Stair Stringer Calculator
From total rise and a maximum riser height, get the number of risers and treads, the exact riser, total run, stringer length and pitch, in inches or millimetres, checked against the US IRC or the Singapore, Malaysia, Hong Kong, Taiwan, Japan or England limits. Free.
Stair Stringer Calculator
Lay out a straight flight from a single measurement. Enter the total rise (floor-to-floor height) and the tallest riser you will accept, and this works out the number of risers and treads, the exact riser height, the total run, the stringer length and the pitch, then checks the layout against the limits of the jurisdiction you pick.
United States — IRC, dwellings
Key limits: riser ≤ 7¾ in (196 mm), tread ≥ 10 in (254 mm); in one flight the largest riser or tread may exceed the smallest by no more than ⅜ in.
Source: International Residential Code R311.7.5.1–.2, as quoted in City of Boise IRC handout #437 (2022).
Scope: One- and two-family dwellings. States and cities adopt different IRC editions, and the section number is the one the 2022 handout quotes. Dimensions exclude carpets, rugs and runners.
A calculator layout is not an approved design. Headroom, handrails, guards, nosings, winders and landing sizes are not checked here, and the authority where you build has the final say.
How to Use the Stair Stringer Calculator
Measure the total rise
The vertical distance from the lower finished floor to the upper finished floor. Every riser depends on it, so include the thickness of any flooring still to go down.
Pick your units and your code
Work in inches or millimetres; switching converts what you have typed. Then choose whose limits to check against: the US IRC, Singapore, Malaysia, Hong Kong, Taiwan, Japan or England. The box under the results names the clause, what it covers and what it leaves out.
Set the tallest riser you will accept
By default the target is a maximum: the total rise is divided by it and the number of risers is rounded up, so no riser comes out taller than the target. The rise is then divided back by that whole number so every riser is identical. Choose “approximate” to round to the nearest whole riser instead; the page tells you when that puts the riser over your target.
Set the tread depth and read the results
The tread (going) is the horizontal depth of each step. The calculator multiplies it by the number of treads for the total run, works out the pitch through the nosings, and flags any limit the layout breaks, including a flight too tall to climb without a landing where the chosen code sets one.
Laying Out a Staircase the Right Way
From One Measurement to a Whole Staircase
A straight flight follows from one number: the total rise, finished floor to finished floor. Divide it by the tallest riser you will accept, round the count up to a whole number, and you have your risers. Then divide the total rise back by that whole number to get the actual riser height, so every step is the same. Codes insist on that: the US IRC lets the largest riser in a flight exceed the smallest by no more than ⅜ inch, and Malaysia’s by-law 106(1) wants rise and tread “uniform and consistent throughout”. There is always one tread fewer than risers, because the top riser lands on the upper floor. The tread count times the tread depth is the total run, and the stringer diagonal is the hypotenuse of the rise and the run.
Why rounding to the nearest step can break your limit
The obvious way to count risers is to round the rise divided by the target to the nearest whole number. About half the time that rounds down, and the riser comes out taller than you asked for. We ran this calculator over floor heights from 2.4 m to 4.5 m in 10 mm steps with a 175 mm target: rounding to the nearest riser put the riser above 175 mm at 102 of the 211 heights, by up to 6.2 mm. The overshoot can approach half the target divided by the number of risers, so it grows on short flights: about 29 mm on a three-riser step. Rounding up never overshoots. That is why the target is treated as a maximum unless you choose otherwise, and why an overshoot is flagged when you do.
Pitch is measured through the nosings
The pitch of a stair is the angle of the line joining the nosings, the front edges of the treads. For equal steps that line rises one riser for every tread, so the pitch is the arctangent of the riser divided by the tread. England’s Approved Document K draws it this way, nosing to nosing, and caps a private stair at 42°. It is not the angle of the total rise over the total run: that line runs from the foot of the bottom riser to the top nosing and reads steeper, by about 20° on a two-riser deck step. A single step has no flight, so it has no pitch.
"The whole staircase unfolds from the total rise: divide for the step count, divide back for the exact riser so every step is equal, and the Pythagorean theorem gives the stringer. One measurement, one triangle, a flight of stairs."
