How to Calculate Stair Rise and Run
Stair geometry comes down to three numbers: total rise, riser height, and tread depth. Get those right and everything else — riser count, total run, stringer length — follows directly. Here's how to work through it step by step.
Key terms
| Term | Definition |
|---|---|
| Total rise | Vertical distance from finished floor to finished floor |
| Riser | Vertical height of one step |
| Tread (run) | Horizontal depth of one step, nose to nose |
| Total run | Total horizontal distance the stair covers |
| Stringer | Diagonal support board the treads sit on |
Step 1 — Measure total rise precisely
Total rise is the finished floor to finished floor height — including any flooring material on both levels. This is the most critical measurement: a ½-inch error here shows up as a ½-inch error on the bottom riser, which fails inspection.
Step 2 — Calculate riser count
Divide total rise by your target riser height and round up. Never round down — it produces a riser that exceeds the IRC maximum.
Example: 108-inch total rise, 7-inch target riser:
Step 3 — Back-derive actual riser height
Once you have the riser count, divide total rise by that number to get the actual uniform riser height. This ensures every step is identical — required by IRC §R311.7.5.1.
Example:108 ÷ 16 = 6.75 inches per riser ✓ (under 7¾" IRC maximum)
Step 4 — Count treads and calculate total run
In a standard mount stair, the deck or landing surface acts as the top tread. So the number of physical treads is always one less than the riser count.
Example:16 risers, 11-inch tread depth: 15 treads × 11" = 165 inches (13 ft 9 in) total run
Step 5 — Calculate stringer length
The stringer is the hypotenuse of the right triangle formed by total rise and total run. Use the Pythagorean theorem:
Example: 108-inch rise, 165-inch run:
Buy the next standard lumber length up — in this case 18-foot 2×12 stringers. Add 6–12 inches to your calculated length for the top plumb cut and bottom seat cut.
The comfort formula
A stair that passes code isn't always comfortable. The ergonomic standard, documented by Nicolas-François Blondel in 1672 and restated in AWC DCA-6, is:
| Rise | Run | Sum | Angle | Feel |
|---|---|---|---|---|
| 7" | 11" | 18 ✓ | 32.5° | Ideal — most comfortable |
| 7.5" | 10" | 17.5 ✓ | 36.9° | Acceptable, slightly steep |
| 7.75" | 10" | 17.75 ✓ | 37.8° | IRC max — noticeably steep |
| 6.75" | 11" | 17.75 ✓ | 31.5° | Comfortable, uses more floor space |
Full worked example
Standard 9-ft floor-to-floor (108 inches), 7-inch target riser, 11-inch treads:
| Calculation | Result |
|---|---|
| Risers = ⌈108 ÷ 7⌉ | 16 risers |
| Actual riser = 108 ÷ 16 | 6.75" ✓ (under 7¾" max) |
| Treads = 16 − 1 | 15 treads |
| Total run = 15 × 11" | 165" (13 ft 9 in) |
| Comfort = 6.75 + 11 | 17.75" ✓ |
| Stringer = √(108² + 165²) | 197.2" (16.4 ft) → buy 18 ft 2×12 |
Skip the manual calculation
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Use the Stair Calculator →FAQ
How do I calculate the number of stairs I need?
Divide your total floor-to-floor height by your target riser height and round up. For example, 108 inches ÷ 7 inches = 15.4, rounded up to 16 risers. Then back-derive the actual riser: 108 ÷ 16 = 6.75 inches per riser.
What is the ideal stair rise and run?
The most comfortable combination is a 7-inch rise with an 11-inch run (sum = 18). The IRC allows up to 7¾-inch rise and requires a minimum 10-inch run. The comfort formula is Rise + Run = 17–18 inches.
How do I calculate stringer length?
Use the Pythagorean theorem: stringer length = √(total rise² + total run²). For 108-inch rise and 154-inch run: √(11,664 + 23,716) = √35,380 = 188 inches (15.7 ft). Buy the next standard lumber length up and add 6–12 inches for cuts.
Why can't I just make the bottom step a different height?
IRC §R311.7.5.1 requires all risers in a flight to be within ⅜ inch of each other. An uneven bottom or top step is both a code violation and the leading cause of stair falls — the foot expects a consistent rhythm and misjudges the last step.
Does the deck or landing count as a tread?
Yes — in standard mount, the deck or landing surface acts as the top tread. This is why treads = risers minus 1. A 15-riser stair has 14 physical treads in the stringer.