Article — Stairs Calculator (Rise & Run)
Stairs calculator: rise, run, and IRC code-compliant step sizing
A residential stair with 108-inch (9-foot) total rise needs 16 risers at 6.75 inches each, paired with 15 treads at 11 inches. Total run is 165 inches. Stringer length is 197 inches. IRC R311.7 caps risers at 7.75 in and treads at 10 in minimum. The 2R+T comfort rule targets 24-25 inches.
Stair design starts with one input: total rise. From there, code limits and the comfort rule lock in the rest of the geometry. This calculator solves the riser count, actual riser height, tread depth check, stringer length, pitch angle, and code compliance in one pass. It matches the IRC R311.7 framework used by every building inspector in North America.
What the stairs calculator does
The calculator takes total rise, target riser height, tread depth, and stair width as inputs. It computes the minimum riser count that keeps actual riser height at or below the target, then back-solves the exact actual riser. Tread count equals risers minus 1 (the top "step" is part of the upper floor). It computes total run, stringer length, pitch angle, and the 2R+T comfort metric.
It also runs four code checks. Riser height must be 4 to 7.75 inches per IRC residential rules. Tread depth must be 10 inches or more. Stair width must be 36 inches or more. The 2R+T comfort value should fall between 24 and 25 inches. A green badge means all four pass; a warning lists any failures so you can adjust inputs.
IRC stair rise and run limits
IRC R311.7.5 sets the residential limits. Maximum riser height is 7.75 inches (197 mm). Minimum tread depth is 10 inches (254 mm), measured from nosing to nosing. Stair width must be at least 36 inches above the handrail height. Riser heights cannot vary by more than 3/8 inch between any two risers on the same flight. Nosing projection must be 0.75 to 1.25 inches.
Commercial buildings under the IBC face tighter limits. IBC 1011 caps risers at 7 inches and requires minimum tread depth of 11 inches. The 2R+T comfort rule is enforced as code, not advice. Stairs serving more than 49 occupants must be 44 inches wide. These rules apply to public buildings, offices, and any rental property with three or more units.
The 7.75-inch riser limit was lowered from 8.25 inches in the 2000 IRC after analysis of fall statistics showed a sharp increase in stair injuries above 7.75 inches. The change added one extra step to most residential staircases but reduced reported stair-related injuries by an estimated 15% in newly built homes.
How to size stairs
Step 1: measure total rise from finished floor to finished floor. Include floor thickness — don't measure stud height. A typical residential story is 105-110 inches. Deck stairs measure from grade or pad to the deck surface.
Step 2: divide total rise by your target riser height (7 in is comfortable, 7.5 in is firmer, 7.75 in is the IRC max). Round up to whole risers. For 108-inch rise with 7-inch target: ceil(108/7) = 16 risers.
Step 3: back-solve actual riser. 108 / 16 = 6.75 inches. This is the height the carpenter cuts. Tread count is 16 - 1 = 15 treads. With 11-inch tread depth, total run is 15 × 11 = 165 inches = 13.75 feet.
Step 4: check comfort and code. 2R+T = 2(6.75) + 11 = 24.5 — within ideal range. Riser is under 7.75 (pass). Tread is at minimum but compliant (pass). Stair is good to build.
Rounding the riser count down lets actual riser height exceed your target and may violate code. The calculator always rounds up. Adding one extra riser at the top of a flight is usually invisible to users but the alternative — a 7.85-inch riser that fails inspection — costs a full stair tear-out to fix.
The 2R+T stair comfort rule
The 2R+T rule states that 2 times the riser height plus the tread depth should equal 24 to 25 inches. The rule comes from François Blondel's 1675 treatise on architecture, in which he documented the relationship between human stride length and comfortable stair geometry. Modern biomechanics studies have confirmed the basic relationship — natural stride ranges from 24 to 26 inches.
Stairs that violate 2R+T feel wrong without being obviously unsafe. Too low (below 24): users feel cramped, taking awkwardly short steps. Too high (above 25): users feel stretched, hesitating between steps. IRC does not enforce 2R+T directly, but IBC does for commercial work, and most experienced builders aim for it on residential projects too.
Stair stringer length
Stringers are the inclined boards that support treads and risers. Stringer length is the diagonal computed from total rise and total run: L = √(rise² + run²). For 108-inch rise and 165-inch run: L = √(11664 + 27225) = 197.2 inches = 16.4 feet.
Add 12-18 inches to the calculated length for the bottom landing connection (where the stringer terminates on the floor) and the top header connection (where it attaches to the upper floor structure). Most residential stringers are cut from 2x12 lumber. The unused triangular pieces from the cuts can serve as kick-rail blocking, so order whole stock and cut to fit.
Stair pitch angle
Pitch angle is the angle from horizontal. It equals arctan(rise/run). For 108-inch rise and 165-inch run: arctan(0.6545) = 33.2°. IRC accepts 20° to 50° but most residential stairs target 30° to 38°. Below 30° feels shallow and wastes floor space. Above 38° feels steep and stresses knees on descent.
Deck stairs sometimes go steeper, up to 40°, because outdoor space is at a premium and users are typically able-bodied. Basement stairs in older homes often exceed 40° — they predate modern code and are grandfathered in. Bringing such stairs up to current code usually requires a full rebuild, which is why most basement remodels rebuild the stair.
If your stair must serve elderly or mobility-limited users, target a 6.5-inch riser and 12-inch tread. The resulting 2R+T = 25 stays within comfort, but the lower riser reduces knee strain on descent. The longer tread gives more time to plant the foot. Pitch drops to around 28° — code-marginal but functional.
Common stair design mistakes
Mistake one is forgetting that tread count equals riser count minus 1. New designers sometimes specify 15 risers and 15 treads, leaving an extra step that either disappears into a landing or creates a tripping hazard. The top step is always part of the upper floor.
Mistake two is mixing tread depth measurement methods. IRC measures nosing to nosing. The visible part of the tread is shorter because of the nosing overhang of the tread above. A 10-inch tread with 1-inch nosing shows 11 inches of horizontal surface but the IRC measurement remains 10 inches (nosing to nosing).
Mistake three is ignoring uniformity. The 3/8-inch variance rule between risers exists because uneven steps cause falls. Two risers at 6.5 inches and one at 7.25 inches creates a 0.75-inch variance — twice the allowed limit. Cut all risers from the same template and dry-fit before final assembly.
Risers ceil(rise / target)Treads risers - 1Stringer √(rise² + run²)Pitch arctan(rise/run)Comfort 2R + T = 24-25 inIRC riser max 7.75 in- 7.75 inches IRC max riser height (residential)
- 10 inches IRC min tread depth (residential)
- 11 inches IBC min tread depth (commercial)
- 3/8 inch max variance between any two risers
- 36 inches minimum stair width (residential)
- 30-38° recommended pitch angle
- 24-25 inches target value for 2R + T comfort rule
- 1675 year François Blondel published the 2R+T rule