Quick answer: divide the total rise (floor to floor) by the maximum riser height of 7¾ inches and round up to get the number of risers. Then divide the total rise by that number for the exact riser height. You always have one fewer tread than risers, so the total run is the number of treads times the tread depth, with a minimum tread of 10 inches. These limits come from the International Residential Code (IRC), as summarized in public handouts from the City of Boise and the Town of Timnath, Colorado.
The Stair Calculator does all of this for you. Below are the formulas, the code rules, and three worked examples.
Step 1: Measure the total rise
Total rise is the vertical distance from the finished floor at the bottom to the finished floor at the top. For deck stairs, measure from the deck surface down to the ground or landing where the stairs end. If new flooring will change the top or bottom height, measure after you know the finished floor.
Step 2: The formulas
Risers = total rise ÷ 7.75 in, rounded UP
Riser height = total rise ÷ number of risers
Treads = risers − 1
Total run = treads × tread depth (minimum 10 in)
Stringer length = √(total rise² + total run²)
Angle = arctan(riser height ÷ tread depth)
There is one fewer tread than risers because the top floor or deck acts as the last step. Rounding the riser count up guarantees every riser is at or under the maximum.
Worked example 1: deck stairs, 42 in rise
- Risers: 42 ÷ 7.75 = 5.42, round up to 6 risers.
- Riser height: 42 ÷ 6 = 7 in.
- Treads: 6 − 1 = 5. Total run: 5 × 10 = 50 in (4 ft 2 in).
- Stringer: √(42² + 50²) = √4,264 = 65.3 in, about 5 ft 5⅜ in. Buy a board at least that long.
- Angle: arctan(7 ÷ 10) = 35.0°.
Worked example 2: basement stairs, 100 in rise
- Risers: 100 ÷ 7.75 = 12.9, round up to 13.
- Riser height: 100 ÷ 13 = 7.69 in (about 7 11/16 in).
- Treads: 12. Run: 12 × 10 = 120 in (10 ft).
- Stringer: √(100² + 120²) = 156.2 in, about 13 ft.
- Angle: 37.6°.
- Comfort check: 2 × 7.69 + 10 = 25.4. A traditional rule of thumb says stairs feel natural when this number is about 24 to 25 inches.
Common rises at a glance
All use a 7¾ in maximum riser and a 10 in tread.
| Total rise | Risers | Riser height | Treads | Total run |
|---|---|---|---|---|
| 30 in | 4 | 7.50 in | 3 | 30 in |
| 42 in | 6 | 7.00 in | 5 | 50 in |
| 60 in | 8 | 7.50 in | 7 | 70 in |
| 96 in | 13 | 7.38 in | 12 | 120 in |
| 100 in | 13 | 7.69 in | 12 | 120 in |
| 108 in | 14 | 7.71 in | 13 | 130 in |
| 120 in | 16 | 7.50 in | 15 | 150 in |
IRC limits you should check
The code handouts summarize these main rules for stairs. Local codes may amend them, so confirm with your building department before you cut stringers.
| Rule | Requirement |
|---|---|
| Riser height (R311.7.5.1) | Not more than 7¾ in, measured vertically between the leading edges of adjacent treads. The tallest riser in a flight may not exceed the shortest by more than ⅜ in. |
| Tread depth (R311.7.5.2) | Not less than 10 in, measured horizontally. Variation limit ⅜ in within a flight. |
| Nosing (R311.7.5.3) | Projection of ¾ to 1¼ in, not required where treads are at least 11 in deep. |
| Headroom (R311.7.2) | At least 6 ft 8 in. |
| Width (R311.7.1) | At least 36 in clear width above the handrail height. |
| Vertical rise and landings (R311.7.3, R311.7.6) | A flight may not rise more than 151 in (12 ft 7 in) between floors or landings. A landing must be at least 36 in in the direction of travel. |
| Handrails | Required on at least one side of flights with four or more risers, 34 to 38 in high. A circular rail should be 1¼ to 2 in in diameter. |
| Guards (R312.1) | Open sides of stairs with more than 30 in of total rise need guards at least 34 in high, with no opening that lets a 4 in sphere pass. |
These are the code limits in force as quoted by the cited handouts (2018 and 2021 IRC editions). Your jurisdiction may have adopted a different edition.
Equal risers matter more than you think
Both handouts require every riser in a flight to be within ⅜ inch of the others. That is why you divide the rise evenly instead of cutting 7¾ in risers and a short one at the top. People trip on uneven risers more than on steep ones.
Marking and cutting stringers
- Use a framing square with stair gauges set at the riser height and tread depth, then step along the board.
- Drop the stringer. The first riser should be shortened by the thickness of the tread so the first step isn’t taller than the others once treads are on. The same applies at the top if the top tread sits flush with the floor.
- Account for tread thickness when the stringer sits on a landing slab versus on a deck.
- Check the number of stringers. Spacing depends on tread material and span, so follow your lumber and decking manufacturer or local code. The calculator on this site does not size stringers structurally.
- Test with a cut-off board. Cut one stringer, set it in place, and check level before cutting the rest.
Open risers
The stair guide notes that open risers are allowed if the opening between treads does not let a 4 inch diameter sphere pass, with an exception for stairs with a total rise of 30 inches or less. Check your local code before leaving risers open on stairs with a child or pet.
Common mistakes
- Using the wrong rise. Measure finished floor to finished floor, not subfloor to subfloor.
- Rounding down. Rounding the riser count down makes risers taller than 7¾ in.
- Counting the top floor as a tread. There are always risers minus one treads.
- Not allowing for the first riser drop. If you ignore tread thickness, the bottom step is wrong.
- Treating code summaries as final. The summaries here are for planning; your inspector’s local rules decide.
Frequently asked questions
How many steps do I need for a 9 foot ceiling?
Floor-to-floor rise depends on floor thickness, not just ceiling height. A 108 in total rise needs 14 risers of about 7.71 in and 13 treads.
How long should a stair stringer be?
√(rise² + run²). For a 42 in rise and 50 in run it is 65.3 in. Round up to the next standard board length.
What is the maximum riser height for stairs?
7¾ inches under IRC R311.7.5.1, with no more than ⅜ in difference between the tallest and shortest riser.
What is the minimum tread depth?
10 inches. Treads of 11 inches or more don’t need a nosing.
Do deck stairs follow the same rules?
Residential exterior stairs generally follow the same stair limits, though local amendments differ. Ask your building department.
Sources
- City of Boise, >IRC Section R311.7.5: Stair Treads & Risers (Handout #437), February 2022: riser and tread limits, variation, nosing.
- Town of Timnath, Colorado, >2018 Residential Stair Guide (IRC R311.7): width, headroom, landings, handrails, guards.
Planning guidance only. Not engineering or legal advice. Confirm all stair requirements with your local building department.