Bottom Line Up Front (BLUF): How to Calculate Stair Stringers & Risers
To lay out stairs, divide the Total Rise (vertical distance from lower finished floor to upper finished floor) by 7.5 inches to find the number of risers. Round to the nearest whole integer, then divide the Total Rise by that number to get the exact riser height. Total Treads = Number of Risers − 1. Multiply by 10"–11" tread depth to get Total Run.
Mastering Staircase Geometry, Stringer Cuts & IRC Codes
1. The International Residential Code (IRC) Stair Rules
IRC residential guidelines mandate: Maximum riser height is 7-3/4" (197 mm), Minimum tread depth is 10" (254 mm), and maximum variation between the highest and lowest riser in a flight cannot exceed 3/8" (9.5 mm).
2. The Comfort Rule / Blondel Formula (2R + T)
For safe and natural walking cadence, François Blondel's classical stair formula requires that two times the riser height plus one tread depth (2 × Riser + Tread) should equal between 24 and 25 inches (60 to 64 cm).
3. Cutting the Bottom of the Stringer (Tread Thickness Drop)
A common beginner mistake is forgetting to cut the bottom of the stringer by the exact thickness of the tread material. Cutting off the tread thickness at the bottom ensures the first step and the top step have identical finished riser heights.
Standard Stair Rise & Run Layout Matrix
| Total Rise (Floor to Floor) | Number of Risers | Exact Riser Height | Number of Treads | Total Run (at 10.5" Tread) | Stringer Angle |
|---|---|---|---|---|---|
| 72" (6 ft) | 10 Risers | 7.200" (7 3/16") | 9 Treads | 94.5" (7' 10 1/2") | 34.4° (Ideal) |
| 84" (7 ft) | 11 Risers | 7.636" (7 5/8") | 10 Treads | 105.0" (8' 9") | 36.0° (Ideal) |
| 96" (8 ft) | 13 Risers | 7.385" (7 3/8") | 12 Treads | 126.0" (10' 6") | 35.1° (Ideal) |
| 108" (9 ft) | 14 Risers | 7.714" (7 11/16") | 13 Treads | 136.5" (11' 4 1/2") | 36.3° (Ideal) |
| 120" (10 ft) | 16 Risers | 7.500" (7 1/2") | 15 Treads | 157.5" (13' 1 1/2") | 35.3° (Ideal) |
Frequently Asked Questions about Stair Construction
What is the best lumber size for cutting stair stringers?
Use 2x12 dimensional lumber (actual size 1.5" × 11.25"). Standard 2x10 lumber does not leave enough throat depth (minimum 3.5" to 5" solid wood remaining under the cutout) to safely support structural loads.
Why is there one less tread than risers?
The top step of a staircase lands directly onto the upper floor level, which acts as the final tread. Therefore, a staircase with N risers requires N - 1 wooden treads.
What is the ideal angle for residential stairs?
The ideal incline angle for residential interior stairs is between 30° and 37°. Angles above 40° become uncomfortably steep and may violate local building codes.