Stair Calculator
Stair calculator works out Risers and Riser height from Total rise, Number of risers and Maximum riser height allowed. The default figures on this page give riser height of 7.4667 in; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- Risers = ceil(112 / 7.75) = 15; riser height = 112 / 15 = 7.466666666666667 in
- Treads = 14; total run = 14 x 10 = 140 in
- Stringer = sqrt(112^2 + 140^2) = 179.28747864811976 in at 38.659808254090095 degrees
- Throat = 11.25 - (7.466666666666667 x 10) / sqrt(7.466666666666667^2 + 10^2) = 5.26710767515317 in
Checks against the limits enteredtable
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
Keep this result
Save it, change one figure, then compare the two
The calculation stays free. Save this scenario, adjust one assumption, save that too, and put them side by side to see exactly what the change costs you. A free account keeps 5 scenarios and 2 comparisons; Personal makes both unlimited and adds exports and private links. Nothing is saved unless you press Save.
What the stair calculator calculates
Lays out a straight flight of stairs: equal riser height from the total rise, tread count, total run, stringer length and cut angle, cut-stringer throat depth, the stairwell opening needed for headroom, and a check of each dimension against the code limits you are working to.
How to use this stair calculator
Enter Total rise, Number of risers, Maximum riser height allowed and Tread depth. Risers updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Risers, Riser height and Treads.
The method follows 2021 International Residential Code Section R311.7, Stairways: R311.7.1 minimum width 36 in, R311.7.2 minimum headroom 6 ft 8 in, R311.7.5.1 maximum riser 7 3/4 in, R311.7.5.2 minimum tread depth 10 in, R311.7.5.3 nosing 3/4 in to 1 1/4 in where tread depth is less than 11 in, and the 3/8 in maximum variation between the largest and smallest riser or tread in a flight, BUILDABLE_REVIEW_NEEDED: geometry is deterministic, the dimensional limits require the adopted code and specialist approval, so every limit is exposed as an input, OpenStax, Elementary Algebra 2e (Pythagorean theorem and proportional relationships used for the stringer length and stairwell opening) and US Department of Commerce Voluntary Product Standard PS 20 (2x12 stringer stock dresses to 11 1/4 in).
112 in rise on IRC limits example
With Total rise: 112, the calculator returns Risers: 15, Riser height: 7.46666667, Treads: 14. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Risers, Riser height and Treads. The inputs you can vary are Total rise, Number of risers, Maximum riser height allowed, Tread depth, Minimum tread depth allowed and Top riser lands on the floor above.
Understanding Risers, Riser height and Treads
Stair dimensions are life-safety requirements enforced by the building code your jurisdiction has adopted, and local amendments are common. The limits here are pre-filled with the 2021 IRC values for one- and two-family dwellings; confirm the governing code and edition with your building department, and have the design reviewed before you cut a stringer.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What information do I need for the stair calculator?
You need Total rise, Number of risers, Maximum riser height allowed, Tread depth, Minimum tread depth allowed, Top riser lands on the floor above, Stair width and Minimum width allowed. The page opens with default figures that give riser height of 7.4667 in, so you can see the scale before entering your own.
What does this stair calculator show?
It shows Risers, Riser height, Treads, Tread depth used, Total run, Stringer length, Stair angle and Stringer throat depth, with the working and any warnings for your entries.
Can I check how the stair calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.