Stair Calculator
Calculate rise, run, stringer length, stair angle, and IRC code compliance for residential and deck stairs. The diagram updates dynamically as you adjust inputs so you can see the geometry as you tune it.
Meets IRC residential limits
Results
Estimates only. Always verify against your local building code before construction. IRC limits referenced here apply to typical residential stairs; commercial and special-use stairs may have different requirements.
How to use this calculator
- 01Enter Total Rise — the full vertical height to climb, measured floor-to-floor in inches. A standard residential floor is 108 inches (9 feet); a typical deck above grade is 36 to 48 inches. Multiply feet by 12 if your number is in feet.
- 02Set Target Rise per Step. 7 inches is the comfort target (the 7-11 rule); IRC max is 7.75 inches. The calculator rounds to a whole number of risers and adjusts the actual rise per step to fit your total rise evenly — so the actual rise often differs slightly from your target.
- 03Set Tread Depth. 11 inches matches the 7-11 rule for comfort; IRC minimum is 10 inches. Standard 2× lumber treads with a 1-inch nose work out to about 10.5–11 inches of usable depth.
- 04Set Stair Width. IRC minimum for residential is 36 inches. Wider stairs (42+ inches) feel more comfortable on main flights; basement and deck stairs are often built to the 36-inch minimum.
- 05Read the diagram and results. The diagram redraws to match your inputs, with a green badge for IRC-compliant stairs or an amber badge with specific issues listed. Stringer length is the raw diagonal — add 6 to 12 inches when ordering lumber for cuts and attachment.
Understanding the math
Three formulas drive every result. Riser count is your total rise divided by your target rise, rounded to the nearest whole number. Treads always equal risers minus one because the top floor itself counts as the last step:
risers = round(totalRise / targetRise) treads = risers − 1 actualRise = totalRise / risers
Total run is treads × tread depth. Stringer length is the diagonal of the rise-run rectangle, by Pythagorean theorem. Stair angle is the arctangent of rise over run:
totalRun = treads × treadDepth stringer = √(totalRise² + totalRun²) angle = atan(totalRise / totalRun)
Worked example: 108 inches of rise at a 7-inch target with 11-inch treads. Risers = round(108 / 7) = 15. Actual rise = 108 / 15 = 7.2 inches. Treads = 14. Total run = 14 × 11 = 154 inches (12.83 ft). Stringer = √(108² + 154²) = √35,380 = 188.1 inches (15.67 ft). Angle = atan(108 / 154) = 35.0°. All within IRC limits — riser ≤ 7.75, tread ≥ 10, angle ≤ 39 — so the stair is compliant.
IRC limits for residential stairs: maximum riser 7.75 inches, minimum tread 10 inches, minimum width 36 inches, maximum angle ≈39°. The calculator flags any input that exceeds these with a specific issue in the compliance badge.
Standard stair dimensions reference
Common stair configurations from a single porch step up through a 10-foot ceiling. Computed at 7-inch (18 cm) target rise (8-inch for the low porch row); asterisks indicate rows where the angle exceeds the IRC code limit of 39°.
| Application | Total Rise | Risers | Actual Rise | Total Run | Stringer | Angle |
|---|---|---|---|---|---|---|
| Single step (porch) | 7" | 1 | 7.0" | n/a | 7.0" | n/a |
| Low porch (3 steps) | 21" | 3 | 7.0" | 22" | 30.4" | 43.7°* |
| Standard porch (4 steps) | 28" | 4 | 7.0" | 33" | 43.3" | 40.3°* |
| Deck stairs (typical) | 36" | 5 | 7.2" | 44" | 56.9" | 39.3°* |
| Tall deck (above grade) | 48" | 7 | 6.9" | 66" | 81.6" | 36.0° |
| Basement stairs | 96" | 14 | 6.9" | 143" | 172.2" | 33.9° |
| Standard residential floor | 108" | 15 | 7.2" | 154" | 188.1" | 35.0° |
| Tall ceiling (10 ft floor) | 120" | 17 | 7.1" | 176" | 213.0" | 34.3° |
Frequently asked questions
How do I calculate how many stairs I need?
Divide your total rise (the height you need to climb, measured from finish floor to finish floor) by your target riser height. For a 9-foot deck (108 inches / 275 cm) at a 7-inch (18 cm) target rise: 108 ÷ 7 = 15.43 → round to 15 risers. Your actual rise per step becomes 108 ÷ 15 = 7.2 inches (18.3 cm). The number of treads is always one less than risers because the top floor itself acts as the last step. So 15 risers means 14 treads and a horizontal run of 14 × tread depth. The calculator above handles all of this and adjusts your actual rise to fit evenly.
