Why it matters
Stair layout is a favourite math topic. You are given a total rise and asked for the number of risers, the unit rise, the run or the stringer length. Work it in a fixed order.
Key points
- Divide total rise by a target riser height (about 180 mm or 7 in) and round to a whole number of risers.
- Unit rise is total rise divided by the number of risers.
- There is one less tread than risers on a standard straight stair.
- Total run is unit run times the number of treads.
- Stringer length comes from the Pythagorean theorem: the square root of rise squared plus run squared.
Study tip
Always check your answer against your local building code limits for rise and run, because the exam may ask which stair is compliant.
Try these
Total rise 2700 mm with 15 risers gives a unit rise of:
- 170 mm
- 180 mm
- 190 mm
- 200 mm
Show answer
B. 180 mm 2700 / 15 = 180 mm.
A straight stair with 14 risers has how many treads?
- 12
- 13
- 14
- 15
Show answer
B. 13 One less tread than risers.
Rise 2.4 m and run 3.2 m give a stringer length of about:
- 3.6 m
- 4.0 m
- 4.4 m
- 5.6 m
Show answer
B. 4.0 m The square root of 5.76 + 10.24 is 4.0.
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