Stair Calculator
This stair calculator determines the number of steps, actual riser height, total run, stringer length, and stair angle from your floor-to-floor rise. Enter the total rise in feet and inches (or total inches), along with your desired riser height and tread depth, to get a complete stair layout with automatic IRC building code compliance checking.
Stair Calculator
Calculate step count, riser height, total run, and building code compliance
Total Rise
IRC: 4"–7.75" (default 7.5")
IRC: min 10" (default 10")
Frequently Asked Questions
How do I calculate the number of stair steps?
Divide the total rise (floor-to-floor height in inches) by your desired riser height, then round to the nearest whole number. For example, a 9-foot (108-inch) floor-to-floor height divided by a 7.5-inch desired riser gives 14.4, which rounds to 14 steps. The actual riser height is then 108 ÷ 14 = 7.71 inches.
What is the maximum riser height for stairs per building code?
The International Residential Code (IRC Section R311.7) sets the maximum riser height at 7¾ inches (7.75 inches) and the minimum at 4 inches for residential stairs. The maximum variation between any two risers in the same staircase is ⅜ inch. Local codes may be more restrictive.
What is the minimum tread depth for stairs?
The IRC requires a minimum tread depth of 10 inches measured horizontally from the nose of one tread to the nose of the next. Tread depth variation across the staircase must not exceed ⅜ inch. A 10-inch minimum tread with a 7.75-inch riser represents the tightest IRC-compliant stair.
What is a comfortable stair riser-to-tread ratio?
The most common comfort formula is 2R + T = 24–25 inches, where R is riser height and T is tread depth. A 7-inch riser paired with an 11-inch tread gives 2(7) + 11 = 25 — the gold standard for comfortable residential stairs. Another check is R + T = 17–18 inches. Both formulas help ensure a stair angle between 30° and 37°.
How do I calculate total run of a staircase?
Total run equals (Number of Steps − 1) × Tread Depth. The top landing does not need a tread, so a 14-step stair with 10-inch treads has a total run of 13 × 10 = 130 inches (10.83 feet). This is the horizontal distance the staircase occupies on your floor plan.
How do I calculate stringer length?
Use the Pythagorean theorem: Stringer Length = √(Total Rise² + Total Run²). For a 9-foot rise (108 inches) and 130-inch run: √(108² + 130²) = √(11664 + 16900) = √28564 ≈ 169 inches (14.1 feet). Add 6–12 inches for seat and plumb cuts at the top and bottom.
What stair angle is considered safe?
Residential stairs typically fall between 30° and 40°. Below 30° the stair occupies too much floor space; above 45° it becomes steep and tiring. The standard IRC stair (7.75-inch riser, 10-inch tread) produces an angle of about 37.8°. For exterior landscape steps, a gentler 20°–30° is preferred.
Does every riser have to be the same height?
Yes. The IRC requires that the greatest riser height in a flight of stairs not exceed the smallest by more than ⅜ inch. Because you must divide the total rise evenly among all risers, using this calculator ensures all risers are identical — eliminating any variation. Unequal risers are a common cause of trips and falls on stairs.
How to Use the Stair Calculator
The Stair Calculator helps contractors, builders, and DIYers design code-compliant staircases. Enter the total rise (floor-to-floor height) and desired riser height to instantly get the exact number of steps, actual riser height, total run, stringer length, and stair angle — with automatic IRC building code compliance checking.
Stair Calculator Guide Contents
1. Stair Formulas
Key Principle: Because the total rise must be divided evenly among all risers, rounding the step count causes the actual riser height to differ slightly from your desired riser height. Always verify the actual riser (Total Rise ÷ Number of Steps) against code limits.
Number of Steps = ROUND(Total Rise ÷ Desired Riser Height)
Actual Riser = Total Rise ÷ Number of Steps
Total Run = (Number of Steps − 1) × Tread Depth
Stringer = √(Total Rise² + Total Run²)
Angle = arctan(Actual Riser ÷ Tread Depth) × (180 ÷ π)
Note that the total run uses (steps − 1)treads because the top landing does not require a tread — the floor itself serves as the last "step."
2. IRC Building Code Requirements
The International Residential Code (IRC Section R311.7) establishes minimum stair dimensions for residential construction. Local jurisdictions may be more restrictive; always verify with your local building department.
| Dimension | IRC Minimum | IRC Maximum | Notes |
|---|---|---|---|
| Riser Height | 4" | 7¾" (7.75") | Variation ≤ ⅜" across all risers |
| Tread Depth | 10" | No maximum | Variation ≤ ⅜" across all treads |
| Stair Width | 36" | No maximum | Clear width above handrail |
| Headroom | 6'8" (80") | No maximum | Measured vertically from tread nose |
Important: This calculator checks riser height and tread depth only. Stair width, headroom, handrail requirements, and landing dimensions are not calculated here. Always consult your local building department for permit requirements.
3. The Comfort Rule
Even when stairs meet code, they may feel awkward to climb. Two classic rules of thumb help you design stairs that feel natural for an average stride:
2R + T = 24–25" Rule
Two risers plus one tread should equal 24 to 25 inches. For a 7" riser and 11" tread: 2 × 7 + 11 = 25. This formula balances the forward motion of a stride against the vertical lift required.
R + T = 17–18" Rule
One riser plus one tread should equal 17 to 18 inches. For a 7.5" riser and 10.5" tread: 7.5 + 10.5 = 18. This is a simpler check for reasonable stair geometry.
Pro Tip:A 7" riser with a 11" tread (2×7 + 11 = 25) is considered the gold standard for comfortable residential stairs and satisfies both comfort rules while staying well within IRC limits.
4. Common Stair Dimensions
| Application | Riser Height | Tread Depth | Angle |
|---|---|---|---|
| Comfortable residential | 7" | 11" | 32.5° |
| Standard residential (IRC default) | 7.5" | 10" | 36.9° |
| Steeper / space-saving | 7.75" | 10" | 37.8° |
| Exterior / landscape steps | 6" | 12"–14" | 23°–27° |
| Basement / utility stair | 7.75" | 10" | 37.8° |
Stair Angle Reference
- 20°–30° — Gentle, easy to climb; requires more horizontal space
- 30°–40° — Comfortable residential range; most common
- 40°–45° — Steep; acceptable for utility stairs, tiring for daily use
- Above 45° — Very steep; approaches ladder territory