Stair geometry calculator

What a stair calculator does

A stair calculator divides a floor-to-floor height into equal risers and the available horizontal run into equal treads, then shows which combinations fall inside the riser and tread limits you set. For a straight flight it lists every workable riser count with its riser height, tread depth (going) and a 2R + G comfort figure.

You enter the limits, so the same tool works for a house under the IRC, a commercial building under the IBC or a metric project under another code: if you set a 7-3/4 in maximum riser and a 10 in minimum tread, only layouts within those numbers are listed. Separately, each layout is flagged within or outside the 2021 IRC R311.7.5 or 2021 IBC 1011.5.2 riser and tread limits and the 600–650 mm 2R + G comfort band, and a headroom check uses the floor depth and minimum headroom you enter. The flags are a prompt to check the adopted code, not a compliance determination.

Every layout assumes the upper floor is the top landing, so a flight with 14 risers has 13 treads. Headroom, landings, nosings, winders, handrails and structure are outside its scope, so treat the result as the geometry to draw, then check it against your adopted code.

How to use the stair geometry calculator

1. Choose Imperial or Metric. Imperial uses feet for the height and run and inches for the riser and tread limits.
2. Enter the floor-to-floor height, measured from finished floor to finished floor.
3. Enter the available horizontal run: the plan length the treads can occupy, from the face of the bottom riser to the face of the top riser.
4. Set the minimum and maximum riser and the minimum and maximum going (tread depth) from your code or design standard, then pick a Rule set to flag: 2021 IRC R311.7.5, 2021 IBC 1011.5.2 or Entered limits only.
5. Choose a Layout: Straight flight, or Two runs with intermediate landing with the landing length that sits inside the run. Enter the upper floor construction depth and the minimum headroom you want to check.
6. Review the options table: risers, goings, riser height, going, 2R + G, the rule-set flag and the 600–650 mm comfort flag for each layout that fits. The results show the first option, its total run, the headroom above the first tread and the stairwell opening length needed, and the notes list every riser height of the first layout. Export PDF, CSV or SVG, or copy the results.

Worked example

Imperial: A 9 ft floor-to-floor height and 12.5 ft run can use 14 risers at 7.71 in and 13 goings at 11.54 in, within the 2021 IRC R311.7.5 limits of 7¾ in and 10 in.

Metric: A 2.8 m floor height and 3.9 m run can use 15 risers at 186.67 mm and 14 goings at 278.57 mm.

IRC and IBC stair riser and tread limits

The two model codes most US projects use set different stair geometry. The IRC covers one- and two-family dwellings and townhouses; the IBC covers most other buildings. The values below are from the 2021 editions. Check the edition and any amendments adopted where you build.

Where IRC treads are less than 11 in deep, a nosing projection of 3/4 in to 1-1/4 in is required (R311.7.5.3). Tread depth is measured horizontally from nosing to nosing, which is the going the calculator uses.

How to calculate stair rise and run

The method is the same whatever limits you use. Worked through for a 109 in floor-to-floor height under the IRC:

• Divide the floor-to-floor height by the maximum riser and round up to get the minimum number of risers: 109 ÷ 7.75 = 14.06, so 15 risers.
• Divide the height by that count for the actual riser height: 109 ÷ 15 = 7.27 in.
• When the upper floor is the top landing, there is one fewer tread than risers: 14 treads.
• Multiply the treads by the minimum tread depth for the shortest total run: 14 × 10 in = 140 in, or 11 ft 8 in.
• If the run does not fit, adding risers makes the stair longer, not shorter. Look for more length, or split the flight with a landing and a turn.

Stair comfort rules of thumb: 2R + T

Codes set limits; comfort comes from the relationship between riser and tread. These traditional rules of thumb are not code requirements, but they help choose between layouts that all fit:

• 2R + T = 24 to 25 in (roughly 610 to 635 mm). Two risers plus one tread approximates a normal stride. The calculator shows this as 2R + G for every option.
• R + T = 17 to 18 in.
• R × T = 70 to 75 (inches × inches).

Worked examples: choosing a layout, and IRC versus IBC

Start with the calculator's default inputs: 9 ft floor to floor, 12 ft 6 in of run, 6 to 7-3/4 in risers and 10 to 14 in goings. It finds three layouts: 14 risers at 7.71 in with 11.54 in goings (2R + G = 26.97 in), 15 risers at 7.20 in with 10.71 in goings (25.11 in) and 16 risers at 6.75 in with 10 in goings (23.50 in). All three fit the limits, but the 15-riser option sits closest to the 24 to 25 in comfort band.

Now take a floor-to-floor height of 109 in (for example, 8 ft ceilings plus about 13 in of floor structure and finishes) and 12 ft of plan length for the stair. With IRC-based limits entered (7-3/4 in maximum riser and 10 in minimum tread, with 6 in and 14 in as practical lower and upper bounds), the calculator returns one layout: 15 risers at 7.27 in and 14 treads at 10.29 in, 2R + G = 24.82 in.

Enter IBC limits instead (4 to 7 in risers, 11 in minimum tread) and no straight flight fits in 12 ft: 16 risers are needed, and 15 treads at 11 in take 13 ft 9 in. With a 14 ft run the calculator finds 16 risers at 6.81 in and 11.20 in treads. For this height the IBC stair needs at least 25 in more run than the IRC stair.

Before you commit, check headroom along the whole flight, landing sizes at the top and bottom, and the 3/8 in uniformity limit: floor finish thicknesses at the top and bottom change the first and last risers.

Who it is for and when to use it

Method, formulas & assumptions

For each integer riser count, riser = floor height ÷ count and goings = count − 1 (count − 2 with an intermediate landing). Going = available run, less landing, ÷ goings. Options must satisfy your entered limits and are flagged against the selected rule set (2021 IRC R311.7.5 or 2021 IBC 1011.5.2) and the 600–650 mm 2R + G comfort band. Headroom above the first tread = floor height − floor depth − riser; stairwell opening length = (minimum headroom + floor depth) × going ÷ riser.

Imperial inputs are converted with exact factors (1 ft = 0.3048 m, 1 lb = 0.45359237 kg, 1 US gal = 3.785411784 L) before the calculation runs in SI, then results are converted back.

Common mistakes to avoid

• Using ceiling height instead of floor-to-floor height. The stair has to climb the floor structure and finishes as well.
• Forgetting finish thickness. Adding 3/4 in hardwood at the top or tile at the bottom changes the first or last riser and can break the 3/8 in uniformity limit.
• Counting as many treads as risers. When the upper floor is the top landing, a flight has one fewer tread than risers.
• Measuring the available run to the wrong point, or including a landing in it. The run is from the face of the bottom riser to the face of the top riser.
• Ignoring headroom. A flight that fits in plan can still hit a beam or floor edge above, so check 6 ft 8 in clear along the slope.
• Treating the entered limits as a compliance check. The tool tests only the numbers you give it.

Scope & limits

Assumes the upper floor is the final landing. Flags compare riser and going only; nosings, uniformity, width, handrails, guards and winder geometry are not checked. Not a compliance determination; confirm with the adopted code.

Frequently asked questions

Further reading

• Stair dimensions: rise and run
• Minimum ceiling height requirements
• Egress and corridor widths
• All drawing & geometry tools
• All free architecture & construction tools
• Harth resource library

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