Riser and tread limits, by jurisdiction
Each limit below is quoted from the text named beside it. The figures cover riser height, tread depth and, where the text sets one, how far a flight may climb before a landing. They are the numbers this calculator checks; the rest of each code is not.
| Where | Riser at most | Tread at least | Flight or landing | Source |
|---|---|---|---|---|
| Singapore, exit staircase within a residential unit | 175 mm | 225 mm | — | SCDF Fire Code 2023, Cl. 2.3.3d(4) |
| Singapore, exit staircase in residential common areas | 175 mm | 275 mm | — | SCDF Fire Code 2023, Cl. 2.3.3d(4) |
| Malaysia, any staircase in a residential building | 180 mm | 255 mm | Landing at least every 4.25 m of height; no flight under 2 risers | UBBL 1984, by-laws 106 and 108 (KPKT consolidated copy) |
| Hong Kong, required (means-of-escape) staircases | 175 mm | 225 mm | 2 to 16 risers a flight | Code of Practice for Fire Safety in Buildings 2011 (2024 edition), B14.2 |
| Taiwan, category 4 stairs | 200 mm | 210 mm | Landing within every 4 m of height | 建築技術規則建築設計施工編 第33條, 第34條 |
| Japan, house stairs | 230 mm | 150 mm | — | 建築基準法施行令 第23条 |
| England, private stair | 220 mm (at least 150) | 220 mm (at most 300) | Pitch at most 42° | Approved Document K (2013), Table 1.1 |
| United States, IRC dwellings | 7¾ in (196 mm) | 10 in (254 mm) | — | IRC R311.7.5, as quoted by the City of Boise (2022) |
Singapore’s figures are for exit staircases (SCDF Fire Code 2023 cl. 2.3.3d). They sit in the Fire Code because, in SCDF’s words, BCA “has removed them from its code”, and the clause carries an amendment date of 1 March 2019. The Fire Code treats access stairs inside a unit as a separate category, and whether these figures apply to the internal stair of a landed house or an HDB maisonette is unsettled: we could not confirm it from the text, so ask your Qualified Person. Hong Kong’s figures are likewise for required staircases, the means-of-escape stairs, and how they apply to a private stair inside a flat is equally unsettled. Above 2,800 mm floor to floor, a single straight flight at 175 mm needs at least 17 risers, one more than Hong Kong’s B14.2 allows. Malaysia’s by-law 106(1) is the one that plainly covers a house stair: it applies to “any staircase”. Malaysian states adopt their own versions of the by-laws, and the IRC edition in force varies by US state and city.
The comfort rule is three centuries old
François Blondel’s Cours d’architecture (1683) set out the rule behind 2R + G. A person’s easy pace on the level is “deux pieds c’est à dire de vingt-quatre pouces”, while a step straight up a ladder is only one foot, so each unit of rise counts as two of going: twice the riser plus the tread should make one pace. Those are French feet and inches, not English ones: two old Paris feet come to roughly 65 cm, an approximate conversion rather than a figure Blondel gives. Blondel himself says he first published the rule in his notes to Savot’s book. Approved Document K calls 2R + G between 550 and 700 mm “the normal relationship” for stairs in England, and the calculator reports where your layout falls against that range. Outside England it is a guide, not a limit.
Where the calculator stops
The layout here is a starting point. It does not check headroom, handrails, guards on open sides, nosings, winders, stair width or the size of landings, and it lays out one straight flight: for a stair with a landing, run each flight separately. The stringer must keep enough solid timber below the step cuts, and its size is set by the span, the load and your code. A layout that passes every number on this page is still not an approved design. The authority where you build decides, and in many places the plans have to be submitted and inspected.
Every riser must match within three eighths of an inch
Risers = total rise ÷ target, rounded up, so no riser is taller than the target.
Divide the rise back by the riser count so every step is exactly equal.
Treads = risers − 1: the top riser lands on the upper floor.
Pitch = atan(riser ÷ tread), measured nosing to nosing (Approved Document K).
IRC R311.7.5: riser ≤ 7¾″ (196 mm), tread ≥ 10″ (254 mm).
Within a flight, the largest riser and tread may exceed the smallest by no more than ⅜″ (IRC R311.7.5).
Singapore: an exit staircase riser may be at most 175 mm (SCDF Fire Code 2023, Cl. 2.3.3d(4)).
Hong Kong: a required staircase flight has 2 to 16 risers (Fire Safety Code B14.2).
Blondel, 1683: twice the riser plus the tread makes one easy pace of two French feet, roughly 65 cm.
Handrails, guards, headroom and landings are set by your local code as well.
Frequently Asked Questions
- Divide the total rise (finished floor to finished floor) by the tallest riser you will accept and round up to a whole number: that is your number of risers. Divide the total rise back by that number for the exact, equal riser height. Treads equal risers minus one, and the total run is the treads times the tread depth. The stringer diagonal is √(rise² + run²), and the pitch is the arctangent of the riser over the tread. This calculator does all of it, in inches or millimetres, and checks the result against the code you choose.
