A stair aimed at a 7½-inch (190.5 mm) riser, a quarter-inch inside the US model code's limit, came out with risers of 184 to 198 mm at all 211 floor-to-floor heights we chose between 2.4 and 4.5 m, rounding the riser count to the nearest whole number. Each is taller than the 175 mm set for exit staircases by Singapore's SCDF Fire Code and for required staircases by Hong Kong's Fire Safety Code, and than the 180 mm Malaysia's by-laws set for any staircase. Whether the Singapore and Hong Kong figures reach a stair inside a home, the texts leave open.
The Fire Code made room for Singapore's exit-stair limits in 2019
Clause 2.3.3d(4) of the SCDF Fire Code 2023 reads: "The height of the riser for any exit staircase shall not be more than 175mm". The minimum depth of tread is 225 mm within residential units and 275 mm for residential common areas. Singapore's "depth of tread" is Malaysia's "tread" and England's "going".
SCDF's rationale says BCA has no specific riser, tread or headroom requirements and "has removed them from its code"; they are "reinstated in this edition", dated 1 March 2019 in the amendment history. We did not establish the rule before then. The clause treats "access staircases in a residential unit" as a separate category, the only stairs allowed winders, wedge-shaped steps on a turn. Neither it nor clause 9.1, on single-household dwellings, says whether such a stair counts as an exit staircase.
Malaysia's by-laws accommodate a riser 5 mm taller than Singapore's
By-law 106(1) of the Uniform Building By-Laws 1984, as consolidated to 2007 by the local government ministry, says "the rise of any staircase shall be not more than 180 millimetres and the tread shall be not less than 255 millimetres". That scope plainly takes in a house stair. States adopt their own versions, which we did not compare.
The 255 mm tread is deeper than Hong Kong's 225 mm and shallower than Singapore's 275 mm for common areas. A flight is the run of steps between landings. In residential buildings, by-law 108(1) puts a landing at least 1.80 m deep at vertical intervals of not more than 4.25 m; of our 211 heights, the 25 from 4,260 mm up climb past that.
Floor heights above 2.8 m overflow a single Hong Kong flight
Clause B14.2 of the Buildings Department's Code of Practice for Fire Safety in Buildings 2011, 2024 edition, puts required staircases in straight flights of "not more than 16 risers nor less than 2 risers". Risers are "not more than 175mm high" and treads at least 225 mm, "measured clear of nosings", a nosing being a tread's front edge. Required staircases are those for means of escape or firefighting access; whether that includes a private stair in a flat or house we could not confirm.
At 175 mm a riser, a floor-to-floor height of 2,800 mm takes 16 risers. Anything higher needs at least 17 in one straight flight, one more than B14.2 permits, so a landing splits the stair into two flights. That covers 170 of our 211 heights.
Risers aimed at 7½ inches pack too few steps into a storey
The International Residential Code, a US model code, sets a riser maximum of 7¾ inches (196 mm) in section R311.7.5, as quoted in the City of Boise's 2022 handout. Our 7½-inch layouts exceeded it at 3 of the 211 heights, yet all 211 held too few risers for 180 mm.
Taiwan's 建築技術規則建築設計施工編 (building technical rules), article 33, gives its general stairs a 級高 (riser) of 20 cm or less. Japan's 建築基準法施行令 (Building Standard Law Enforcement Order), article 23, lets a house stair's 蹴上げ (riser) reach 23 cm. All 211 layouts fitted both.
Until 12 October 2026 our stair stringer calculator worked in inches from a 7½-inch default and checked the IRC alone. At its default target and tread, its risers were over all three regional limits at all 211 heights, while its verdict placed 208 within the IRC. It rounded to the nearest riser; its "stair angle" was the overall slope of the flight, 38.35° at its defaults against a pitch of 36.30°. The revision made that day takes millimetres, treats the target as a maximum, measures pitch through the nosings and names each code's clause and scope. A layout inside a code's numbers on a calculator is not an approved design.
Rounding to the nearest step squeezes out a riser at nearly half the heights
The riser count is the floor-to-floor height divided by the target riser, rounded to a whole number. Rounding to the nearest drops a riser whenever the division leaves a fraction under one half, and every remaining riser grows. At a 175 mm target that happened at 102 of our 211 heights; rounding up, at none.
At 3 m, 3,000 divided by 175 is 17.14 on our arithmetic, so rounding to the nearest gives 17 risers of 176.5 mm, and rounding up gives 18 of 166.7 mm. The worst overshoot is about 87.5 mm divided by the riser count. Across 2.4 to 4.5 m in millimetre steps, it peaked at 181.2 mm with 14 risers, over Malaysia's limit too.
A pitch line hugs every nosing on the flight
Pitch is the slope of the line running through the nosings; its tangent is the riser height divided by the going. The overall angle from the foot of the bottom riser to the top nosing is steeper, because a flight has one tread fewer than risers. Sixteen 175 mm risers on 250 mm goings give a 35.0° pitch and a 36.7° overall angle, on our arithmetic.
England's Approved Document K of 2013 caps a private stair's pitch at 42°. A straight line touches every nosing only if every step matches, as Malaysia's by-law requires: rise and tread "uniform and consistent throughout".
Blondel fitted his rule to a stride of two French feet
François Blondel gave his stair rule in Book III, chapter XIV of his Cours d'architecture, a work published in parts from 1675 (Internet Archive scan). "La longueur du pas aisé d'un Homme qui marche de niveau est de deux pieds": a man's easy stride on the level is two feet, which he gives as twenty-four inches. Reckoning a climber's upward step at about one foot, he counted each unit of rise as two of going, so twice the riser plus the tread, 2R + G, makes the stride.
Those inches were pouces (French inches), twelve to the pied du roi (king's foot). On an assumed, approximate pied of 324.84 mm, unchecked against a metrology source, the stride is about 650 mm, or 25.6 English inches. Nor was the rule new there: the chapter before says Blondel had given it in a note to Savot's book.
Approved Document K now calls 2R + G "between 550mm and 700mm" the "normal relationship" of rise and going; a 175 mm riser on a 250 mm going gives 600 mm by our arithmetic. None of the Singapore, Malaysian or Hong Kong texts we opened states 2R + G as a requirement.
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