Stair Calculator
Split a total rise and run into steps and get the riser height, tread depth, stringer length and a comfort check.
The formula
Number of risers = total rise ÷ preferred riser height, rounded to the nearest whole number. Riser height = total rise ÷ number of risers, so every riser is equal. The top step is the upper floor, so there is one less tread than risers: number of treads = risers − 1, and tread depth (the going) = total run ÷ treads.
Stringer length = √(total rise² + total run²), the straight line along the nosings. Pitch = arctan(rise ÷ run). The comfort check also uses the Blondel formula, 2 × riser + tread, which for a comfortable step is usually in the range of 550 to 700 mm.
Worked example
A floor-to-floor rise of 2,700 mm with a 175 mm preferred riser gives 2,700 ÷ 175 = 15.4, so 15 risers of 2,700 ÷ 15 = 180 mm. There are 14 treads. With 3,600 mm of run, each tread is 3,600 ÷ 14 = 257.1 mm. The stringer is √(2,700² + 3,600²) = 4,500 mm, and the pitch is arctan(2,700 ÷ 3,600) = 36.9°. 2 × 180 + 257.1 = 617.1 mm, inside the guide range.
What the comfort check tests
- Riser between 150 and 220 mm (about 6 to 8⅝ in).
- Tread (going) at least 220 mm (about 8⅝ in).
- 2 × riser + tread between 550 and 700 mm.
- Pitch no steeper than 42°.
- These are guide values for comfort, not building code. Codes differ by country and by type of stair. For example, US residential code limits risers to 7¾ in (about 197 mm) and requires treads of at least 10 in (254 mm), which is stricter than the guide values here, so check yours.
Limits
- It assumes a straight flight with equal steps, and the top step is the upper floor. Winders, landings and spiral stairs are not covered.
- It uses the rise and run you enter. If the preferred riser gives a tread or pitch that fails the check, change the run or the preferred riser and try again.
- The tread depth is the going from nosing to nosing, with no nosing overhang or thickness of the finished tread added.
- The stringer length is the straight-line length along the pitch. A real stringer board needs extra length for the cuts at both ends, and a cut stringer needs a board deep enough to keep material under the notches.
- Headroom is not checked.
- Changing the units box does not convert the numbers already typed in.
More worked examples
Imperial: a total rise of 108 in and a run of 140 in, with the preferred riser left blank (7 in). That gives 15 risers of 7.200 in and 14 treads of 10.000 in, a pitch of 37.6° and a stringer of 176.816 in. 2 × riser + tread is 24.400 in, within the guide ranges.
Metric with a 200 mm preferred riser: a rise of 2,700 mm divided by 200 is 13.5, which rounds up to 14 risers of 192.9 mm. With a run of 3,600 mm that is 13 treads of 276.9 mm, and 2 × riser + tread is 662.6 mm, within the guide range.
How the preferred riser changes the layout
| Rise 2,700 mm, run 3,600 mm | Risers | Riser | Tread | Comfort check |
|---|---|---|---|---|
| Preferred 150 mm | 18 | 150.0 mm | 211.8 mm | Tread too short, 2 × riser + tread too low |
| Preferred 175 mm (default) | 15 | 180.0 mm | 257.1 mm | Within the guide ranges |
| Preferred 200 mm | 14 | 192.9 mm | 276.9 mm | Within the guide ranges |
When the check flags a problem
A rise of 2,700 mm squeezed into a 2,000 mm run gives 14 treads of only 142.9 mm and a pitch of 53.5°. The comfort check then lists three problems: the tread is under 220 mm, 2 × riser + tread (502.9 mm) is outside 550–700 mm, and the pitch is steeper than 42°. Going the other way, a 6,000 mm run gives 428.6 mm treads and 2 × riser + tread of 788.6 mm, so it also says to check. Only the 2 × riser + tread test fails, because a very deep tread does not trip the tread limit.
Edge cases
- A rise of 150 mm with the default 175 mm preferred riser rounds to a single riser and no treads, so the tool shows "The rise is too small for a flight with more than one riser."
- A rise of 300 mm with a 500 mm run is allowed: 2 risers of 150.0 mm and a single 500.0 mm tread. It is flagged because 2 × riser + tread is 800.0 mm.
- A preferred riser of 0 shows "Please enter valid, positive values." Leaving it blank uses 175 mm (7 in).
Frequently asked questions
Why is there one less tread than riser?
The last riser lands on the upper floor, which acts as the top step. A flight with 15 risers therefore has 14 treads.
How is the number of steps chosen?
The total rise is divided by your preferred riser height and rounded to the nearest whole number. That gives the closest equal riser to your preference, which can be a little higher or lower than the number you typed.
What riser height and tread depth should I use?
The comfort check flags values outside commonly used ranges, but the limits that apply to you are set by local building rules and the type of stair, so check them before building.
Does it include the top landing or the thickness of the floor?
No. Measure the total rise from the finished lower floor to the finished upper floor, which already includes the floor thickness, and enter it directly.
Why is my riser height not the one I typed?
The preferred riser is only used to choose the number of steps. The tool rounds the rise ÷ preferred riser to a whole number and then splits the rise equally, so with a preferred 175 mm and a 2,700 mm rise you get 15 risers of 180.0 mm.
What does "Check:" in the comfort result mean?
At least one of the five guide tests failed. The text names each one: riser under 150 or over 220 mm, tread under 220 mm, 2 × riser + tread outside 550–700 mm, or a pitch steeper than 42°. Change the run or the preferred riser and look again.
Does a longer run always make the stair more comfortable?
No. A very long run makes the treads deep, which can push 2 × riser + tread above 700 mm. A 6,000 mm run on a 2,700 mm rise gives 428.6 mm treads and is flagged.