Stair calculator (staircase rise, run and steps)

How to use the stair calculator

Measure the total rise from finished floor to finished floor, pick the rules to check against, and set a target riser and going. The calculator rounds to a whole number of equal risers and shows whether each limit passes.

1. Pick Region presets at the top; it chooses the units and the code preset for your country. You can change either.
2. Enter the total rise including floor finishes on both floors. Finishes left out of the rise make the first and last steps a different height from the rest.
3. Leave the target riser and going at the preset's values, or set your own. The calculator never lets the riser exceed the preset's maximum.
4. Enter the thickness of the upper floor to get the stairwell opening needed for headroom.
5. Read the checks. Pass means the value is inside the preset's limit; Check means change the inputs.

How to calculate stairs: steps, riser and tread

Divide the total rise by a target riser height and round to a whole number: that's the number of risers. The actual riser is the total rise divided by that number; there is one tread fewer than risers, and the total run is treads × going.

Risers   n = total rise ÷ target riser, rounded  (at least total rise ÷ max riser)
Riser    R = total rise ÷ n
Treads     = n − 1   (the upper floor is the last step)
Run        = (n − 1) × G
Pitch      = atan(R ÷ G)
Stringer  ≈ √(run² + total rise²)

Worked example: a 2.6 m floor-to-floor height (UK)

1. 2,600 ÷ 190 mm target = 13.7, rounded to 14 risers (never fewer than 2,600 ÷ 220 mm max = 11.8, so 12).
2. Riser: 2,600 ÷ 14 = 185.7 mm. Treads: 13.
3. Run: 13 × 250 mm = 3,250 mm. Pitch: atan(185.7 ÷ 250) = 36.6°.
4. 2R + G = 621 mm, inside the 550–700 mm range, and the pitch is under 42°. With the rise and going also inside the private-stair limits, it passes every Approved Document K check in the calculator.
5. Stringer: √(3.25² + 2.6²) = 4.16 m.

Worked example: a 9 ft floor-to-floor height (US)

108 in ÷ 7.5 in = 14.4, so 14 risers of 7.71 in, under the IRC maximum of 7¾ in. With 10½ in treads, 13 treads make a run of 136.5 in (11 ft 4.5 in) at 36.3°.

Stair building code limits by country

Building codes cap riser height and set a minimum going, and some limit 2R + G and the pitch. For homes: the US IRC allows risers up to 7¾ in with treads of at least 10 in; UK Approved Document K allows rises of 150–220 mm with goings of 220–300 mm.

US riser and tread limits from IRC R311.7.5 as quoted by the City of Boise, and headroom from R311.7.2 as quoted by the City of Kindred; UK from Approved Document K Table 1.1 and para 1.11; Australia from NCC 2022 Housing Provisions Table 11.2.2a; Canada from BC Building Code 2018 section 9.8 (based on the 2015 National Building Code). India's values are from secondary summaries of NBC 2016, not the code text, so treat them as typical (sources give 2.1 or 2.2 m headroom). We found no Pakistani stair rule, so Pakistan, the Gulf and other regions use the comfort preset. The comfort preset's riser, going and headroom limits and the Australian headroom are typical figures, not code values. Check with your local authority.

2R + G: what makes a stair comfortable

Two risers plus one going should roughly match a person's stride on stairs, a rule that goes back to the 17th-century French architect François Blondel. The calculator's comfort band is 600–650 mm, a convention rather than a code value; UK and Australian codes accept 550–700 mm.

Germany's occupational safety institute BAuA prefers a step length of 59–65 cm. A stair can meet the code and still feel steep or choppy, so the calculator shows 2R + G whichever preset you use, and checks it where the preset sets a range.

Headroom and the stairwell opening

Headroom is measured straight up from the pitch line through the nosings. The upper floor has to stop where that line comes within the headroom of its underside; from there to the top of the flight is the opening. For the UK example with a 250 mm floor and 2.0 m headroom, the opening is 3,029 mm long.

Opening = run − (total rise − floor thickness − headroom − R) ÷ tan(pitch)

Headroom minimums: 6 ft 8 in under the IRC, 2.0 m under Approved Document K (less in some loft conversions), 1.95 m for stairs in a single dwelling in the Canadian preset. A longer opening or a steeper stair both buy headroom.

Stair or staircase: the words used

A stair or staircase is one or more flights of steps. The rise (riser) is the height of each step, the going or run its depth, the nosing its front edge, the pitch its angle, and the stringer the board or beam that carries the treads.

For a reinforced-concrete (RCC) staircase, with a sloping waist slab and steps cast on top, or a dog-legged stair with a landing, use this calculator for the geometry of each flight, then the concrete calculator and rebar calculator for materials.

Assumptions and limits

The calculator works out one straight flight with equal risers. It checks the riser and going, plus 2R + G and pitch where the preset limits them, and sizes the opening for the preset's headroom; it doesn't check width, handrails, guards or landings.

• For stairs with a landing, split the rise between flights and work each one, keeping the riser the same throughout.
• Codes also limit how much risers and goings may vary within a flight (⅜ in under the IRC), so build to the calculated sizes rather than rounding each step.
• Stringer length is the straight-line length; add the cut at the top and bottom and the timber size your carpenter needs.

Sources

Constants and limits come from these standards, manufacturers' data and trade bodies. Where practice varies, the calculator lets you change the value.

• Stair treads and risers: IRC R311.7 requirements (handout)City of Boise · March 2022
• Approved Document K: Protection from falling, collision and impactUK Government (Department for Levelling Up, Housing and Communities) · 2013 edition incorporating 2013 amendments
• NCC 2022 Housing Provisions, Part 11.2: Stairway and ramp constructionAustralian Building Codes Board · 2022
• BC Building Code 2018, Section 9.8: Stairs, ramps, handrails and guards (based on NBC 2015)Province of British Columbia · 2018
• The design of safe stairs (step-length rule 2R + G)German Federal Institute for Occupational Safety and Health (BAuA) · current

Found a value that doesn’t match your local practice? Tell us and we’ll review it.