Stair Calculator
This stair calculator turns a total rise into the number of risers, the riser height, the number of treads, the total run, the diagonal from the floor to the top edge and the stair angle. Enter the rise, the biggest riser you want to allow and the tread depth, then choose whether the top floor counts as the last step. It is stair rise and run math for a straight stair, and nothing more.
Quick answer: risers = total rise ÷ maximum riser height, rounded up. Riser height = total rise ÷ risers, and treads = risers − 1. A 9 ft rise with a 7 3/4 in maximum riser gives 14 risers of about 7 11/16 in and 13 treads, which is 130 in of run at 10 in per tread.
This calculator does not size stringers, check spans, connections or fasteners, compute loads, or design handrails, guards or footings. Stairs can need a permit and an inspection, so check with your local building department, use the code edition adopted where you build, and ask a qualified professional about stringer size, spans, connections, footings, handrails and guards.
Stair layout starts with the total rise, from finished floor to finished floor. Divide it by the biggest riser you want to allow and round up to get the number of risers, then divide the rise by that number to get the actual riser height. With the top floor as the last step, the stair has one tread fewer than risers. The total run is the treads times the tread depth.
Example: a 9 ft rise is 108 in. With a 7 3/4 in maximum riser, 108 ÷ 7.75 = 13.94, so 14 risers of 108 ÷ 14 = 7.714 in, about 7 11/16 in. That gives 13 treads, and at 10 in each the run is 130 in, which is 10 ft 10 in. The diagonal from the floor to the top edge is √(108² + 130²) = 169.0 in, and the stair angle is arctan(7.714 ÷ 10) = 37.6°.
Method
How this calculator works
The geometry is exact. The code numbers are limits quoted from named sources and editable defaults, never a pass or fail check.
Risers, riser height, treads and run
The number of risers is the total rise divided by the maximum riser height, rounded up, and never less than 1. The actual riser height is the total rise divided by that number, so every riser is equal. With the top floor as the last step, a stair of n risers has n − 1 treads. If you build a top tread, it has n. The run is the number of treads times the tread depth.
Risers = round up (Total rise ÷ Maximum riser height)Riser height = Total rise ÷ RisersTreads = Risers − 1 (or Risers with a top tread)Total run = Treads × Tread depthDiagonal and stair angle
The diagonal runs from the floor at the foot of the first riser to the top edge of the run. It is a layout aid, and the real stringer board is longer because of the end cuts, so lay the stringer out full size or on a framing square. The stair angle is the slope of the line through the nosings, which is the arctangent of the riser height over the tread depth. The arctangent of the total rise over the total run belongs to the diagonal and overstates the slope.
Diagonal = √(Total rise² + Total run²)Stair angle = arctan (Riser height ÷ Tread depth)Code limits quoted
The limits are 7 3/4 in for the riser, 10 in for the tread, 3/8 in of variation within a flight, a nosing of 3/4 to 1 1/4 in unless the tread is 11 in or more, and 147 in of rise in one flight. They come from 2015 and 2018 IRC text as reproduced in AWC DCA 6 and county and city handouts (Knox County, Boise, and a Simpson Strong-Tie handout hosted by Portage, Michigan). No other edition was opened, so none is cited. Check the code edition and amendments adopted where you build.
Defaults: Maximum riser height 7 3/4 in · Tread depth 10 inTop of the stair and the comfort rule
Whether the upper floor acts as the top step depends on how the stair ends, so the calculator lets you choose both ways. It also shows 2 × riser + tread as an information line. Autodesk gives 24 to 25 in for it and Houzz says 25 in works well in most circumstances. It is a rule of thumb from secondary sources and not code, and it never changes the result.
