Stair calculator
Enter the total rise, from the finished lower floor to the finished upper floor, to get the risers, riser height, treads, total run, stringer line length and angle, checked against the IRC limits.
Type feet and inches such as 9' 0" or 8' 11 1/2", or inches alone, such as 108. Metric works too, for example 2743 mm. The starting values are an example.
How stair numbers are figured
Take the example above: a 108 inch total rise (9 feet), a 7 3/4 inch maximum riser and 10 inch treads.
- Risers: divide the total rise by the maximum riser and round up. 108 / 7.75 = 13.94, so 14 risers.
- Riser height: 108 / 14 = 7 5/7 in (7.714 in). To the nearest 1/16 in that reads 7 11/16 in.
- Treads: risers minus 1, because the upper floor is the top step. 13 treads.
- Total run: 13 × 10 in = 130 in = 10' 10".
- Stringer line: the square root of (108² + 130²) = 169.0 in = 14' 1".
- Angle: the arctangent of 108 / 130 = 39.7 degrees.
Rounding each riser to 1/16 in does not add up: 14 risers of 7 11/16 in measure 107 5/8 in, which is 3/8 in short of the 108 in rise. Mark every step from its own height above the lower floor instead of stepping one rounded riser after another. The table under the results lists each height, rounded one at a time.
| Total rise | Risers | Riser height | Treads | Total run |
|---|---|---|---|---|
| 8' 0" | 13 | 7 3/8" | 12 | 10' 0" |
| 8' 6" | 14 | 7 5/16" | 13 | 10' 10" |
| 9' 0" | 14 | 7 11/16" | 13 | 10' 10" |
| 9' 6" | 15 | 7 5/8" | 14 | 11' 8" |
| 10' 0" | 16 | 7 1/2" | 15 | 12' 6" |
| 11' 0" | 18 | 7 5/16" | 17 | 14' 2" |
IRC stair limits
These are the main dimensions in Section R311.7, Stairways, of the 2021 International Residential Code. Cities and counties adopt their own edition and often amend it, so confirm with your building department before you build.
- Maximum riser height: 7 3/4 in (R311.7.5.1).
- Minimum tread depth: 10 in (R311.7.5.2).
- Within one flight, the tallest riser and the deepest tread may exceed the smallest by no more than 3/8 in (R311.7.5.1 and R311.7.5.2).
- Minimum stair width: 36 in (R311.7.1).
- Minimum headroom: 6 ft 8 in (R311.7.2).
- Maximum vertical rise between floors or landings: 12 ft 7 in (R311.7.3).
- Handrail height: 34 to 38 in above the tread nosings (R311.7.8.1).
Source: International Code Council, 2021 International Residential Code, Chapter 3, Section R311.7. Other countries and other code editions use different limits.
Questions
How many risers do I need for my stairs?
Divide the total rise by the maximum riser height and round up. A 108 inch rise with a 7 3/4 inch maximum riser gives 108 / 7.75 = 13.9, so 14 risers.
How do I find the riser height?
Divide the total rise by the number of risers. 108 inches / 14 risers = 7 5/7 inches, which is 7.714 inches or 7 11/16 inches to the nearest 1/16.
How many treads does a staircase have?
One fewer than the risers, because the upper floor is the top step. 14 risers have 13 treads.
How do I figure the stair stringer length?
The stringer line is the hypotenuse of a triangle with the total rise and the total run as its sides: the square root of (rise squared plus run squared). For a 108 inch rise and a 130 inch run that is 169 inches, or 14' 1". The board you buy must be longer than that line.
What is the maximum riser height under the IRC?
7 3/4 inches (R311.7.5.1 in the 2021 International Residential Code). The largest riser in a flight may not be more than 3/8 inch taller than the smallest.
What is the minimum tread depth under the IRC?
10 inches (R311.7.5.2). The largest tread in a flight may not be more than 3/8 inch deeper than the smallest.
What is the steepest stair the IRC allows?
A 7 3/4 inch riser with a 10 inch tread is a rise of 7.75 over a run of 10, which is an angle of about 37.8 degrees. Deeper treads or lower risers make a gentler stair.