Stair Calculator

Rise, Run, and the Right Triangle Behind Every Staircase

Stairs and rafters are the same geometry wearing different clothes — that is why the roof pitch calculator and this stair calculator solve identical equations. In a roof, rise over run defines pitch and the rafter is the hypotenuse. In a stair, each step's stair rise and run define the pitch — the riser is the vertical rise per step, the tread is the horizontal run per step, and the stringer is the hypotenuse carrying both. The stringer's total length, √(rise² + run²), is exactly the rafter line length formula used to size roof members.

The consequence is practical: if you can lay out a rafter, you can lay out a stair. Clamp a straightedge across a 2x12, step off your riser and tread with a framing square and stair gauges, and you have traced the same triangle a rafter template uses. The angle where the stringer meets the floor equals the angle where a rafter meets the wall plate — both are atan(rise ÷ run). Run the same numbers through the rafter angle calculator and you will see the same degrees this page reports for your stair.

Any stair calc — whether a framing app, a spreadsheet, or the panel above — is just automating three steps: divide the total rise by a target riser and round, multiply the resulting tread count by the tread depth to get the run, and close the triangle for stringer length and angle. Everything else (comfort checks, landing rules, headroom) is a rule applied to those three numbers.

IRC Comfort Rules: 7-3/4 in Riser, 10 in Tread

The International Residential Code draws a box around stair geometry, and most US jurisdictions adopt it nearly verbatim. The headline limits: maximum riser height 7-3/4", minimum tread depth 10", headroom above the nosings at least 6'-8" (80"), and no riser in a flight may differ from another by more than 3/8". That last number is the one DIY builders miss — a flight of 7-1/2" risers with one 7-7/8" step at the bottom fails, and more importantly it trips people, because feet memorize a rhythm within two or three steps.

Comfort has its own formula, older than the code: the Blondel rule, 2R + T ≈ 24"–25". Two riser heights plus one tread depth should total about 25 inches — the stride a person naturally takes. A 7.5" riser and 10" tread give 2 × 7.5 + 10 = 25", which is why that pairing is the residential default. Shorter risers want deeper treads (7"/11" sums to 25") and tall risers want shorter treads. The calculator flags any combination outside 23.5"–25.5".

A worked example, end to end

Take a 105" floor-to-floor rise (8'-9", typical for a two-storey home with floor joists). Target a 7.5" riser: 105 ÷ 7.5 = 14 risers exactly, so the actual riser is 7.5" and every step matches. Treads = 14 − 1 = 13, and 13 × 10" = 130" of total run (10'-10"). The stair angle is atan(7.5 ÷ 10) = 36.87°. Blondel: 2 × 7.5 + 10 = 25, dead center. Stringer length = √(105² + 130²) = 167.1" = 13' 11-1/8", which fits 16' 2x12 stock. That is the full layout the dashboard above just reproduced from three inputs.

Remember the first-riser correction: the bottom riser gets trimmed by the tread thickness (5/4 decking ≈ 1", 2x6 ≈ 1.5") so the top of the first tread — not its bottom edge — starts exactly one riser height above the lower floor. Skip that trim and every step in the flight is off by the tread thickness.

Stair Angle: How Steep Is My Staircase?

The angle of stairs is arctangent of riser over tread — the same arctangent a speed square computes when you read a pitch. A 7.5" riser over a 10" tread is atan(0.75) = 36.87°. Angle matters because it converts abstract dimensions into a feeling: below 30° stairs sprawl and waste floor area; above 40° they start to climb like a ladder. The comfortable residential band is roughly 30° to 38°, and 45° — the diagonal — is universally considered too steep for a normal stair.

What angle should stairs be?

Aim for the mid-30s. A stair angle near 37° balances climb effort against floor space: the IRC's own limits (7-3/4" riser, 10" tread) produce 37.8° at the steepest code-compliant point, and the beloved 7"/11" public-stair pairing sits at 32.5°. If your computed angle lands above 40°, you are trading safety for floor area — the 8"/9" combination in the table is 41.6°, too steep for IRC stairs, and the usual fix is a landing with a 90° turn rather than taller risers. Space-saver and ship-ladder layouts do exist for lofts and mezzanines, but they are restricted edge cases: verify local code before committing a tight space to one.

Stringer Length, Depth, and Notching

The stringer is the sawtooth backbone of the stair, and its length is the hypotenuse: stringer length = √(rise² + run²). For the worked example — 105" rise, 130" run — that is 167.1", or 13' 11-1/8". Buy your boards with margin: a 2x12 (11.25" of actual depth) is the standard stringer stock because the notches for treads and risers remove roughly 3.5" to 4" of depth at each step. The commonly cited minimum is 3.5" of unnotched wood remaining above the treads — go below that and the stringer can crack along the notch line under load. A 2x10 (9.25" actual) leaves too little wood for a 7.5"/10" stair; that is the trap the "Don't" callout below warns about.

