Stair layout: the rise-and-run math that earns easy marks on the Red Seal carpentry exam

Why stairs are free marks — if the arithmetic is right

Stair layout is one of the few carpentry topics where the answer is decided by arithmetic instead of judgement. You are given a total rise, the code fixes the limits on the riser and the tread run, and everything else follows: the unit rise, the number of treads, the total run, the stringer length. Candidates who lose these questions rarely misunderstand stairs. They slip one step in the chain, usually by counting treads where they should count risers. With a 70% national pass mark, four or five layout questions are a real slice of your margin.

The code numbers you need on the tip of your tongue

Under Part 9 of the National Building Code (Housing and Small Buildings), stairs serving a single dwelling unit — "private stairs" — must satisfy:

• Rise (measured nosing to nosing): minimum 125 mm, maximum 200 mm (Table 9.8.4.1). Public stairs top out at 180 mm.
• Run: minimum 255 mm, maximum 355 mm (Table 9.8.4.2). Public stairs: minimum 280 mm, no maximum.
• Uniformity (Article 9.8.4.4): risers and tread runs must be uniform within one flight, with a tolerance of 5 mm between adjacent treads or landings and 10 mm between the tallest and shortest riser in the flight. The slope of a tread may not exceed 1 in 50.
• Stringers (Article 9.8.9.4): minimum effective depth of 90 mm measured perpendicular to the bottom of the stringer at its weakest point, overall depth of at least 235 mm, and not more than 900 mm on centre in a stair serving one dwelling unit.

Two more limits that show up in multiple-choice questions: clear height over stairs is 1,950 mm in a dwelling unit (2,050 mm elsewhere), and exit stairs serving a single dwelling unit must be at least 860 mm wide.

Worked example: 2,750 mm floor to floor

Take a finished floor to finished floor rise of 2,750 mm.

• Number of risers: 2,750 ÷ 200 = 13.75, so 13 risers is impossible. 14 risers gives a unit rise of 2,750 ÷ 14 = 196.4 mm, comfortably inside the 125–200 mm band. Choose 14 risers at 196 mm.
• Number of treads: always one less than the number of risers, because the upper level is a floor, not a tread. 14 − 1 = 13 treads.
• Total run: 13 × 280 mm = 3,640 mm, measured nosing to nosing. A 280 mm run sits in the middle of the 255–355 mm band.
• Stringer length: the stringer is the hypotenuse of that triangle. √(2,750² + 3,640²) = √20,812,100 ≈ 4,562 mm of rise-and-run, plus the bearing at the top and bottom. Buy stock longer than that number and cut the notches into the stock.

The comfort check carpenters use in the field (not a code article): 2 × riser + 1 tread should land between 550 mm and 700 mm. Here 2(196.4) + 280 = 672.8 mm — a comfortable stair. Push that past 700 mm and the stair feels shallow and sprawling; drop under 550 mm and it feels like a ladder.

The three traps that cost the mark

• Counting 14 treads instead of 13. The single most common arithmetic error in stair questions, and the distractors are built around it.
• Measuring the rise from subfloor to subfloor. The rise is finished surface to finished surface. Floor thickness, tread thickness and a future finish change the number — and that is exactly how the wrong options are made to look plausible.
• Ignoring the tolerance. If a question hands you 14 risers with one at 210 mm, that stair fails twice: over the 200 mm maximum, and more than 10 mm off the flight. The correct answer is "add a riser and re-space the flight," not "shim the tread."

Practise it the way it is asked

Red Seal carpentry questions on stairs almost always ask one of four things: the unit rise, the number of risers, the total run, or the stringer length. Drill that sequence until you can produce all four from a rise and a run in under two minutes, then check your work against the code numbers: riser inside 125–200 mm, run inside 255–355 mm, uniformity inside 5 mm and 10 mm. Set a framing square at 196 mm and 280 mm, step it off 13 times on a piece of stock, and the layout stops being theory. On exam day, the stair question is a calculation you have already run a hundred times.