Stair Calculator
Find step count, rise, run, stringer length, and angle for decks, basements, and interior staircases.
Vertical height from the lower floor/ground to the upper floor or deck surface. 9 ft floor-to-floor ≈ 108 in.
Your Stair Measurements
- Measure total rise - the vertical floor-to-floor (or ground-to-deck) height in inches - this is the one measurement that drives everything.
- Pick tread depth - 11 in is the residential standard; IRC requires at least 10 in.
- Set preferred riser - the calculator divides rise evenly and never exceeds the 7¾ in code maximum.
- Buy stringers by length - purchase 2×12 boards at least the stringer length shown, plus ~10% for cuts.
- Add stringers for width - two stringers up to 36 in wide; add a center stringer beyond that.
A 105 inch floor-to-floor rise - a typical 8 foot ceiling once you add the floor system - needs 14 steps at 7.5 inches each. With 10 inch treads that is a 130 inch total run and a stringer just under 14 feet, so buy one 14 foot 2×12 per stringer and plan on three stringers for a 36 inch wide stair. The IRC caps risers at 7¾ inches and requires treads of at least 10 inches, with every riser in the flight within ⅜ inch of the others. Enter your total rise above for the exact layout.
Anatomy of a Stair
How Stair Dimensions Are Calculated
Every stair starts from one number: total rise, the vertical height the stairs must climb. Divide it by a comfortable riser height (around 7 to 7.5 inches) and round to a whole number of steps, then divide the total rise back by that step count so every riser is identical. The IRC caps riser height at 7¾ inches and requires all risers in a flight to be within ⅜ inch of each other - which is why you divide evenly rather than rounding individual steps.
From the step count, the rest is geometry. Total run is the number of treads (one fewer than the steps) times the tread depth. Stringer length is the diagonal - the square root of total rise squared plus total run squared. The stair angle is the arctangent of rise over run; comfortable residential stairs land between 30 and 37 degrees.
Stair Code Limits at a Glance
The residential limits the IRC sets for a standard flight - your local code may be stricter:
| Dimension | IRC residential limit |
|---|---|
| Riser height | Max 7¾ in |
| Tread depth | Min 10 in |
| Riser / tread variance | Max ⅜ in between the largest and smallest in a flight |
| Stair width | Min 36 in |
| Headroom | Min 6 ft 8 in above the nosing line |
| Handrail height | 34 to 38 in; required on any flight of 4 or more risers |
| Max vertical rise per flight | A landing is required where a flight rises more than 12 ft 7 in |
| Nosing | ¾ to 1¼ in projection where treads are less than 11 in deep |
What Makes a Stair Comfortable
Code sets the outer limits; comfort lives inside them. The old carpenter test is the 2R+T rule (Blondel): two risers plus one tread should land between 24 and 25 inches. A 7 inch riser with an 11 inch tread hits 25 inches exactly, which is why 7/11 is the sweet spot for everyday interior stairs.
Angle is the other tell. Comfortable residential stairs sit between 30 and 37 degrees. Below 30 feels shallow and eats floor space; push past about 42 degrees and the stair starts to climb like a ladder. For a fixed total rise, a deeper tread or a lower riser both pull the angle down and stretch the run out, so the trade is always comfort against the floor space you can spare. The calculator flags any layout that drifts outside the comfortable band.
Typical Stair Dimensions by Application
Common rise, run, and angle ranges by stair type:
| Application | Rise per Step | Tread Depth | Angle |
|---|---|---|---|
| Interior residential | 7–7¾ in | 10–11 in | 33–38° |
| Deck / exterior | 6–7 in | 11–12 in | 27–33° |
| Basement | 7–7¾ in | 10–11 in | 33–38° |
| Gentle / accessible | 5–6 in | 12–14 in | 20–27° |
Steeper stairs save floor space but are harder to climb; gentler stairs eat more run. For a given total rise, a deeper tread or lower riser both push the angle down and the run out.
Stair Formulas
The math behind the results:
Rise per step = Total rise ÷ number of steps
Total run = (Number of steps − 1) × tread depth
Stringer length = √(Total rise² + Total run²)
Stair angle = arctangent(Total rise ÷ Total run)
There is one fewer tread than riser because the upper floor serves as the top "tread." Always cut stringers from straight, knot-free 2×12 stock.
Related Calculators
Code Notes
- The IRC limits residential risers to 7¾ inches and treads to a 10 inch minimum, and every riser in a flight must fall within ⅜ inch of the tallest so the stair climbs at an even, predictable rhythm - uneven risers are a leading trip hazard and a common inspection failure.IRC R311.7.5 - Stair treads and risers
- A flight needs at least 36 inches of clear width and 6 feet 8 inches of headroom, a handrail on any run of four or more risers, and a landing where a single flight would rise more than 12 feet 7 inches.IRC R311.7 - Stairways
After You Lay Out the Stair
The stringer length and step count feed the rest of the build:
Building a deck or interior stair? Browse the full construction calculator collection for framing, footings, and lumber.
Frequently Asked Questions
How many steps for an 8-foot rise?
An 8-foot rise is 96 inches. At a 7.5-inch target riser that is about 13 steps, giving an actual rise of 7.38 inches per step - comfortable and well within code. The calculator divides the rise evenly so every riser is identical, which the IRC requires.
What is the maximum riser height by code?
The IRC sets the maximum riser at 7¾ inches and the minimum tread depth at 10 inches. This calculator never returns a riser above 7¾ inches - if your preferred height would exceed it, the step count is automatically increased.
How long should my stringers be?
The stringer length shown is the straight diagonal distance. Buy 2×12 boards at least that long, and add roughly 10% for the notch cuts and the top and bottom connections. For a typical 9-foot floor-to-floor stair, plan on stringers around 14–15 feet.
What is a comfortable stair angle?
Between 30 and 37 degrees is the comfortable range for everyday residential stairs. Below 30 degrees feels gentle but uses a lot of floor space; above 38 degrees feels steep and is harder on the knees. Deck and exterior stairs are often built a little shallower, around 27 to 33 degrees.
How wide should a staircase be, and how many stringers?
Residential stairs must be at least 36 inches wide. A standard 36 inch stair uses three stringers - two at the edges and one down the middle - to keep the treads from flexing; two stringers only suit a narrow stair or thick 2× treads. Space stringers no more than about 16 inches apart for thinner tread stock.
How many steps do I need for a 9-foot or 10-foot ceiling?
Work from the real floor-to-floor rise, not the ceiling height - a 9 foot ceiling is usually a 108 to 117 inch rise once you add the floor system, and a 10 foot ceiling runs higher still. As a guide, a 108 inch rise comes out to 14 steps at 7.71 inches each, and a 120 inch rise to 16 steps at 7.50 inches. Measure the exact vertical from finished floor to finished floor and enter it above; the calculator divides it evenly and never lets a riser exceed 7¾ inches.
What size lumber should stair stringers be?
Cut stringers from straight, knot-free 2×12 stock. After the riser and tread notches are cut, the IRC wants at least 5 inches of solid wood left in the narrowest part of the stringer, which a 2×12 provides but a 2×10 usually does not. A 36 inch wide stair takes three stringers - two at the edges and one down the middle - to keep the treads from flexing. The calculator rounds the stringer length up to the next stock 2×12 length for you.