Stair Calculator
Rise, run, stringer length, stair angle, and Imperial IRC-style checks for straight residential and deck stairs. The diagram updates as you adjust inputs, so you can see the geometry while tuning it.
Results
Estimates only. Verify against your local building code before construction. Local codes can be stricter than IRC. The limits referenced here apply to typical residential stairs. Commercial and special-use stairs may have different requirements. TakeoffCalc isn't responsible for material over- or under-orders or code violations.
Meets IRC residential limits
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 (275 cm, or 9 feet). A typical deck above grade is 36 to 48 inches (91 to 122 cm). Multiply feet by 12 if your number is in feet.
- 02Set Target Rise per Step. 7 inches (18 cm) is the comfort target (the 7-11 rule). IRC max is 7.75 inches (19.7 cm). 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 (28 cm) matches the 7-11 rule for comfort. IRC minimum is 10 inches (25.4 cm). Standard 2× lumber treads with a 1-inch (2.5-cm) nose work out to about 10.5-11 inches (27-28 cm) of usable depth.
- 04Set Stair Width. IRC minimum for residential is 36 inches (91 cm). Wider stairs (42+ inches, 107+ cm) feel more comfortable on main flights. Basement and deck stairs are often built to the 36-inch (91-cm) minimum.
- 05Read the diagram and results. The diagram redraws to match your inputs. In Imperial mode, it also shows a green IRC reference badge or an amber badge with specific issues listed. Metric mode keeps the focus on geometry. Stringer length is the raw diagonal. Add 6 to 12 inches (15 to 30 cm) when ordering lumber for cuts and attachment.
Understanding the math
Three formulas drive every result. Riser count is total rise divided by target rise, rounded to the nearest whole number. Treads always equal risers minus one, since 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 (275 cm) of rise at a 7-inch (18-cm) target with 11-inch (28-cm) treads. Risers = round(108 / 7) = 15. Actual rise = 108 / 15 = 7.2 inches (18.3 cm). Treads = 14. Total run = 14 × 11 = 154 inches (391 cm, or 12.83 ft). Stringer = √(108² + 154²) = √35,380 = 188.1 inches (478 cm, or 15.67 ft). Angle = atan(108 / 154) = 35.0°. In Imperial mode, this example is within the IRC reference limits (riser ≤ 7.75 in, tread ≥ 10 in, angle ≤ 39°).
IRC reference limits for residential stairs include a maximum riser of 7.75 inches, minimum tread of 10 inches, minimum width of 36 inches, and maximum angle of about 39°. The Imperial result panel flags inputs that exceed these with a specific issue in the badge. Metric mode reports the geometry without a US code pass/fail check.
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 to calculate stair risers?
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 this and adjusts your actual rise to fit evenly.
How to calculate stair stringers?
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 doesn't leave enough wood after notching the steps. The calculator above computes raw stringer length. Budget extra for cuts.
How to calculate stair rise and run?
Rise is the vertical height between treads. Run is the horizontal depth of each step. To calculate, divide your total vertical rise (floor to floor) by your target rise per step (typically 7-7.5 inches / 18-19 cm) to find the number of risers, then round to a whole number. The number of treads is one less than the number of risers, since the top floor itself counts as the last step. Total run equals treads multiplied by tread depth (typically 10-11 inches / 25-28 cm). For a 108 in (275 cm) total rise at 7 in target: 15 risers × 14 treads × 11 in tread = 154 in (391 cm) total run.
How to calculate stair angle?
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. In Imperial mode, the calculator computes the angle from your inputs and flags it if it exceeds the IRC reference limit.
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, since uneven risers cause trips. In Imperial mode, the calculator flags inputs that exceed these IRC reference limits. Metric mode shows the stair geometry without a US code pass/fail panel. Local codes can be stricter, so verify before construction.
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. Include landings in your stair design from the start. They aren't optional, and adding them later is expensive.
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