Stair Calculator

How to use this stair calculator — step by step

The calculator above takes rise per step (riser height) and run per step (tread depth) and returns the stair angle. To go from a total floor-to-floor height to a complete stair design, follow the six-step procedure below.

1. Measure the total floor-to-floor height in inches. This is the vertical distance from the finished surface of the lower floor (or deck, or grade) to the finished surface of the upper floor or landing. For an interior stair to a 9-foot ceiling with 1/2 inch finished flooring on both levels, the total rise is typically 109-110 inches.
2. Divide total rise by 7.5 to get a starting riser-count estimate. For 109 inches: 109 ÷ 7.5 = 14.5, round to 14 or 15. Try both numbers in step 3.
3. Compute exact riser height = total rise ÷ riser count. For 109 inches with 14 risers: 7.79 inches each (just over the 7-3/4 IRC limit, not allowed). With 15 risers: 7.27 inches each (well within limits, allowed). 15 risers it is.
4. Pick a tread depth between 10 and 11 inches. Standard residential is 10 inches; 10-1/2 or 11 inches makes a more comfortable stair if you have the floor space. The number of treads = number of risers minus 1 (the top "tread" is the upper floor itself).
5. Compute the total stair run = (riser count − 1) × tread depth. For our 15-riser stair with 10-inch treads: 14 × 10 = 140 inches = 11 ft 8 inches of horizontal floor space.
6. Plug riser height (7.27") and tread depth (10") into the calculator above to get the stair angle and slope, then size the stringer using the stringer math in the dedicated section below.

Stair rise and run — the IRC limits and what they mean

Stair rise and run are the two dimensions that define every stair design. Rise is the vertical distance from one tread surface to the next; run is the horizontal depth of one tread (measured nose-to-nose, not the full board width — the tread typically overhangs the riser by 3/4 to 1-1/4 inches and that overhang is not part of run). Standard stair rise run combinations cluster around 7" rise / 11" run for comfortable stairs, 7-3/4" rise / 10" run for the steepest IRC-allowed stair.

The IRC R311.7.5 rules for residential stairs: maximum riser height 7-3/4 inches; minimum tread depth 10 inches; the largest riser within a flight cannot exceed the smallest by more than 3/8 inch; the largest tread cannot exceed the smallest by more than 3/8 inch. Tread depth is measured along the line of nosings, with no nosing projection over 1-1/4 inches and a minimum of 3/4 inch.

A practical rise-run formula many builders use: 2 × rise + run = 24 to 25 inches. A 7" rise + 11" run = 25 (comfortable). A 7-3/4" + 10" = 25.5 (steep but legal). A 6" + 13" = 25 (gentle, takes more floor space). The rule is empirical — it produces stairs that match natural human walking gait — and is independent of code limits. For homeowners searching "stairs rise run" or "angle stairs" online, the dimensions ratios in this section combined with the angle calculator above give the complete picture: rise/run determines angle (7"/11" = 32.5°, 7-3/4"/10" = 37.8°), and angle determines comfort.

How to figure out rise and run of stairs from a real-world measurement: measure the total height (floor-to-floor including finished surfaces); divide by an estimated riser count to get a candidate riser height; verify the riser height is at or below 7-3/4"; pick a matching tread depth (10-11" typical) that gives total stair run within the available floor space. The 6-step procedure in the "how to use" section above turns this into an algorithm. How to find the rise and run of stairs that already exist: measure one riser top to next riser top (rise) and one nosing to next nosing (run); both should be consistent within 3/8" across the entire flight.

How to calculate the rise and run of stairs from a total height, in summary: (1) total rise / riser count = rise per step, (2) tread depth × (riser count − 1) = total run. Use the calculator above to verify the resulting angle is comfortable (typically 30-37° for residential) and code-compliant.

Stair stringer calculator — sizing the cut stringer

A stair stringer is the diagonal structural member that supports the treads and risers. Sizing the stringer is what most users actually need a stair stringer calculator for — once you know rise per step, tread depth, and step count, the stringer dimensions follow from straightforward geometry.

Stringer length (the diagonal) = √(total rise² + total run²). For our 109"-rise, 140"-run interior stair: √(109² + 140²) = √(11,881 + 19,600) = √31,481 = 177.4 inches = 14 ft 9-1/2 inches. Order a 16-foot 2x12 to allow trim cuts at top and bottom. Stair stringer dimensions for the same stair: cut from 2x12 stock, the cut-line saw-tooth pattern uses the same rise and run as the steps; the smallest remaining cross-section between cuts must be at least 5 inches deep for adequate strength (the IRC requires 5 inches minimum for a residential stringer).