- Singapore’s SCDF Fire Code 2023 (cl. 2.3.3d(4)) caps the riser of an exit staircase at 175 mm, with a tread of at least 225 mm within residential units and 275 mm in residential common areas. Malaysia’s Uniform Building By-Laws 1984 (by-law 106) allow a rise of up to 180 mm with a tread of at least 255 mm in any staircase, and by-law 108 asks for a landing at vertical intervals of not more than 4.25 m in residential buildings. Hong Kong’s Code of Practice for Fire Safety in Buildings (B14.2) sets 175 mm and 225 mm for required (means-of-escape) staircases, in flights of 2 to 16 risers. Malaysia’s rule plainly covers a house stair; whether Singapore’s and Hong Kong’s escape-stair figures apply to the internal stair of a home is unsettled, so check with the professional who submits your plans.
- Because a riser limit is a maximum, and rounding to the nearest whole riser rounds down about half the time, which makes every riser taller than the one you aimed at. Over floor heights from 2.4 m to 4.5 m with a 175 mm target, rounding to nearest overshot at 102 of 211 heights; rounding up never did. You can still choose “approximate”, and the page will say when the riser ends up over your target.
- The oldest rule is François Blondel’s, from his Cours d’architecture of 1683: twice the riser plus the tread should equal one easy pace, which he put at two French feet (roughly 65 cm, in an approximate conversion). Approved Document K, for England, calls 2R + G between 550 and 700 mm the normal relationship. The calculator shows your 2R + G and where it falls against that range, but it is a guide rather than a limit everywhere except England, where it sits in Table 1.1. The riser and tread limits of your own code come first.
- Codes require it. The US IRC lets the largest riser or tread in a flight exceed the smallest by no more than ⅜ inch, and Malaysia’s by-law 106(1) says the rise and tread “shall be uniform and consistent throughout”. That is why the calculator divides the total rise by a whole number of risers to give one exact riser height, rather than leaving an odd step at the top or bottom.
- Under the International Residential Code, section R311.7.5 as quoted in the City of Boise’s 2022 handout, the maximum riser height is 7¾ inches (196 mm) and the minimum tread depth is 10 inches (254 mm), with the largest riser or tread in a flight no more than ⅜ inch over the smallest. Dimensions are measured without carpets, rugs or runners. States and cities adopt different editions, and commercial stairs fall under other rules, so confirm the requirements with your local building department.
- The stringer length shown is the straight-line diagonal of the rise and the run, the shortest board before the step cuts. Buy stock longer to allow for the top and bottom connections and any waste. The stringer must keep enough solid timber below the step cuts; its size, and how many you need across the width, depend on the span, the load and your code.
- Where the chosen code sets a limit, the calculator tells you. Hong Kong’s B14.2 allows no more than 16 risers in a flight, so above 2,800 mm floor to floor a single straight flight at 175 mm is one riser too many; Malaysia’s by-law 108(1) wants a landing at vertical intervals of not more than 4.25 m in residential buildings; Taiwan’s 第34條 wants one within every 4 m of stair height. The calculator lays out a single straight flight, so for a stair with a landing, run each flight’s rise separately. Landing sizes, and the landing rules of the other codes, are not checked here.
- The pitch is the angle of the line through the nosings, which for equal steps is the arctangent of the riser divided by the tread. Approved Document K measures it that way and limits a private stair in England to 42°. It is not the angle of the total rise over the total run, which reads steeper because that line starts at the foot of the bottom riser. A single step has no pitch.
- The geometry is the same for deck, porch and garden stairs. Measure the total rise from the lower surface (ground or pad) to the deck surface and proceed as normal. Exterior stairs may have their own requirements, so check the rules for outdoor stairs where you build.
- Yes. Switch the units to millimetres and pick Singapore, Malaysia, Hong Kong, Taiwan, Japan or England under “Check against”, and the layout is checked against that text’s riser, tread and landing figures instead of the IRC’s. Do not type millimetres into the inch fields: the page will warn you if the numbers look like the wrong unit. Each code also covers things this calculator does not check, and passing these numbers does not make a stair an approved design, so confirm the rules with your local authority wherever you build.
Method & sources
How it computes
Risers = total rise ÷ target riser, rounded up by default so no riser exceeds the target (or to nearest, flagging an overshoot); riser = rise ÷ risers; treads = risers − 1; run = treads × tread; stringer = √(rise² + run²); pitch = atan(riser ÷ tread), nosing to nosing. Checked against the chosen code: IRC R311.7.5, SCDF Fire Code 2.3.3d(4), UBBL by-laws 106/108, HK FS Code B14.2, 建築技術規則 第33/34條, 施行令 第23条 or ADK Table 1.1. StairKernel, tested.
