Stair Calculator
Divide the total rise by 7 3/4 in (the IRC maximum riser) and round up: a 9 ft (108 in) rise needs 14 risers of 7 11/16 in and 13 treads of at least 10 in.
Stair layout
How the stair math works
risers = total rise ÷ 7.75, rounded up riser height = total rise ÷ risers treads = risers − 1 total run = treads × tread depth stringer = √(total rise² + total run²) angle = arctan(total rise ÷ total run)
Worked example: a 108 in rise ÷ 7.75 = 13.935, rounded up to 14 risers. 108 ÷ 14 = 7.714 in (7 11/16 in) per riser. 13 treads at 10 1/2 in give a run of 136.5 in (11 ft 4 1/2 in). The stringer is √(108² + 136.5²) = 174.1 in (14 ft 6 1/16 in), and the stair rises at 38.4°.
Treads are one fewer than risers because the upper floor is the last step. Measure total rise between finished floor surfaces: flooring added later changes the top and bottom risers, which the IRC limits to 3/8 in difference across the flight.
IRC stair limits (R311.7)
| Rule | Limit | Section |
|---|---|---|
| Riser height | ≤ 7 3/4 in | R311.7.5.1 |
| Tread depth (nosing to nosing) | ≥ 10 in | R311.7.5.2 |
| Riser or tread variation in a flight | ≤ 3/8 in | R311.7.5.1 / .2 |
| Nosing projection (treads under 11 in) | 3/4 to 1 1/4 in | R311.7.5.3 |
| Headroom | ≥ 6 ft 8 in | R311.7.2 |
| Stair width | ≥ 36 in | R311.7.1 |
| Handrail height | 34 to 38 in | R311.7.8 |
These are the model International Residential Code numbers as reprinted by the City of Boise, Knox County (2018 IRC) and the City of Grinnell (2015 IRC). Your city or county may adopt a different edition or amend it, and decks, basements and commercial buildings can have other rules. Your building department has the final word.
What angle should stairs be?
The code does not set an angle directly: it follows from the riser and tread. The steepest stair the IRC allows, 7 3/4 in risers on 10 in treads, works out to arctan(7.75 ÷ 10) = 37.8°. Deeper treads or shorter risers make a gentler stair.
Frequently asked questions
How do I calculate the number of stairs I need?
Divide the total rise by the maximum riser height, 7 3/4 in under the IRC, and round up. For a 108 in (9 ft) rise: 108 ÷ 7.75 = 13.94, so 14 risers of 7 11/16 in each. You need one tread fewer than risers: 13 treads.
What is the maximum riser height for stairs?
IRC R311.7.5.1 sets the maximum riser height at 7 3/4 inches, and the tallest riser in a flight may not exceed the shortest by more than 3/8 inch.
What is the minimum tread depth for stairs?
IRC R311.7.5.2 sets the minimum tread depth at 10 inches, measured horizontally from nosing to nosing. Treads under 11 inches deep need a nosing projection of 3/4 to 1 1/4 inches.
How long should a stair stringer be?
The stringer runs along the slope, so its length is the square root of (total rise² + total run²). For a 108 in rise with 13 treads of 10 1/2 in, the run is 11 ft 4 1/2 in and the stringer is about 14 ft 6 1/16 in. Buy longer stock to allow for the top and bottom cuts.
How many steps for a 30 inch rise?
30 ÷ 7.75 = 3.87, so 4 risers of 7 1/2 in and 3 treads. With 11 in treads the total run is 2 ft 9 in.
How much headroom and width does a stair need?
The IRC requires at least 6 ft 8 in of headroom (R311.7.2) and a stair at least 36 in wide (R311.7.1). Handrails go 34 to 38 in above the tread nosings (R311.7.8). Local amendments can differ, so check with your building department.
Sources
- PDS #437 IRC Code Handout: R311.7.5 Stair Treads and Risers (2022), City of Boise, ID (reprints the International Residential Code). Used for: IRC R311.7.5.1 riser 7 3/4 in max, R311.7.5.2 tread 10 in min, 3/8 in variation, R311.7.5.3 nosing.
- Stairs (2018 IRC handout), Knox County, TN Code Administration & Inspection. Used for: IRC R311.7.2 headroom 6 ft 8 in and R311.7.8 handrail height 34 to 38 in.
- Residential Stairs handout (2015 IRC), City of Grinnell, IA Building & Planning. Used for: IRC R311.7.1 minimum width 36 in.
Estimates only. Check local codes and your product's label. Found a number that does not match its source? Send a correction.