How many stair stringers do I need? For typical residential 36-inch-wide interior stairs: 3 stringers — one at each side and one in the middle. Wider stairs (over 36 inches) need 4 stringers; very wide commercial stairs need stringers every 16 inches on center. How many stringers for 36-wide stairs: 3 stringers is the residential standard; 2 stringers is undersized and produces tread sag. How many stringers do I need for stairs of any width: total width / 16 inches, rounded up to the nearest whole number, minimum 3.

Material specifications for typical residential stair stringers: 2x12 dimension lumber (1.5 × 11.25 inches actual), grade #2 or better, species selected for span and load. For exterior or deck stairs, pressure-treated 2x12 (rated for ground contact) is standard. Engineered options for longer spans or heavy loads include LVL stringers and steel stringers, both running 2-3× the cost of dimension lumber but allowing thinner, more open stair designs. The LVL beam calculator on this site sizes engineered lumber if you need to spec an LVL stringer for an unusually long stair span.

How to measure stair stringers: lay the cut 2x12 across the planned rise and run; mark each tread cut using a framing square set to the rise dimension on the tongue and the tread dimension on the body; mark the top plumb cut and bottom level cut; verify the smallest remaining wood depth between cuts is at least 5 inches before any cut is made. A common mistake is forgetting to subtract one riser height from the bottom cut to account for the tread thickness — the first riser to the bottom of the lowest tread, when the tread is installed, must equal the same riser height as every other riser. The bottom of the stringer cut is correspondingly one tread thickness short.

Deck stairs and outdoor steps — what is different from interior stairs

A deck stair calculator and a deck step calculator follow the same rise-run math as interior stairs, but with a few outdoor-specific considerations that affect material and construction choices. The math is identical; the materials and details differ.

Material: deck stair stringers are pressure-treated 2x12 (rated for ground contact, typically .40 retention or higher), not standard SPF dimension lumber. Treads are pressure-treated decking, composite decking, or cedar — never standard dimension lumber, which will rot. Risers can be open (no riser board) or closed with treated material; open is more common on deck stairs because it sheds water and snow.

Frost heave and bottom support: an outdoor stair landing must be supported on a footing below frost depth in cold-climate regions, or the bottom of the stair will heave each winter and the rise dimension will change. A 4-inch concrete pad on tamped gravel is the typical detail; in deep-frost regions, the pad rests on a frost-protected footing or extended deck post.

Geometry differences from interior stairs: deck stairs are usually shorter (3-7 risers vs 13-17 for interior) but the per-step rise and run rules are the same. A typical deck step calculation for a 30-inch high deck: 4 risers at 7.5" each + 3 treads at 11" each = 33" of horizontal run, easily fits in most yards. A 48-inch high deck: 6 risers at 8" each (slightly over IRC) or 7 risers at 6.86" each (more comfortable). Deck stairs calculator math: same formula, just smaller numbers.

Code applies to deck stairs the same as interior stairs: max 7-3/4" rise, min 10" tread, 3/8" max variation between any two risers or treads. A handrail is required if the stair has 4 or more risers (R311.7.8). Deck stairs over 30 inches above grade typically need guards as well (R312).

Stair calculator with landing — landings, mid-runs, and U-turns

A landing is a flat platform between two stair runs — used for U-turn stairs, L-shape stairs, or to break up a tall flight that would otherwise exceed the IRC R311.7.6 maximum vertical rise of 12 feet between landings. A stair calculator with landing functionality treats the two runs as independent stairs, with the landing absorbing the height and depth between them.

Each run independently must meet rise/run rules: max 7-3/4" rise, min 10" tread, consistent within 3/8" inside that run. The two runs do not need to have the same number of steps — a typical L-shape design might have 7 steps in the lower run, a 36" × 36" landing, and 8 steps in the upper run for a total of 15 risers between floors.

Landing dimensions: minimum 36" × 36" for a residential stair landing per IRC R311.7.6, larger if the door opens onto the landing (the landing must allow door swing without forcing a person backward down the stair). Landing height equals one riser dimension above the lower run's last tread, equivalent to one riser dimension below the upper run's first tread. The landing platform itself is framed like a small floor — for sizing the platform joists, use the floor joist calculator on this site with the landing dimensions as inputs.

Total run with landing: lower-run run + landing depth + upper-run run. For our 36" landing on a 15-riser stair (7 + 8 split): (6 × 10") + 36" + (7 × 10") = 60 + 36 + 70 = 166" of horizontal floor space, vs 140" for the same stair without a landing. The landing costs 26 inches of horizontal space but provides a comfortable rest point and a safer mid-stair geometry.

