Stair layout and the common IRC figures

A straight flight of stairs is laid out from one measurement: the total rise from the lower finished floor to the upper one. Everything else — riser count, riser height, total run, stringer length, angle — follows from that number and two layout choices. This guide walks through the arithmetic the stair calculator performs, explains the commonly adopted IRC figures it checks against and what those checks do and do not mean, and shows the misreadings that produce a flight that does not fit the opening.

A boundary first: the tool computes geometry and quantities only. It sizes no stringer, determines no code compliance, and rules on no structure; stringer sizing, attachment, guards, handrails, landings, and headroom need a licensed professional and a local permit review.

Start with the total rise

Measure vertically from finished floor to finished floor with the tape held plumb. The form takes the rise as feet plus an optional inches box: inches are divided by 12 and added to the feet, so 8 ft 9 in becomes 8.75 ft, then multiplied back out to 105 in, because the whole layout runs in inches. In metric mode the rise enters in metres and is converted with the exact definition 1 ft = 0.3048 m; the options enter in millimetres and are divided by 25.4. The engine accepts a total rise up to 360 in (30 ft).

If the upper finish floor is not down yet, measure to the subfloor and enter the finish thickness in the optional field. The tool adds it before dividing, so the top step lands on the finished surface. Example D below is that case: 100 in to the subfloor plus a 0.75 in finish floor gives an effective rise of 100.75 in.

Step 1 — the riser count

The riser count is the fewest equal risers that keep every one at or under the maximum riser height: ⌈rise ÷ max riser⌉. The default maximum is the commonly adopted IRC figure of 7.75 in (7 3/4"); the optional field replaces it. Rounding up matters: rounding to the nearest whole number could produce a riser taller than the limit, and a fraction of a riser cannot be built.

Example A: 105 ÷ 7.75 = 13.5484, which rounds up to 14 risers. Each riser is then the rise divided by the count, exactly: 105 ÷ 14 = 7.5 in. Example D is the boundary case, where the effective rise divides evenly — 100.75 ÷ 7.75 = 13 — and the engine guards the ceiling against floating-point noise so the exact division never gains a phantom riser: 13 risers at 7.75 in, on the limit.

Lowering the maximum raises the count. Example E lays out the same 105 in rise as A under a 7 in maximum and needs 15 risers at 7 in instead of 14 at 7.5 in. One riser more or less changes every downstream figure.

Step 2 — the riser height on the tape

Rise ÷ count rarely lands on a sixteenth of an inch, and a tape measure has no mark for 7.2667. So the tool snaps the exact riser height to the nearest 1/16 and says whether it moved. In Example A the exact figure 7.5 in is already on the grid, and the tape reading is 7 1/2" with nothing to disclose. In Example B a rise of 109 in needs 15 risers at 7.2667 in; the nearest sixteenth is 7 1/4", and the result is flagged as rounded.

The remainder does not vanish. Marking all 15 risers at exactly 7 1/4" would land the flight 1/4" (0.25 in) short of the upper floor. That is why the result is flagged as rounded: the exact 7.2667 in figure is reported beside the tape fraction so the 1/4" remainder is not lost. Where it is absorbed is a layout decision the tool does not make. The feet & inches calculator works on the same 1/16 grid, and the guide to feet, inches, and fractions explains that grid.

Step 3 — treads, run, stringer, angle

A flight has one fewer tread than risers, because the top landing is not a tread: 14 risers means 13 treads. The total run is treads × tread run. The default tread run is the commonly adopted IRC minimum of 10 in; Example A runs 13 × 10 = 130 in (10.83 ft), the floor space the flight needs. Example C shows the option in use: a 42 in deck rise with an 11 in tread gives 5 treads and a 55 in run.

The stringer length is the hypotenuse of the rise-and-run triangle, √(rise² + run²): for Example A, √(105² + 130²) = 167.11 in (13.93 ft). The stair angle is the slope of that same triangle, 38.9° for A. Both are pure geometry from the first rise to the last — the hypotenuse is not the board you buy.

