Stair Calculator
Calculate stair dimensions including number of risers, tread depth, total run, and stringer length with building code compliance check. See also Concrete Calculator and Roofing Calculator.
Stair Dimensions
108 in = 9 ft (standard floor-to-floor)
IRC code: max 7-3/4 in (7.75 in)
How to Calculate Stair Dimensions
Stair calculation starts with the total rise — the vertical distance from one finished floor to the next. Divide the total rise by your desired riser height to determine the number of risers. The number of treads is always one less than the number of risers. Use the 7-11 rule (riser + tread = 17-18 inches) to determine tread depth. The stringer length is calculated using the Pythagorean theorem from the total rise and total run.
Stair Calculation Formulas
Number of Risers = Total Rise / Desired Riser Height (rounded)
Number of Treads = Number of Risers - 1
Actual Riser Height = Total Rise / Number of Risers
Tread Depth = 17.5 - Actual Riser Height (7-11 rule)
Total Run = Number of Treads x Tread Depth
Stringer Length = sqrt(Total Rise^2 + Total Run^2)
IRC Building Code Requirements:
Max riser height: 7-3/4 inches (7.75 in)
Min tread depth: 10 inches
Min headroom: 6 ft 8 in (80 in)
Min width: 36 inches
Example Calculation
Total rise: 108 inches (9 ft floor-to-floor)
Desired riser: 7.5 inches
Risers = 108 / 7.5 = 14.4, rounded to 14
Actual riser = 108 / 14 = 7.71 inches
Treads = 14 - 1 = 13
Tread depth = 17.5 - 7.71 = 9.79 inches
Total run = 13 x 9.79 = 127.3 inches (10.6 ft)
Stringer = sqrt(108^2 + 127.3^2) = 166.9 inches (13.9 ft)
The 7-11 Rule Explained
The 7-11 rule states that the sum of one riser and one tread should equal approximately 17 to 18 inches. This ratio produces stairs that feel comfortable and safe to climb. A 7-inch riser with an 11-inch tread (7 + 11 = 18) is considered ideal. Stairs that deviate significantly from this ratio feel either too steep (high riser, short tread) or too shallow (low riser, deep tread). Building codes enforce minimum and maximum dimensions to ensure safety.
Stringer Calculation
The stringer is the diagonal board that supports the treads and risers. Its length is calculated using the Pythagorean theorem: stringer = square root of (total rise squared + total run squared). Use 2x12 lumber for stringers — after cutting the notches, at least 3.5 inches of wood must remain at the narrowest point. For spans over 6 feet, add a center stringer for additional support.
Common Stair Dimensions Reference
| Total Rise | Risers | Riser Height | Tread Depth | Total Run | Stringer Length |
|---|---|---|---|---|---|
| 8 ft (96 in) | 13 | 7.38 in | 10.12 in | 121.5 in (10.1 ft) | 155.4 in (12.9 ft) |
| 9 ft (108 in) | 14 | 7.71 in | 9.79 in | 127.3 in (10.6 ft) | 166.9 in (13.9 ft) |
| 9 ft (108 in) | 15 | 7.20 in | 10.30 in | 144.2 in (12.0 ft) | 180.2 in (15.0 ft) |
| 10 ft (120 in) | 16 | 7.50 in | 10.00 in | 150.0 in (12.5 ft) | 192.1 in (16.0 ft) |
| 10 ft (120 in) | 17 | 7.06 in | 10.44 in | 167.1 in (13.9 ft) | 205.7 in (17.1 ft) |
Frequently Asked Questions
What is the standard riser height for stairs?
The IRC building code allows a maximum riser height of 7-3/4 inches (7.75 in). The ideal riser height is 7 to 7.5 inches. All risers in a staircase must be uniform — the maximum variation between any two risers is 3/8 inch.
What is the minimum tread depth?
The IRC requires a minimum tread depth of 10 inches, measured from nosing to nosing. The nosing (overhang) should be 3/4 to 1-1/4 inches. Deeper treads (11-12 inches) are more comfortable but require more horizontal space.
How do I calculate stringer length?
Stringer length = square root of (total rise squared + total run squared). For a 9 ft rise with 10.6 ft run: sqrt(108^2 + 127.3^2) = 166.9 inches or about 14 feet. Buy lumber at least 1 foot longer than calculated to allow for cutting.
How many stringers do I need?
Stairs up to 36 inches wide need a minimum of 3 stringers (two outside, one center). For stairs wider than 36 inches, add additional stringers so that no tread spans more than 16-18 inches unsupported.
What is the minimum headroom for stairs?
The IRC requires minimum 6 feet 8 inches (80 inches) of headroom measured vertically from the nosing line to any overhead obstruction. This applies to the entire length of the stairway, including landings.
Do I need a landing?
A landing is required at the top and bottom of every stairway. The landing depth must be at least as wide as the stair width (minimum 36 inches). For stairs with more than 12 feet of vertical rise, an intermediate landing is recommended.
What size lumber for stair stringers?
Use 2x12 lumber for stair stringers. After cutting the notches for treads and risers, at least 3.5 inches of solid wood must remain at the narrowest point. Use pressure-treated lumber for exterior stairs. Douglas fir or southern yellow pine are preferred for strength.