Stair Calculator — Risers, Treads, Run & Stringer Length
Measure your floor-to-floor height once and this planner splits it into equal risers, sizes the treads with Blondel’s comfort rule, and works out the total run, stringer length and angle of your staircase.
Your floor-to-floor height
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Your staircase
Your staircase in profile
The flight drawn to scale — the dashed line is the stringer, cut along the angle shown in your results.
- One measurement drives everything: the floor-to-floor rise — 280 cm at the defaults — is split into 16 exactly equal risers of 17.50 cm; your target riser is only ever a starting point.
- Blondel’s rule sizes the treads from the actual riser: 2 × riser + going aims at the classic 63 cm comfort stride, with the going held between 25 and 32 cm.
- You also get the total run (420 cm at the defaults), the stringer length and the stair angle — plus a headroom check against the 203.2 cm (80 in) IRC minimum when you enter the opening and floor thickness.
Keep exploring
Three companion tools for the same project.
How it works
Three steps from one measurement to a buildable flight.
Measure the total rise
Finished floor to finished floor, straight up. This one number is fixed — everything else divides out of it.
Set a target riser
The total rise is divided by your target and rounded to a whole number of risers, so every step ends up exactly the same height.
Read the flight
Blondel’s rule sizes each tread from the actual riser, and the run, angle and stringer length follow from the triangle they form.
The math behind the stairs
A staircase works because every riser is exactly equal — your legs notice a 5 mm difference. So the planner never uses your target riser directly: it divides the total rise by the target, rounds to a whole number of risers, then divides again so the risers share the height perfectly. Tread depth comes from Blondel’s rule, the 17th-century observation that a comfortable stride on stairs satisfies 2 × riser + going ≈ 63 cm. The stringer is then just the hypotenuse of the rise–run triangle.
Worked examples:
| Staircase | Working | Result |
|---|---|---|
| Total rise 280 cm, target riser 17.5 cm | 280 ÷ 17.5 = 16 risers exactly · going = 63 − 35 = 28.0 · run = 15 × 28 | 16 risers of 17.50 cm · run 420 cm · stringer 504.8 cm · angle 33.7° |
| Total rise 260 cm, target riser 17.5 cm | 260 ÷ 17.5 = 14.86 → 15 risers · actual 17.33 · going = 63 − 34.67 = 28.33 · run = 14 × 28.33 | 15 risers of 17.33 cm · run 396.7 cm · stringer 474.3 cm · angle 33.2° |
Why is there one fewer tread than risers? The top riser lands you on the upper floor itself — the last “tread” is the floor you were climbing to, so a flight of 16 risers needs only 15 treads of its own.
Go deeper
Why 63 cm, and what the building codes add on top.
François Blondel noticed in the 1670s that climbing a stair shortens your stride in a predictable way:
- The trade-off: every centimetre a step rises costs you two centimetres of forward stride — hence going = 63 − 2 × riser.
- The comfort band: totals between about 62 and 65 cm feel natural; this calculator aims at exactly 63 and keeps the going between 25 and 32 cm, flagging it if your riser forces the going outside that range.
- Too steep: a riser of 20 cm leaves a going of just 23 cm — your foot overhangs and the stair feels like a ladder.
- Too shallow: a riser of 14 cm stretches the going to 35 cm — you start taking a step-and-a-half per tread, which is its own trip hazard.
Geometry gets you a staircase that fits; regulations decide whether you may build it:
- Typical limits: many codes cap riser height around 19–20 cm and set a minimum going near 25 cm for homes — the comfort range used here sits inside those limits, but your local code rules.
- Headroom: you also need roughly 2 m of clear height above the pitch line everywhere along the flight — a stairwell opening that is too short fails even a perfectly proportioned stair.
- Uniformity: codes limit how much risers may vary within a flight (often just a few millimetres) — another reason this planner divides the rise into perfectly equal risers.
- Landings and winders: long flights may need a landing, and winders or spirals follow extra rules. Treat this page as the planning maths; have the final design checked locally.
Building code: the riser, tread, and handrail rules that govern
Stair dimensions are regulated because bad stairs injure people. In the United States, the International Residential Code — adopted with local amendments in most jurisdictions — limits riser height to a maximum of 7¾ inches (197 mm) and requires a minimum tread depth of 10 inches (254 mm) for residential stairs, with no more than ⅜ inch (9.5 mm) of variation between the tallest and shortest riser, or between the deepest and shallowest tread, in any flight. Handrails are required on at least one side for stairs with four or more risers, at a height of 34 to 38 inches above the tread nosings, and guardrails are required on open sides where the drop exceeds 30 inches.
