Stairs have to fit two fixed numbers — the height between floors and the space available — while keeping every step the same size. This calculator takes the total rise, divides it into equal risers no taller than your maximum, and gives the treads, total run, stringer length and the stair's angle so you can check the design before cutting a single board.
How to use the stair calculator
- Measure the total rise from the finished surface at the bottom to the finished surface at the top. Include flooring thickness that isn't installed yet.
- Keep the maximum riser at 7¾ in for US homes, or enter your local limit.
- Enter the tread depth — 10 in minimum under the IRC; 10½–11 in feels more comfortable.
The results update instantly. Check that the total run fits the space at the bottom of the stairs.
Stair formulas
Riser height = total rise ÷ risers
Treads = risers − 1
Total run = treads × tread depth
Stringer ≈ √(total rise² + total run²)
Angle = arctan(riser height ÷ tread depth)
Rounding the riser count up guarantees no step exceeds the maximum. Dividing the rise evenly then makes every riser identical — building codes allow only a tiny variation (⅜ in in the IRC) between the tallest and shortest riser, because uneven steps cause falls.
Worked example: a basement staircase
- Total rise: 108 in (9 ft)
- Risers: 108 ÷ 7.75 = 13.9 → 14 risers
- Riser height: 108 ÷ 14 = 7.71 in
- Treads: 14 − 1 = 13 treads
- Total run at 10 in per tread: 13 × 10 = 130 in (10 ft 10 in)
- Stringer: √(108² + 130²) = 169 in — about 14 ft, so buy 16 ft stringer stock
Stairs by total rise
7¾ in maximum riser, 10 in treads.
| Total rise | Risers | Riser height | Treads | Total run | Stringer |
|---|---|---|---|---|---|
| 84 in (7 ft) | 11 | 7.64 in | 10 | 100 in | 130.6 in |
| 96 in (8 ft) | 13 | 7.38 in | 12 | 120 in | 153.7 in |
| 105 in | 14 | 7.50 in | 13 | 130 in | 167.1 in |
| 108 in (9 ft) | 14 | 7.71 in | 13 | 130 in | 169.0 in |
| 112 in | 15 | 7.47 in | 14 | 140 in | 179.3 in |
| 120 in (10 ft) | 16 | 7.50 in | 15 | 150 in | 192.1 in |
Common US residential stair rules (IRC)
- Maximum riser height: 7¾ in; minimum tread depth: 10 in.
- Riser and tread sizes may vary by no more than ⅜ in within a flight.
- Minimum headroom: 6 ft 8 in measured from the tread nosing line.
- Handrails are required on flights with four or more risers.
These are summaries of the International Residential Code; your jurisdiction may adopt a different edition or local amendments. For decks, outdoor stairs follow the same rules — see the Deck Calculator for the deck itself.
Frequently asked questions
How do I calculate the number of stairs?
Divide the total rise in inches by the maximum riser height and round up. For a 108 in rise and a 7¾ in maximum, 108 ÷ 7.75 = 13.9, so 14 risers. Each riser is then 108 ÷ 14 = 7.71 in.
Why is there one fewer tread than risers?
The top step lands on the upper floor, so it doesn't need its own tread. A staircase with 14 risers has 13 treads.
What is the maximum riser height and minimum tread depth?
The US International Residential Code (IRC) limits risers to 7¾ in and requires treads of at least 10 in. Commercial buildings and other countries use different limits, and local amendments apply — check with your building department.
How long should a stair stringer be?
Roughly the diagonal of the total rise and total run: √(rise² + run²). Buy a board longer than that so you have room to cut the top and bottom, and check the span against code or an engineer for long staircases.
What is a comfortable stair angle?
Most residential stairs fall between about 30° and 38°. Lower risers and deeper treads make a gentler, easier staircase that needs more floor space.