measures that uncut depth to the saw kerf.

The stock length above says nothing about strength. For deck stairs, the Journal of Light Construction gives a 2×12 stringer a maximum recommended unsupported span of 6 feet, and it says overspanned stringers can be repaired with intermediate support posts, so plan support for a long flight.

Frequently Asked Questions

These cover the questions that come up most often.

How Many Steps Do I Need for a 9 Foot Rise?

A 9 foot rise is 108 inches. At a 7 1/2 inch target, that takes 15 risers of 7.20 inches and 14 treads. At the 7 3/4 inch maximum in the 2021 IRC, it takes 14 risers of 7.71 inches and 13 treads.

What Is the Maximum Stair Riser Height?

The 2021 IRC sets the riser height at not more than 7 3/4 inches, and the tallest riser in a flight can exceed the shortest by no more than 3/8 inch. Your local code can differ, so check with your building department.

How Deep Should Stair Treads Be?

The 2021 IRC sets the tread depth at not less than 10 inches, measured from nosing to nosing. It also calls for a nosing of 3/4 inch to 1 1/4 inches, unless the tread depth is at least 11 inches.

Why Are There Fewer Treads Than Risers?

The floor at the top serves as the last step, so a stair always has one fewer tread than risers. That is why total run uses the tread count and not the riser count.

How Do I Measure Total Rise?

Measure from the finished floor at the bottom to the finished floor at the top. For a deck, the Journal of Light Construction says to measure to the elevation of the actual landing spot, which is not necessarily straight down from the deck, since the ground may slope away.

How Long Should a Stair Stringer Be?

Take the square root of the total rise squared plus the total run squared, then add 12 to 18 inches for waste, as Swanson Tool suggests. For a 108 inch rise and a 140 inch run, the diagonal is 176.82 inches, or about 14 ft 9 in.

Sources

Every figure on this page comes from the sources below, or from the math shown.

This result is an estimate. Check your measurements before you order. If we got something wrong, please contact us.

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