Length is not the only limit — span is. Sawn 2x12 stringers commonly serve up to about 14 risers before the middle of the board starts to flex under traffic; beyond that, a center support (a bearing wall, post, or kickplate under the stringer's midpoint) is prudent. A standard 36"-wide stair uses 3 stringers — one on each wall or edge and one in the center — with 5/4 decking treads pulling that spacing down to 16" on center maximum. Two stringers alone are only adequate for very short, narrow flights with thick treads.

Using it as a stair stringer calculator

The dashboard above doubles as a stair stringer calculator: it computes the hypotenuse from your rise and run, tells you whether the length fits 16' 2x12 stock (and by how much), and warns when a flight has outgrown a single board. Feed it a 105" rise and 10" treads and you get 13' 11-1/8" — about 2' to spare on a 16' board. Push the rise past roughly 160" with a 10" tread and the stringer crosses 16' — at that point you either hunt scarce longer stock or, far more sensibly, split the flight with a landing. Cut one pattern stringer, test-fit it, and trace the remaining ones from it.

Stair Landings: When You Need One

A stair landing is a flat platform inserted mid-flight, and the code trigger is vertical rise. IBC 1011.8 caps a single flight's vertical rise at 12 feet — about 19 risers at 7.5" — so in IBC jurisdictions, any flight climbing more than 12' must break at an intermediate landing. That is a hard cap, not a suggestion. Below the cap, practice takes over: many local residential amendments and decades of framing habit put landings around 14–16 risers, because a flight that long feels exposed, concentrates the climb, and starts to make long stringers awkward. The calculator mirrors both triggers — "required" past 12' of rise, "recommended" at 16+ risers — and defers to local code.

Size the landing like a tread: its depth must be at least the tread depth, and most residential layouts keep landings ≥ 36" in both directions so two people can pass and a door (if any) can swing clear. In the riser math, a landing behaves as a zero-rise step — the riser count includes the transition, and each flight restarts the same riser height after it. Landings also unlock L-shaped and U-shaped plans that fit a stair into a shorter wall.

Winders — angled treads that turn a corner without a platform — have their own dimensional rules (tread depth measured at the walk line, minimum widths at the narrow end), and some jurisdictions restrict them in required egress paths. If your layout wants winders, verify local code before framing; a square landing is almost always simpler to build and to pass inspection.

Metric Stairs: UK and Australian Rules

Switch the calculator to Metric and the same triangle solves in millimetres under different comfort windows. UK Building Regulations Part K (private stairs in a dwelling) allows a rise of 150–220 mm and a going of 220–300 mm, with a maximum pitch of 42°. Australia's NCC (private stairs, Riser/Going rule) allows 115–190 mm rise and 240–355 mm going. Both countries express the Blondel rule as 2R + G between 550 and 700 mm — the millimetre twin of the American 24"–25" target.

Worked metric example: a 2667 mm floor-to-floor rise ÷ 15 = 177.8 mm risers, comfortably inside both the UK (150–220) and Australian (115–190) windows. The 14 goings × 250 mm = 3500 mm of run, and 2R + G = 2 × 177.8 + 250 = 605.6 mm, mid-range of 550–700. Note the pitch check: atan(177.8 ÷ 250) = 35.4°, well under the UK's 42° ceiling. The calculator's Metric mode performs this exact chain — riser count, actual riser, run, stringer length, angle, and the 550–700 mm Blondel check — from three inputs. As always, verify local code; national summaries are not a substitute for the current edition.

Deck Stairs and Handrail Basics

Deck stairs run the same stair calc as interior flights, with three deck-specific twists. First, tread stock: 5/4 decking (a true 1" board) needs stringers at 16" o.c. or closer so the thin treads do not spring — which on a 36" wide stair means three stringers placed roughly 16" apart on center, with the outer pair flush to the edges. Second, the stringers sit exposed to weather, so they are pressure-treated 2x12, and the bottom ends are cut to bear on a footing or buried pad rather than a floor. Third, the total rise is measured from the deck surface to the grade below — not to the top of the footing — and the first riser is trimmed by the tread thickness exactly as indoors.

Handrails follow the stair up: 34"–38" above the tread nosings, graspable (a 1-1/4" to 2" circular profile is the reference), and generally required at 4 or more risers — verify locally, since some jurisdictions exempt very low deck stairs and others do not. Guards are the taller fall-blocking assemblies, required where a walking surface — including a landing — sits more than 30" above grade, with baluster spacing that rejects a 4" sphere. On the stair itself, keep the riser openings ≤ 4" as well: a child's head or foot should not pass through the triangle between two treads.

For everything above the stairs — the deck framing the flight serves — the Rafter Calculator sizes roof members the same right-triangle way, and the free rafter calculators hub lists spacing and span tools for the whole build.