What this tool implements
- Method: risers = total rise ÷ target, rounded UP by default so no riser is taller than the target; "approximate" rounds to nearest and flags any overshoot. Pitch = atan(riser ÷ tread), the line through the nosings that Approved Document K draws "from nosing to nosing". Until 2026-10-12 the page showed atan(total rise ÷ run) as the pitch and rounded to nearest: at a 175 mm target over 211 floor heights (2.4–4.5 m, 10 mm steps) the riser came out above 175 mm at 102 of them, worst 181.2 mm.
- US: IRC R311.7.5.1–.2 as reproduced in City of Boise handout #437 (2022): riser not more than 7 3/4 in (196 mm), tread not less than 10 in (254 mm), the largest riser or tread in a flight no more than 3/8 in over the smallest, exclusive of carpets, rugs or runners. The ICC site refused the request; any 2024 renumbering is not verified.
- Singapore: SCDF Fire Code 2023 Cl. 2.3.3d(4): "The height of the riser for any exit staircase shall not be more than 175mm and depth of tread shall not be less than: (a) 225mm within residential units and 275mm for common areas of residential buildings"; 2.3.3d(5): clear headroom at least 2m. The clause binds EXIT staircases (amendment date 1 Mar 2019); SCDF states BCA removed these requirements from its code. Whether the figures apply to the internal stair of a landed house or HDB maisonette is unsettled.
- Malaysia: Uniform Building By-Laws 1984 (KPKT consolidated copy, amendments to K.P.U. 6/2007), by-law 106(1): rise not more than 180 mm, tread not less than 255 mm, "uniform and consistent throughout"; 108(1): in residential buildings a landing at vertical intervals of not more than 4.25 m; 108(2): no flight of fewer than two risers. State versions were not checked.
- Hong Kong: Code of Practice for Fire Safety in Buildings 2011 (2024 edition), B14.2: required staircases in straight flights without winders of not more than 16 nor less than 2 risers, treads not less than 225mm clear of nosings, risers not more than 175mm; B14.4: clear headroom not less than 2000mm. These are means-of-escape (required) staircases; application to a private stair inside a flat is unsettled. Above 2,800 mm floor to floor a single straight flight at 175 mm needs 17 risers, one more than B14.2 allows. Malaysia's by-law 106(1) reads "any staircase" and plainly covers a house stair.
- Taiwan: 建築技術規則建築設計施工編 第33條, category 4: riser 20 cm or less, tread 21 cm or more; 第34條: a landing within every 4 m of stair height. Japan: 建築基準法施行令 第23条, house stairs (excluding the common stairs of apartment buildings): riser up to 23 cm, tread at least 15 cm.
Sources
- City of Boise. IRC Code Handout #437: Stair Treads & Risers (IRC Section R311.7.5), March 2022. https://www.cityofboise.org/media/14405/437-treads-risers_march-2…
- Singapore Civil Defence Force. Fire Code 2023, Chapter 2, Clause 2.3 Means of escape requirements (Cl. 2.3.3d). https://www.scdf.gov.sg/fire-safety-services-listing/fire-code-20…
- Malaysia. Uniform Building By-Laws 1984 (G.N. 5178/1984), incorporating amendments to K.P.U. 6/2007, by-laws 106–108. KPKT. https://jkt.kpkt.gov.my/wp-content/d/sites/default/files/2019-06/…).pdf
- Buildings Department, Hong Kong. Code of Practice for Fire Safety in Buildings 2011 (2024 Edition), Clauses B14.2 and B14.4. https://www.bd.gov.hk/doc/en/resources/codes-and-references/code-…
- Ministry of the Interior, Taiwan. 建築技術規則建築設計施工編 第33條 and 第34條. https://law.moj.gov.tw/LawClass/LawSingle.aspx?pcode=D0070115&fln…
- Japan. 建築基準法施行令 第23条 (e-Gov law data). https://laws.e-gov.go.jp/api/1/articles;lawId=325CO0000000338;art…
- HM Government. Approved Document K: Protection from falling, collision and impact (2013 edition, for use in England), Table 1.1 and para 1.12. https://assets.publishing.service.gov.uk/media/60d5bdcde90e07716f…
- Blondel F. Cours d'architecture, quatrième, cinquième et dernière partie. Paris; 1683. Livre III, ch. XIV. Internet Archive (Getty Research Institute copy). https://archive.org/details/coursdarchitectu00blon
Abridged — the full review record for this tool runs longer than the list above.
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