How to use the stair calculator
- Measure the total rise — the vertical distance from the finished floor at the bottom to the finished floor at the top. Measure to finished surfaces: flooring thickness changes every step.
- Set the maximum riser height. 7¾ in is the limit in the International Residential Code (IRC) used across most of the US; commercial stairs under the IBC are limited to 7 in.
- Enter the tread depth (the horizontal run of each step, not counting nosing). The IRC minimum is 10 in.
The calculator finds the smallest number of equal risers that stays under your maximum, then works out the total run, the length of the stringer and the angle of the stair.
Stair formulas
Riser height = Total rise ÷ Risers
Treads = Risers − 1
Total run = Treads × Tread depth
Stringer length = √(Total rise² + Total run²)
There is one fewer tread than risers because the top step is the upper floor itself.
Worked example
For a total rise of 108 in with a 7¾ in maximum: 108 ÷ 7.75 = 13.9, so you need 14 risers of 7.71 in each. That gives 13 treads; at 10 in deep, the total run is 130 in (10.83 ft) and the stringer is about 169.01 in (14.08 ft) long, at an angle of 39.7°.
Residential stair code requirements (IRC)
| Requirement | IRC (homes) |
|---|---|
| Maximum riser height | 7¾ in |
| Minimum tread depth | 10 in |
| Minimum stair width | 36 in |
| Minimum headroom | 6 ft 8 in |
| Max variation between risers or treads | ⅜ in |
| Handrail height | 34–38 in above the tread nosing |
| Nosing (treads under 11 in) | ¾–1¼ in |
These are the model-code figures; your city or county may adopt amendments, so confirm with your local building department before building.
The comfort rule
Stairs feel natural when two risers plus one tread add up to roughly 24–25 in (about one walking stride). A 7½ in riser with a 10 in tread scores 25 in; a steep 8 in riser with a 9 in tread scores 25 too, but would fail code. The calculator shows the result so you can adjust the tread depth.
Stair chart by total rise
Using a 7¾ in maximum riser and 10 in treads:
| Total rise | Risers | Riser height | Treads | Total run |
|---|---|---|---|---|
| 24 in (2.0 ft) | 4 | 6.00 in | 3 | 2.50 ft |
| 36 in (3.0 ft) | 5 | 7.20 in | 4 | 3.33 ft |
| 48 in (4.0 ft) | 7 | 6.86 in | 6 | 5.00 ft |
| 60 in (5.0 ft) | 8 | 7.50 in | 7 | 5.83 ft |
| 72 in (6.0 ft) | 10 | 7.20 in | 9 | 7.50 ft |
| 84 in (7.0 ft) | 11 | 7.64 in | 10 | 8.33 ft |
| 96 in (8.0 ft) | 13 | 7.38 in | 12 | 10.00 ft |
| 108 in (9.0 ft) | 14 | 7.71 in | 13 | 10.83 ft |
| 120 in (10.0 ft) | 16 | 7.50 in | 15 | 12.50 ft |
Cutting stringers
- Use 2×12 lumber for most residential stringers; the throat (the narrowest part left after cutting the notches) should usually be at least 3½–5 in deep.
- Cut the bottom of the stringer short by one tread thickness so the first step comes out the same height as the rest.
- Space stringers no more than about 16–18 in apart for 1-in treads; check the tread manufacturer's span.
- Check that the total run fits the space, and that headroom stays above 6 ft 8 in along the whole flight.
Plan the whole job
Pricing the stringers and treads? The board foot calculator totals the lumber. Outdoor steps can be poured instead — the concrete calculator has a steps mode. For the full rules, read our stair code guide.
Frequently asked questions
How many steps do I need for a 9 ft rise?
A 9 ft (108 in) rise needs 14 risers of about 7.71 in to stay under the 7¾ in IRC limit, which means 13 treads.
How do I calculate stair rise and run?
Divide the total rise by your maximum riser height and round up to get the number of risers. Divide the total rise by that number for the exact riser height. Multiply the number of treads (risers − 1) by the tread depth to get the total run.
What is the maximum stair riser height?
7¾ in for homes under the International Residential Code, and 7 in for commercial buildings under the International Building Code. Local codes may differ.
How long should a stair stringer be?
Use the Pythagorean theorem: stringer length = √(total rise² + total run²). Add a little extra for the top and bottom cuts and buy the next standard lumber length.
What is a good stair angle?
Most comfortable residential stairs are between about 30° and 37°. Stairs built to the IRC limits (7¾ in riser, 10 in tread) are close to 38°.
Does total rise include the flooring?
Yes. Measure from finished floor to finished floor. If the flooring isn't installed yet, add its thickness at the top and bottom so every riser comes out equal.
Sources & standards
This calculator's formulas and default values are based on the following codes, standards and published data. Codes are adopted and amended locally, so check with your building department for permitted work. See how we build and check our calculators.
- International Residential Code (IRC) R311.7: stairways (riser height, tread depth, headroom, width, handrails).
- IRC R312: guards and opening limits.
- American Wood Council, DCA 6 Prescriptive Residential Wood Deck Construction Guide: exterior stair stringers.