How to calculate stairs
Every stair calculation starts with one number: the total rise, measured from finished floor to finished floor. Floor finishes matter — a 20 mm tile on the lower floor and 15 mm parquet on the upper one change the height of the first and last step if you forget them. Divide the total rise by the maximum riser height you are willing to accept and round up; that is the number of risers. Then divide the total rise by that whole number to get the actual, equal riser height.
A straight flight has one tread fewer than risers, because the last step up lands on the upper floor. Multiply the number of treads by the tread depth to get the total run — the horizontal length the stair occupies on plan.
riser R = total rise ÷ n
treads = n − 1, total run = (n − 1) × T
angle = atan(R ÷ T), stringer = √(rise² + run²)
comfort (Blondel): 600 mm ≤ 2R + T ≤ 650 mm
Worked example
A house has 2800 mm floor to floor and you want risers no taller than 180 mm. 2800 ÷ 180 = 15.6, so round up to 16 risers. 2800 ÷ 16 = 175 mm each. With a 280 mm tread you get 15 treads and a total run of 15 × 280 = 4200 mm. The angle is atan(175 ÷ 280) ≈ 32°, and Blondel gives 2 × 175 + 280 = 630 mm — right in the comfortable range. The pitch line is √(2800² + 4200²) ≈ 5048 mm.
If the plan only has 3.6 m for the stair, the run does not fit. You can reduce the tread (but keep 2R + T above 600 mm), accept a steeper riser within code, or turn the stair with a landing so the run is split into two flights.
Typical stair dimensions
| Type | Riser | Tread | Angle |
|---|---|---|---|
| Public building / school | 150–170 mm | 300–320 mm | 26–30° |
| Residential, comfortable | 170–180 mm | 270–290 mm | 30–34° |
| Residential, compact | 185–196 mm | 250–260 mm | 36–38° |
| US IRC limit | max 7¾" (196 mm) | min 10" (254 mm) | ≈ 38° |
| Attic / service stair | 200–220 mm | 200–230 mm | 42–48° |
Headroom, width and landings
Beyond rise and run, check the clear headroom above the pitch line (the IRC asks for 6 ft 8 in, about 2030 mm; many European codes ask for 2.0–2.1 m), the stair width (around 900 mm in homes, more in public buildings) and landings: a long straight flight usually needs an intermediate landing after about 16–18 risers. Handrails are typically 850–1000 mm above the nosing line. These limits are set by your national building code, so confirm them before you finalise drawings.
Frequently asked questions
How many steps do I need for a 2.8 m (9 ft) floor height?
For 2800 mm with a maximum riser of 180 mm you need 16 risers of 175 mm and 15 treads. For 9 ft (108 in) with a 7 3/4 in maximum riser you need 14 risers of about 7.71 in and 13 treads.
What is the difference between risers and treads?
A riser is the vertical height of one step, a tread is the horizontal part you stand on. A straight flight always has one tread fewer than risers, because the last step up is the upper floor itself.
What is the Blondel formula?
The Blondel rule says that two risers plus one tread should equal one walking stride, about 600 to 650 mm (roughly 24 to 25.5 in). Stairs within this range feel natural to climb.
What is the maximum riser height allowed by code?
Under the US International Residential Code (IRC R311.7.5) the maximum riser is 7 3/4 in (196 mm) and the minimum tread is 10 in (254 mm). European national rules typically allow 170 to 190 mm risers in homes and less in public buildings. Always check your local code.
What is a comfortable stair angle?
Most comfortable stairs are between about 30 and 37 degrees. Above 42 degrees a stair starts to feel like a ladder; below 25 degrees it feels more like a ramp and uses a lot of floor space.
How long is the stair stringer?
The calculator gives the length of the pitch line, the square root of total rise squared plus total run squared. Add extra length for the cut at the top and bottom and the board thickness when ordering timber.