These are the code maxima and minima, not design targets: a stair built exactly at the 7¾-inch riser maximum with 10-inch treads is legal but steep, and most comfortable residential stairs use risers of 7 to 7½ inches with treads of 10½ to 11 inches. Local amendments vary — some jurisdictions require 11-inch treads, and commercial codes (the International Building Code) differ again — so the code figures here are the widely adopted baseline, and the local building department’s requirements govern any actual construction. The calculator checks your dimensions against these baseline rules and flags violations; it does not approve a design.
Stringers: how the cut is laid out, and how many you need
The stringer is the diagonal board that carries the treads and risers, and laying it out is the skilled part of stair building. The layout marks each step on the stringer with a framing square set to the riser height on one leg and the tread depth (the going) on the other, stepping the square along the board. The top and bottom of the stringer are adjusted: the bottom riser is shortened by the tread thickness (because the first tread sits on top of the stringer’s bottom step), and the top is cut to meet the upper floor or landing level. Getting either adjustment wrong makes the first or last step a different height from the rest — the exact trip hazard the code’s ⅜-inch variation limit exists to prevent.
Stringer count depends on width and material. A stair up to about 36 inches wide can often be carried on two stringers, but wider stairs, stairs carrying heavy loads, or stairs with treads of thinner material need a third, centre stringer to prevent flex and bounce. Cut stringers (sawtooth profile) are the common do-it-yourself form; closed stringers, where the treads sit in routed housings, are stronger and neater but need a router and jigs. Whichever form you build, the stringer material should be straight, knot-free lumber of the specified size — a knot at the narrowest point of a cut stringer is a future failure.
Frequently asked questions
Quick answers about planning a staircase.
How many risers do I need for a 280 cm floor-to-floor rise?
Divide the rise by a comfortable riser height: 280 ÷ 17.5 = exactly 16 risers. When the division is not exact — say 260 ÷ 17.5 = 14.86 — round to the nearest whole number (15) and let each riser take an equal share of the height (260 ÷ 15 = 17.33 cm), so no step in the flight is taller than another.
What is a comfortable riser height and tread depth?
For most homes, a riser of 17–18 cm with a tread depth (going) of 27–29 cm feels natural. The two are linked by Blondel’s rule — 2 × riser + going ≈ 63 cm — so a 17.5 cm riser pairs with a 28 cm going, and raising the riser always means shortening the tread.
Why does a staircase have fewer treads than risers?
Because the final riser steps up onto the upper floor itself. A flight with 16 risers climbs 16 times but needs only 15 treads of its own — the sixteenth landing surface is the floor you were heading to. That is why total run is (risers − 1) × going, not risers × going.
How do I work out the stringer length?
The stringer is the hypotenuse of the staircase triangle: √(total rise² + total run²). For a 280 cm rise over a 420 cm run that is √(78,400 + 176,400) = 504.8 cm. Order a little extra — the true cut length depends on how the stringer is notched and how it meets the floors at each end.
What is the ideal angle for a staircase?
Most comfortable domestic stairs sit between 30° and 37°. The angle is atan(rise ÷ run): the default flight here (280 up, 420 along) lands at 33.7°, right in the band. Beyond about 42° a stair starts to feel like a ladder; below 27° it eats floor space and feels like a ramp with bumps.
What is Blondel’s rule?
A rule from the 1670s, still used today: on a comfortable stair, 2 × riser height + tread depth (the “going”) should total about 63 cm — one natural stride. This calculator uses it to size the going from your actual riser, then keeps the going within 25–32 cm and tells you if it had to be held at either limit.
How much headroom does a staircase need?
US residential code (IRC R311.7.2) requires at least 6 ft 8 in (203.2 cm) of headroom, measured vertically from the sloped line through the tread nosings up to the ceiling or the underside of the floor above. Enter your stairwell opening length and floor thickness in the calculator and it works out the headroom at the edge of the opening, where the clearance is tightest.
How many steps do I need for a given total rise?
Divide the total rise by a comfortable riser height (7 to 7.5 inches) and round to the nearest whole number of risers, then divide the total rise by that count for the exact riser height. Example: 105 inches ÷ 7 = 15 risers of exactly 7 inches. The number of treads is one fewer than the number of risers, because the top step is the upper floor.
What is the 7/11 rule for stairs?
A rule of thumb that a comfortable stair has about a 7-inch riser and an 11-inch tread (the going). It satisfies the common comfort formula — two risers plus one tread totalling 24 to 26 inches (2×7 + 11 = 25) — and sits inside the usual code limits. It is a design guide, not a code requirement.
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Disclaimer
This calculator is for planning and estimation. Staircases are safety-critical and regulated: riser limits, minimum goings, headroom, handrails and landing rules vary by jurisdiction. Have any final design checked against your local building code before cutting timber.