2 × Riser + Tread, information onlyLimits the calculator quotes
| Limit | Value | Where it appears in the text | How the calculator uses it |
|---|---|---|---|
| Maximum riser height | 7 3/4 in (196 mm) | 2015 IRC R311.7.5.1 (Simpson reproduction), 2018 IRC (Knox County), AWC DCA 6 | The default for Maximum riser height. A warning shows if the riser comes out above it. |
| Variation between risers | 3/8 in within a flight | Same sources | Warning text only. All risers are equal by construction, but real ones must stay within 3/8 in, so measure the real rise. |
| Minimum tread depth | 10 in (254 mm), measured between the foremost projections of adjacent treads | 2015 IRC R311.7.5.2, 2018 IRC (Knox County), AWC DCA 6, City of Boise handout | The default for Tread depth. A warning shows if the tread is under 10 in. |
| Nosing | 3/4 to 1 1/4 in projection, not required where the tread is 11 in or more | City of Boise handout, 2018 IRC (Knox County), AWC DCA 6 | A note shows when the tread is under 11 in. |
| Rise of one flight | 147 in (12 ft 3 in) between floors or landings | 2015 IRC R311.7.3 (Simpson reproduction). AWC DCA 6 asks for an intermediate landing on deck stairs above 12 ft. | A warning shows if the total rise is over 147 in. The calculator still computes. |
What each field does
| Field | What to enter |
|---|---|
| Total rise | The vertical distance from finished floor to finished floor, or from the deck surface to finished grade. Measure it. Feet and inches in the US view, meters and centimeters in the metric view. The default is 9 ft. |
| Maximum riser height | 7.75 in (7 3/4 in) by default, 196 mm in the metric view. It is the limit in the 2015 and 2018 IRC text, and your local code may differ. Fractions work. |
| Tread depth | 10 in by default, 254 mm in the metric view. Measured nosing to nosing, level. The 2015 and 2018 IRC text gives 10 in as a minimum. |
| Top of the stair | Top floor is the last step (treads = risers − 1), which is the default, or Build a top tread (treads = risers). |
What the results mean
| Result | What it is |
|---|---|
| Number of risers | The headline answer: total rise ÷ maximum riser height, rounded up. At least 1. |
| Actual riser height | Total rise ÷ risers, so every riser is equal. Shown to three decimals, with the nearest 1/16 in in the US view. |
| Treads | Risers − 1, or equal to the risers if you build a top tread. |
| Total run | Treads × tread depth, with feet and inches in the US view. |
| Diagonal, floor to top edge (not the board length) | √(total rise² + total run²). It is a layout aid and not the length of the stringer board. |
| Stair angle | arctan(riser height ÷ tread depth), in degrees. It is not shown for a single step. |
| 2 × riser + tread (rule of thumb 24 to 25 in, not code) | An information line only. It never blocks or flags a result. |
Worked example: a 9 ft rise
Arithmetic checkedThese are the calculator's own example values: a 9 ft total rise, 7 3/4 in maximum riser, 10 in tread, and the top floor as the last step.
| Step | Math | Result |
|---|---|---|
| Total rise | 9 × 12 | 108 in |
| Number of risers | 108 ÷ 7.75 = 13.935, rounded up | 14 |
| Actual riser height | 108 ÷ 14 | 7.714 in, about 7 11/16 in |
| Treads | 14 − 1 | 13 |
| Total run | 13 × 10 | 130 in = 10 ft 10 in |
| Diagonal, floor to top edge | √(108² + 130²) | 169.009 in = 14 ft 1 in |
| Stair angle | arctan(7.714 ÷ 10) | 37.6° |
| 2 × riser + tread | 2 × 7.714 + 10 | 25.43 in |
| You would see | 14 risers, 13 treads, 130 in of run | |
Disclaimer
Results are planning estimates based on the dimensions and assumptions you enter. They are not engineering, structural or building-code advice. Product yields, densities and coverage vary by manufacturer, batch and site conditions. Check product labels, your supplier and your local building department before you order materials or start work. Read the full calculation disclaimer.
Accuracy
What affects your estimate
The formulas are exact. What changes the answer is how you measure the rise, how the stair ends at the top and what your local code allows.
Building a top tread
The same 9 ft rise with a top tread has 14 treads instead of 13. The run is 140 in, which is 11 ft 8 in, and the diagonal is 176.816 in, which is 14 ft 8 13/16 in. The riser height and the angle do not change.
A deck stair at the limit
A 31 in rise to grade gives 31 ÷ 7.75 = 4 exactly, so 4 risers of 7.75 in, which is the limit and allowed. It has 3 treads, a run of 30 in, a diagonal of 43.139 in (3 ft 7 1/8 in) and an angle of 37.8°. An exact fit does not round up to an extra riser.
Measure the real rise
Measure to the finished surfaces, including flooring. Every riser must stay within 3/8 in of the others. The Boise handout says the code dimensions are exclusive of carpets, rugs or runners, but carpet and pad still take depth from the tread you walk on.
The diagonal is not the stringer length
The stringer board is longer than the diagonal because of the plumb and level end cuts and the stock left for the connection. No allowance is invented here. Lay it out full size, as in the guide on how to lay out stair stringers, and size it with a professional.
