Quick answer: A 3,000 mm floor-to-floor height with risers of at most 180 mm needs ⌈3000 ÷ 180⌉ = 17 risers of 176.5 mm and 16 treads; with 280 mm treads the stair runs 4,480 mm at 32.2°.
How it's calculated
Divide the total rise by the highest riser you accept and round up: that is the number of risers. Divide the total rise by that number to get equal risers. A straight flight has one tread fewer than risers, because the top step is the upper floor. Some calculators keep every riser at the maximum and leave a shorter first step; building codes ask for equal risers (the IRC allows at most ⅜ in, 9.5 mm, between the tallest and shortest), so this calculator divides the rise evenly.
Total run = treads × tread depth. The angle is atan(riser ÷ tread), and the stringer (the sloping side board) is about √(rise² + run²) before trimming.
The US International Residential Code (R311.7.5) limits risers to 7¾ in (196 mm) and requires treads of at least 10 in (254 mm). The comfort rule 2 × riser + tread ≈ 24–25 in (600–650 mm), known as Blondel's formula, matches a normal walking stride.
Worked examples
- 3,000 mm rise, max riser 180 mm, tread 280 mm: 17 × 176.5 mm, 16 treads, run 4,480 mm, 32.2°
- 108 in rise, max riser 7.5 in, tread 11 in: 15 × 7.2 in, 14 treads, run 154 in
Common riser and tread limits
| Rule | Riser | Tread |
|---|---|---|
| IRC R311.7.5 (US homes) | ≤ 196 mm (7¾ in) | ≥ 254 mm (10 in) |
| IBC 1011.5 (US commercial) | 102–178 mm (4–7 in) | ≥ 279 mm (11 in) |
| Comfort rule | 2R + T = 600–650 mm |
Frequently asked questions
How many steps for a 3 m floor height?
With risers up to 180 mm, 17 steps of about 176.5 mm. With risers up to 196 mm, 16 steps of 187.5 mm.
What is the best stair angle?
Most comfortable stairs are between 30° and 37°. Steeper stairs save space but are harder to climb.
Why is there one tread fewer than risers?
The last riser lands on the upper floor, which acts as the final tread.
How wide should stairs be?
In a home, at least 90 cm is common (36 inches is the US residential minimum), and 100 to 120 cm feels a lot more comfortable when you're carrying furniture. Your local building code sets the legal minimum.
How much headroom does a staircase need?
The US residential code asks for at least 2.03 m (6 ft 8 in), measured straight up from the edges of the treads. Many designers go for 2.1 m or more so nobody has to duck.
What is a stair nosing?
The front edge of a tread that sticks out over the riser below, usually by 2 or 3 cm. It gives your foot a bit more room without making the stair any longer.