How do I calculate stair stringer length?
Stringer length comes from the Pythagorean theorem applied to the total rise and total run. Stringer = square root of (totalRise² + totalRun²). For 108 inches of rise and 154 inches of run (275 cm × 391 cm): stringer = √(11,664 + 23,716) = √35,380 = 188 inches, or 15.7 feet (4.78 m). Add 6-12 inches (15-30 cm) for cuts, mounting attachment, and trimming, so order at least 16-foot lumber. Standard stringer material is 2×12 — anything smaller does not leave enough wood after notching the steps. The calculator above computes raw stringer length; budget extra for cuts.
What is the 7-11 rule for stairs?
The 7-11 rule states that a comfortable stair has a 7-inch (18 cm) rise and 11-inch (28 cm) tread. Together they total 18 inches (46 cm), which matches the natural human stride. Stairs much steeper (small tread, tall rise) feel like climbing a ladder; stairs much shallower (small rise, wide tread) feel awkward and waste horizontal space. Most building codes allow rise up to 7.75 inches (19.7 cm) and tread as low as 10 inches (25.4 cm), but 7-11 remains the comfort target. The calculator above defaults to 7-inch rise and 11-inch tread (18 cm and 28 cm in metric mode).
What is the IRC code for stair rise and run?
The International Residential Code (IRC) sets these limits for residential stairs: maximum riser height 7.75 inches (19.7 cm), minimum tread depth 10 inches (25.4 cm), minimum stair width 36 inches (91.4 cm), and minimum headroom 6 feet 8 inches (203 cm). Risers must be uniform within 3/8-inch (1 cm) tolerance — uneven risers cause trips. The calculator above flags inputs that exceed IRC limits with a code compliance indicator. Local building codes can be stricter than IRC; always verify before construction. Commercial stairs follow IBC (International Building Code) which has different limits.
How do I calculate the angle of stairs?
Stair angle is the arctangent of total rise divided by total run. For 108 inches of rise and 154 inches of run (275 cm and 391 cm): angle = atan(108/154) = atan(0.701) = 35.0 degrees. Standard residential stairs fall between 30 and 37 degrees. The IRC allows up to about 39 degrees for typical stairs. Steeper than 39 degrees is technically a ladder, with different code requirements. The calculator above computes the angle from your inputs and flags it with the code compliance indicator if it exceeds the limit.
How long should my deck stair stringers be?
Deck stringers depend on your deck height and stair angle. For a 36-inch deck (90 cm, 3 feet up), at a typical 35-degree angle, you need about 60 inches (152 cm, 5 feet) of stringer length, plus 6-12 inches (15-30 cm) for attachment and cuts. For a 48-inch deck (122 cm), plan for 80 inches (203 cm) stringer plus extras. Most residential decks under 4 feet (122 cm) need 8-foot 2×12 stringers; decks 4-7 feet (122-213 cm) need 10 to 12-foot stringers. The calculator above gives exact stringer length — add a buffer for cuts and attachment hardware.
What is the difference between rise, run, and stringer?
Rise is the vertical height of one step (typical 7 to 7.75 inches / 18 to 19.7 cm). Run is the horizontal depth of one tread (typical 10 to 11 inches / 25 to 28 cm). Total rise is the full vertical climb (floor to floor). Total run is the full horizontal distance the stair occupies. Stringer is the diagonal supporting board on the side of the stair, cut with notches for each step. The stringer length is the diagonal of the rise-run rectangle, calculated by Pythagorean theorem. Builders measure the stringer along its bottom edge, not its centerline.
Do my stairs need a landing?
The IRC requires a landing at the top and bottom of every flight of stairs, with a minimum dimension equal to the stair width (typically 36 inches / 91 cm square). A landing is also required if the total rise exceeds 12 feet (147 inches / 373 cm) — long stair flights must be broken into shorter sections. Landings are also required when stairs change direction. Doors at the top of stairs need a landing at least the door's width and depth. Always include landings in your stair design — they are not optional, and adding them later is expensive.
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Estimates only. Always verify against your local building code before construction. IRC limits referenced here apply to typical residential stairs; commercial and special-use stairs may have different requirements. TakeoffCalc is not responsible for material over- or under-orders or code violations.