Over 147 in, under 10 in, steeper than 45°
A rise over 147 in shows a warning, and deck stair guides ask for an intermediate landing above 12 ft. A tread under 10 in, or under 11 in for the nosing note, also shows a warning. An angle above 45° is called steeper than usual, which is a geometry observation and not a code number.
Single step and metric view
A rise that needs only 1 riser has a run of 0 and needs no stringer. In the metric view the rise is in meters and centimeters (2.74 m by default), the maximum riser is 196 mm and the tread is 254 mm, and results are shown in millimeters.
This calculator shows layout geometry and quotes limits from 2015 and 2018 IRC text. It does not certify a stair against any code. It does not size stringers, check spans or fasteners, compute loads, or design handrails, guards, landings or footings. Check with your local building department about permits and the code adopted where you build, and use a qualified professional for the structure.
Common mistakes
Using the diagonal as the stringer board length
The diagonal is 169.009 in for the example, but the board needs extra for the end cuts. Treat the diagonal as a layout aid and lay the stringer out full size.
Using arctan(rise ÷ run) as the stair angle
That is the angle of the diagonal: 39.7° for the example. The stair slope is arctan(riser ÷ tread), which is 37.6°.
Counting as many treads as risers
When the upper floor is the top step, 14 risers have 13 treads. One tread too many adds 10 in of run that the stair does not have.
Measuring the rise before the finished floors are in
A thick flooring layer changes the rise, and risers must stay within 3/8 in of each other. Measure to the finished surfaces.
Treating the numbers as a code approval
The calculator quotes typical limits from two IRC editions and never certifies a stair. Check the code edition and amendments adopted where you build.
Questions people ask
How do I calculate stairs?
Divide the total rise by the biggest riser you want and round up to get the number of risers. Divide the rise by that number for the riser height, then use one tread fewer than risers when the top floor is the last step. The guide on stair rise and run works through it.
What is the standard riser height and tread depth?
The 2015 and 2018 IRC text, as reproduced in AWC DCA 6 and county and city handouts, gives a maximum riser of 7 3/4 in and a minimum tread of 10 in. Your local code may differ, so check the edition adopted where you build.
How many steps do I need for a 9 ft rise?
A 108 in rise with a 7 3/4 in maximum riser needs 14 risers of 7.714 in, and 13 treads when the top floor is the last step.
How do I find the stair angle?
Take the arctangent of the riser height divided by the tread depth. A 7.714 in riser and a 10 in tread give 37.6°, and 7 3/4 in over 10 in gives 37.8°.
How long is the stair stringer?
The calculator shows the diagonal, floor to top edge, which is a layout aid and not the board length. The board is longer, and you lay it out full size or on a framing square. Stringer size and span are not computed.
Does this calculator check building code?
No. It quotes typical limits as information and warnings, never as a pass or fail result. Ask your local building department whether you need a permit and which code applies.
Can I use it for a deck stair?
Yes, for the layout numbers. Use the rise from the deck surface to finished grade. Footings, stringer size and handrails are outside it, and the Deck Calculator counts boards and joists only.
Related calculators and guides
Sources
Where the numbers come from
- Simpson Strong-Tie, deck inspection code references (2015 editions), hosted by Portage, Michigan a manufacturer's reproduction of 2015 IRC text: 7 3/4 in riser, 10 in tread, 3/8 in variation and 147 in of rise, accessed October 17, 2026.
- Knox County, Tennessee, 2018 IRC residential stairs information 7 3/4 in riser, 10 in tread, nosing and 6 ft 8 in headroom, accessed October 17, 2026.
- City of Boise, IRC R311.7.5 stair treads and risers (handout 437) riser, tread and nosing limits, with dimensions exclusive of carpets, rugs or runners; edition not printed, accessed October 17, 2026.
- American Wood Council, DCA 6 Prescriptive Residential Wood Deck Construction Guide tread and riser detail (Figure 27) based on the 2015 IRC, and an intermediate landing on deck stairs above 12 ft, accessed October 17, 2026.
- Autodesk Revit help, interior stair formulas the 2 × riser + tread rule of thumb of 24 to 25 in (secondary source, not code), accessed October 17, 2026.
- Houzz, key measurements for designing the perfect stairway two risers plus one tread of about 25 in (secondary source, not code), accessed October 17, 2026.