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. Every later number depends on it: a ½-inch error here ends up as a ½-inch difference on the first or last riser, more than the ⅜-inch variation the IRC allows within a flight.
Step 2 — Calculate riser count
Divide total rise by your target riser height and round up. Rounding down gives fewer, taller risers — taller than your target, and over the 7¾-inch IRC maximum if your target was already close to it. For example, 108 ÷ 7 rounded down is 15 risers at 7.2 inches: still legal, but steeper than planned. Whichever way you round, check the actual riser height in Step 3.
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 keeps every step the same height — IRC §R318.7.5.1 allows no more than ⅜ inch of variation within a flight. See stair building code requirements for the full set of IRC limits.
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 upper landing surface serves as the top step, so it isn't cut into the stringer. For this layout, the number of physical treads is 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
In a standard mount stair, the stringer is the hypotenuse of a right triangle whose legs are the total run and the total rise minus one riser. Use the Pythagorean theorem:
Example: 108-inch total rise minus one 6.75-inch riser = 101.25-inch stringer rise, with a 165-inch run:
Add 6–12 inches to your calculated length for the top plumb cut and bottom seat cut, then buy the next standard lumber length up — in this case 18-foot 2×12 stringers.
Checking rise and run together
The IRC sets limits on each dimension — a riser of no more than 7¾ inches (§R318.7.5.1) and a tread of at least 10 inches (§R318.7.5.2) — but no formula linking the two. England's Approved Document K (Table 1.1) does give one: “twice the rise plus the going (2R + G) equals between 550mm and 700mm”, about 21.7 to 27.6 inches. It's UK guidance, not a US code requirement, but it's a published check on proportion.
In the US, carpenters commonly use a simpler rule of thumb: rise plus run of about 17–18 inches (7 + 11 = 18). It isn't a code requirement, but it's widely used and our stair calculator shows it as a quick check.
| Rise | Run | 2R + G | Angle | IRC limits |
|---|---|---|---|---|
| 7" | 11" | 25" (635 mm) ✓ | 32.5° | Within both |
| 7.5" | 10" | 25" (635 mm) ✓ | 36.9° | Within both; tread at minimum |
| 7.75" | 10" | 25.5" (648 mm) ✓ | 37.8° | Max riser and min tread — steepest allowed |
| 6.75" | 11" | 24.5" (622 mm) ✓ | 31.5° | Within both |
Full worked example
9-ft floor-to-floor (108 inches), 7-inch target riser, 11-inch treads, standard mount:
| 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) |
| 2R + G = 2 × 6.75 + 11 | 24.5" (622 mm) ✓ (550–700 mm) |
| Stringer = √((108 − 6.75)² + 165²) | 193.6" (16.1 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 IRC doesn't define an ideal. It sets limits: risers no more than 7¾ inches (§R318.7.5.1) and treads at least 10 inches deep (§R318.7.5.2). For proportion, England's Approved Document K gives 2 × rise + going between 550 mm and 700 mm (about 21.7–27.6 inches). A 7-inch rise with an 11-inch tread meets the IRC limits and gives 2R + G = 25 inches (635 mm).
How do I calculate stringer length?
Use the Pythagorean theorem: stringer length = √((total rise − one riser)² + total run²). In a standard mount stair the deck face is the top step, so the stringer climbs one riser less than the total rise. For a 108-inch total rise with 16 risers of 6.75 inches and 15 treads of 11 inches (165-inch run): √(101.25² + 165²) = √37,476.6 ≈ 193.6 inches (16.1 ft). Add 6–12 inches for cuts and buy the next standard lumber length up — 18 ft here.
Why can't I just make the bottom step a different height?
IRC §R318.7.5.1 says the greatest riser height within any flight shall not exceed the smallest by more than ⅜ inch. A bottom or top step that differs from the rest by more than that violates the rule, so spread any remainder evenly across all risers instead.
Does the deck or landing count as a tread?
Yes — in standard mount, the deck or landing surface serves as the top step, so it isn't cut into the stringer. That's why treads = risers minus 1 for this layout. A 15-riser stair has 14 physical treads in the stringer.