How to measure stairs and stair risers

Measuring an existing stair is necessary for replacement projects, refinishing work, and any modification that requires matching the existing geometry. How to measure stairs: measure each riser separately (top of one tread to top of the next), measure each tread separately (nose to nose), measure the total height (lower floor to upper floor), and measure the total run (back of bottom step to face of upper floor).

How to calculate stair risers from total height: total floor-to-floor height ÷ riser count = per-riser height. The riser count is determined by what produces a riser height under 7-3/4" — try total height ÷ 7.5 as a starting estimate, round up if needed. For a 109-inch total: 109 ÷ 7.5 = 14.5; try 15 risers; 109 ÷ 15 = 7.27 inches per riser. Always end up with a number ≤ 7-3/4 inches.

Measuring for a staircase before installation: measure the available horizontal floor space at the bottom of the stair (this is your total run constraint) and the floor-to-floor vertical height. The stair must fit both. If the run space is short, you may need a U-shape with a landing. If the run space is generous, a comfortable 7"/11" rise/run ratio is achievable.

A common measuring mistake is forgetting that the lower floor finish material adds to the bottom riser height. If you measure subfloor-to-subfloor and design the stair to that height, then install 1/2" of finished flooring at the top and 1" of tile at the bottom, your bottom riser is now 1/2" taller than every other riser. Always measure to the planned final finish heights, not subfloor heights.

Angle of stairs — degrees and slope

The angle of stairs in degrees is computed from rise per step and run per step using arctan: stair angle = arctan(rise / run) × 57.2958. For a 7" rise / 11" run stair: arctan(7/11) × 57.2958 = arctan(0.636) × 57.2958 = 32.5°. For a 7-3/4" rise / 10" run stair (steepest IRC-legal): arctan(0.775) × 57.2958 = 37.8°. For a comfortable 6" rise / 12" run stair: arctan(0.5) × 57.2958 = 26.6°.

Typical residential stairs fall in the 30-37° angle range. Below 30° the stair feels overly long and uses excessive floor space; above 37° it exceeds IRC limits and feels unsafe to descend. The angle of steps is the same whether the stair is interior, deck, or basement; only the materials and details differ.

Convert stair angle to slope percentage: slope% = tan(angle in degrees) × 100. A 33° stair = tan(33°) × 100 = 65% slope — much steeper than any roof or ramp. ADA-compliant ramps top out at 8.33% slope (1:12 rise:run, about 4.76°). The 30-37° range that defines a comfortable stair is far steeper than any other walkable surface — stair geometry is fundamentally different from roof or ramp geometry, even though the math is the same.

Stair runner calculator — sizing carpet runner for a stair

A stair runner is a strip of carpet running down the centre of a stair, leaving the outer edges of treads and risers exposed. A stair runner calculator sizes the runner length based on stair geometry: total runner length = (riser height + tread depth) × number of treads + 12 inches for waste and trim.

For our 15-riser stair (14 treads at 10" each, 7.27" rise per step): runner length = (7.27 + 10) × 14 + 12 = 17.27 × 14 + 12 = 241.8 + 12 = 254 inches = 21 ft 2 inches. Standard residential runner widths are 27" and 32"; the runner sits centred on the stair tread, leaving 4-5 inches of exposed wood on each side for a 36"-wide stair.

Order an extra 12-18 inches beyond the calculated length to allow for trimming at top and bottom and for matching pattern repeats. Runner installation is hardware-driven — typically tackless strips at every tread/riser intersection plus a stair rod at the riser nose. Budget 4-6 hours of installation time for a typical residential staircase.

How we sourced these numbers

The rise/run formula and stair geometry math are accepted construction conventions, not sourced to a single citation. Code limits (max 7-3/4" rise, min 10" tread, max 3/8" variation, max 12 ft between landings) come directly from the 2024 International Residential Code (IRC) Section R311.7. Stringer-depth requirements come from R311.7.5.4 (5-inch minimum throat). Handrail and guard requirements come from R311.7.8 and R312.

The "2 × rise + run = 24-25" empirical comfort formula is attributed to François Blondel's 17th-century stair treatise and remains the operational standard taught in carpentry programs today. Material specs (2x12 stringers, pressure-treated for outdoor) reflect standard residential framing practice as documented in the American Wood Council's Wood Frame Construction Manual and Fine Homebuilding's deck and stair construction guides. Cost ranges are not given on this page because lumber pricing varies regionally; the calculator focuses on geometry, which is universal.

For related framing work, this site has dedicated tools across the full house picture. The stud calculator handles wall framing including stairwell partitions. The floor joist calculator handles floor framing supporting stair landings. The LVL beam calculator covers engineered headers over stair openings. The cost to build a house calculator covers full-project budgeting. The siding calculator handles exterior cladding. For roof framing above stairs, the rafter length calculator covers the roof structure separately.