Stair Calculator

About this tool

A staircase comes down to two numbers that are easy to get wrong: how tall each step is, and how deep each step is. Both grow out of a single measurement — the total rise from one floor surface to the next — and one design choice, how tall a step you are willing to climb.

The height of a step is not the number you type into the tallest-riser box. That box sets a ceiling. The real step height is the total rise divided by the number of steps, and the number of steps is that ceiling rounded up to a whole step, because four tenths of a step cannot be built. A 2,743 mm rise with a 190 mm ceiling works out at 14.4 steps, so it becomes 15 steps of 182.9 mm each.

Treads come one fewer than risers. The top of the flight ends on the upper floor, and that floor is the finish rather than a step you build, so fifteen risers carry fourteen treads. The total run is those fourteen treads deep, and the stringer is the sloping beam that spans the rise and the run together. All of the numbers fall out of the same two inputs, which is why they belong on one screen.

Why the real step height is not the number you type in

The box asks for a ceiling, not a height. The tool divides the total rise by that ceiling, rounds up to a whole number of steps, then divides the rise by that count — so a 2,743 mm rise with a 190 mm ceiling becomes 15 steps of 182.9 mm.

Stairs are built from whole steps. If the rise divides by your ceiling and leaves a remainder, that remainder cannot become a fractional step at the top; it is spread evenly across every riser instead. The only way to spread it evenly is to decide the step count first and then divide, which is exactly the order this tool works in.

The difference is small enough to be dangerous. Someone who reads 190 mm off the box and starts cutting gets a stair that is 190 mm at every step by design, which over fifteen steps is 39 mm too tall — and the error only shows up when the last step does not meet the floor. Measuring each riser up from the one below compounds it further.

One detail sits underneath the rounding. When the rise divides exactly, the arithmetic in binary floating point can land a hair above the whole number — 2,660 divided by 190 can come out slightly over 14 rather than exactly 14. A tiny tolerance is subtracted before rounding up, so an exact 14 stays 14 instead of becoming 15 steps for no reason.

Why there is always one fewer tread than riser

The top step ends on the upper floor, and that floor is the finish rather than part of the stair, so fifteen risers carry fourteen treads. The total run is the tread depth multiplied by fourteen.

Think about walking up. Your first step leaves the lower floor, which is its own surface, and your last step arrives on the upper floor, which is another. Every riser in between needs a tread in front of it, but the final riser does not, because the upper floor already is the landing.

That single missing tread is what makes the flight fit or not. Fourteen treads at 254 mm is a run of 3,556 mm, close to three and a half metres of floor given up to the stair. Budget the run by counting risers instead of treads and the whole staircase overshoots the opening it was meant to sit in.

The same count settles the stringer. Its length is the diagonal of the rise against the run, so a run that is one tread too long drags the stringer longer with it, and the beam no longer reaches the floor where you intended to land it.

What the usual step limits are, and why they are guidance

A riser of up to about 200 mm and a tread of at least about 250 mm is the common domestic range, with two risers plus one tread landing between roughly 610 and 640 mm. The exact figures vary by country, so treat them as a sanity check rather than a ruling.

The comfort rule behind all of them is old and simple: two risers plus one tread should come close to a natural stride. Around 610 to 640 mm covers a wide span of riser and tread pairs — shallow treads with tall risers make you climb, deep treads with short risers make you shuffle — and the middle of that band is where most domestic stairs are built.

The two other guards are separate and answer different questions. How tall a riser may be is about effort: past about 200 mm each step stops feeling like a step and starts feeling like a climb. How shallow a tread may be is about safety: a foot needs somewhere to land, and below about 250 mm the ball of the foot hangs over the edge on the way down.

None of these numbers is universal. Building codes set their own limits and they differ from country to country and between dwellings and public buildings, so the tool shows where your figures sit against the common range and leaves the ruling to the code that applies to you.

Everything becomes integer millimetres, so riser times steps can be asserted

Input may be feet and inches, centimetres or millimetres, but inside the model it is always integer millimetres. That turns riser height times step count equals total rise into an equation a test can check, rather than an approximate-looking number.

Feet and inches are the only input that arrives with fractions built in (7 ft 8.5 in), and centimetres behave the same way. Mixing those while dividing invites the 0.1 plus 0.2 class of drift, and here such drift turns directly into one step too many or too few.

Rounding the step count up subtracts a 1e-9 tolerance first, as insurance rather than as a patch: if a rise happens to divide evenly, floating point can return 14.000000000000002 and the ceiling turns it into 15, inventing a step. Sweeping rises from 2000 to 3200 mm against risers from 150 to 200 mm found no case that actually triggers it — but the cost is one subtraction, not worth gambling on.

Output stays in the unit you chose, with an internal millimetre figure alongside: schedules and cutting lists are quoted in millimetres, while occupants think in feet and inches, and both readings earn their place.

One tread fewer than risers follows from the same identity: the last step lands on the upper floor, not on a separate board. Fifteen risers therefore correspond to fourteen treads, and the tests check both sides.