Seven worked flights

Every figure below is computed at build time by the same engine that runs the calculator. The two flag columns report the riser against 7 3/4" and the tread run against 10 in, exactly as the tool does.

Flight M is the metric entry: a 2.7 m rise is 106.2992 in, a 280 mm tread is 11.0236 in, and the layout comes back as 14 risers at 192.86 mm (7 9/16" on the tape), a run of 3.64 m, and a stringer of 4.532 m at 36.6°. Metric mode changes which units lead the display; the arithmetic is the same inch-based layout.

Flight F is the one to study before trusting a flag. Its 8.25 in maximum riser and 9 in tread are both past the common figures, so the layout honours them — 13 risers at 8.0769 in over a 108 in run, at 44.2° — and the flags report OVER and UNDER against the IRC figures regardless. The tool never blocks an entry for exceeding the common figures; it reports the comparison. What it does reject is an option past the engine's practical ceilings — a maximum riser above 24 in or a tread run above 36 in — and the error message names the limit, as it does for the 30 ft rise ceiling.

The common IRC figures, and their status

The engine carries four figures from the 2018 International Residential Code, as quoted in the City of Boise IRC Code Handout #437 (02/2022) and on ICC Digital Codes. They are held as commonly adopted convenience figures: local amendments vary, and a permit reviewer, not the calculator, decides compliance.

The inch figures are the code's. The metric column is this site's exact arithmetic conversion at 25.4 mm per inch — the same conversion the methodology page runs — and not the code's own metric text: the code prints rounded millimetre equivalents beside its inch figures, and the engine's source notes quote them that way. A millimetre figure read from a code handout, or from the calculator's metric-mode flag label, can therefore differ from this column by that rounding. The engine compares against the inch figure.

Read the flags literally. Riser within means the computed riser height is at or under 7.75 in; tread within means the tread run is at or over 10 in. With the defaults in place the riser flag reads within for any tape-measure entry, because the count was chosen to keep it there — the flag earns its keep when you override the maximum, as Flight F shows. The variation and headroom figures are displayed and never tested: the tool cannot see what is above the flight, so headroom is a site measurement, and equal risers satisfy the variation rule only if the flight is built to the layout.

Reading the output, and the misreadings that bite

Feet are not feet-point-inches. The rise box takes decimal feet, with a separate inches box beside it. Typing 8.9 to mean 8 ft 9 in enters 8 ft 10.8 in — a 106.8 in rise instead of 105 in. The engine lays that out: 14 risers at 7.6286 in (7 5/8") rather than 14 at 7.5 in, and every riser is 0.1286 in taller than the opening calls for. Put the inches in the inches box.

Inches typed as feet. Entering 105 in the feet box asks for a 105 ft rise, which is above the 30 ft ceiling and is rejected outright — the error message names the limit. A wrong-box entry under that ceiling is not caught, so a riser count that looks absurd for the opening is the signal to check units.

The stringer figure is geometry, not a cut list. It is the hypotenuse from the first rise to the last; it does not include the top and bottom cuts or the attachment at the header, and it is not a stock length. "Within the common limit" is not approval. It is a comparison against one commonly adopted figure that your jurisdiction may have amended.

What the model leaves out

The engine lays out a straight flight from one total rise. It does not model landings or turns, and it sizes nothing: no stringer, no attachment, no guard, no handrail. It makes no ruling on building-code compliance, load, bearing, or engineering suitability, and it does not know your jurisdiction's amendments. A one-riser "flight" — a single step, such as a 7 in rise — has 0 treads, 0 in of run, and a 90° angle by convention. Everything it reports is a quantity or a geometric length, computed at full precision and rounded only for display, as the methodology page documents.

Frequently asked questions

Lay out your own flight with the stair calculator, chain the landing and tread additions on the feet & inches calculator, read the companion guide on feet, inches, and fractions, or browse all guides.

Every stair figure on this page was computed at build time by the calculator's own engine, and the tool itself runs the arithmetic locally — measurements never leave your browser. The full estimation pipeline is documented on the methodology page.