Stair calculator
A flight of 112 inches divided by a 7 inch target gives exactly 16 risers at 7 inches. If the rise were 114 inches you would still use 16 risers, at 7.125 each, not fifteen at seven and one odd one at nine. People climb stairs by feel, not by looking, and a single riser that differs by more than about 5 mm is the classic trip hazard that building regulations exist to prevent.
Divide the total floor-to-floor rise by a comfortable riser height, round to a whole number of steps, then divide the rise back by that count to get the riser you will actually cut. A 112 inch rise against a 7 inch target lands on 16 risers of exactly 7 inches, 15 treads, a 150 inch run and a pitch of 35 degrees — one riser over one going, which is the pitch line a building code measures.
How to set out a staircase
The riser count has to be a whole number and every riser has to be identical, which together are the whole reason this is a calculation rather than a measurement. Your target riser is a preference; the rise between two floors is a fact. Dividing 2,700 mm by a 180 mm target gives 15 exactly, so the target survives. Give it 2,745 mm instead and 15.25 rounds to 15 risers of 183 mm, and all fifteen are 183. People climb stairs by pattern rather than by looking, and a single step out of step with its neighbours is the classic trip, which is why codes police the variation rather than the ideal.
The going and the rise trade against each other, and the rule that ties them is old. François Blondel set it out in the 1670s: twice the rise plus the going should equal a natural pace, which he put at roughly 630 to 650 mm. English building regulations use a wider band of 550 to 700 mm for 2R + G, and American carpentry practice narrows it to 24 to 25 inches. Both defaults on this page land at 610 mm, or 24 inches, which is inside the English band and at the bottom edge of the American one. Comfortable, slightly brisk, and a reminder that these are overlapping bands rather than one right answer.
The outer limits are set by regulation and they differ by country and by what the stair serves. In England and Wales a private stair inside a dwelling may rise at most 220 mm per step, must have a going of at least 220 mm, and must not pitch steeper than 42 degrees; a utility stair, meaning one that is not the everyday route between levels, is held to 190 mm and 250 mm instead. The American model codes go the other way, allowing a taller riser but demanding a deeper tread: 7¾ inches maximum rise against a 10 inch minimum tread. A flight legal in one country can be illegal in the other while sitting on the same stringer.
Two of the outputs need reading carefully. Total run is the going multiplied by the number of treads, so it measures the horizontal ground the flight consumes and deliberately ignores nosings, which overlap the step below and add nothing to the run. Stringer length is the straight hypotenuse of that rise and run: the sloping line, not a cutting list. Add material at both ends for the plumb cut at the top, the seat cut at the bottom and however the flight lands on the floor, and mark the cuts off the actual riser and going rather than off a length in millimetres.
What people use it for
- Setting out a loft conversion or a basement stair
- Building deck steps or garden steps down a slope
- Cutting a stringer from a single board without wasting it
- Checking an existing flight against current regulations before selling
- Working out whether a rise can be done in one flight or needs a landing
- Converting a stair design between inches and millimetres
- Deciding how much floor space a new flight will swallow
- Sanity-checking a joiner’s drawing against the height you measured
Questions
Around 7 inches, or 175 to 180 mm. Below 6 inches the flight feels shuffling and takes far more floor; above 8 it becomes tiring and starts reading as a ladder.
Twice the rise plus the going, checked against a band that matches a natural pace. England allows 550 to 700 mm, American practice narrows it to 24 to 25 inches, and Blondel’s original was 630 to 650 mm.
Because a 7 inch riser with a 10 inch tread comes to exactly 24, which is inside every band but at the brisk end. Widen the tread to 11 inches and it lands on 25.
In England and Wales a private stair is capped at 42 degrees. The American codes set no pitch limit directly, but the 7¾ inch riser and 10 inch tread limits put the steepest legal flight at about 38 degrees.
The top riser arrives at the upper floor, and that floor is the last tread. Sixteen risers means fifteen treads to cut.
The two codes answer differently. England requires every rise in a flight to be the same. The American model codes permit the largest riser to exceed the smallest by 3/8 of an inch, about 9.5 mm, and no more.
The hypotenuse of the total rise and total run, shown above. A 112 inch rise over a 150 inch run gives 187.2 inches, and you buy longer than that to leave material for the cuts at both ends.
Not for this calculation. A nosing overhangs the step below rather than extending the flight, so it adds tread depth underfoot without adding to the total run.
Two metres measured vertically from the pitch line in England and Wales, and 6 feet 8 inches under the American codes. On a loft conversion this is usually what fails first, well before the rise and going do.
The total run, plus landing space at both ends. A 2,600 mm rise at a 180 mm target gives 14 risers and 13 treads, so at a 250 mm going the flight alone eats 3.25 m of floor. That number decides where a stair can go long before comfort does.
It never does. Round the step count and let the riser height fall where it falls; the tool divides the rise back by the whole count for exactly that reason.
Yes, with a limit. Where children under five may use the stair, the gap must not let a 100 mm sphere pass, which in practice means each tread overlapping the one below by at least 16 mm.
This works out straight flights only. A winder changes the going across the tread, and it is measured on a walking line set in from the inside edge, which is a different calculation entirely.
Yes, and it is the easier case, since a deck rise is usually short enough to absorb a slightly generous riser. Measure from the finished ground surface rather than from soil that will settle.