Stair Calculator
Calculate stair rise, run, angle, and number of steps for any staircase height.
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About
Stair Calculator
Building a staircase looks like a simple job and turns out to involve a surprising number of measurements, calculations and code requirements. This page works out every parameter from the figures you already have, and the diagram beside the calculator labels each one so the terms below line up with something visible.
The basic version takes a total rise and either one run or a total run, then lays out every option from 13 to 26 steps so you can pick the one that fits the space. The comprehensive version pins down a single staircase, adding tread thickness, headroom and the choice between a standard and a flush stringer mount.
Stair terminology
Run and tread
The run, or tread, is the part of the stairway a person steps on. Its length is measured from the outer edge of the step, which includes the nosing where one is present, back to the vertical part of the stair called the riser.
Two details catch people out when measuring a total run. The tread above the last riser is not included, and where nosing is present the total run is not simply the sum of the tread lengths, because the overhang has to be subtracted.
Rise and riser
The rise, the height of a step, is measured from the top of one tread to the top of the next. It is not the physical height of the riser board, because that excludes the thickness of the tread sitting on it.
It is the number of risers, not the number of treads, that determines how many steps make up a staircase, and those two numbers are never the same. A flight with 17 treads has 18 risers, because the last riser lands on the floor above rather than on another tread. That is why the calculator reports both, and why the stringer height comes out one riser short of the total rise on a standard mount.
Nosing
The nosing is the protrusion at the edge of a tread that overhangs the riser below. Not every step has one, but where present it counts towards the tread length. Its purpose is safety: it gives the foot extra landing area without lengthening the staircase.
Headroom
Headroom is measured from the top of a tread to the ceiling above it. The codes are set well above average human height, because the space also has to allow furniture and appliances to be carried up.
Stair width
Stair width is measured edge to edge across the tread, perpendicular to the tread length. Conventionally a rectangle's length exceeds its width, but with a step the width is usually the longer dimension. It does not include the handrail.
Handrails and guards
A handrail is the rail running up the incline for users to hold. A guard is a building component, or a system of components, at the open side of an elevated walking surface that reduces the chance of a fall to the level below. Guards can be rails, but they can equally be a wall, a half-wall or even a bench.
Stringer
The stringer is the structural member carrying the treads and risers. There are usually three: one each side and one down the middle. Stringers are not always visible, but they show on stairs with open sides. They can be cut to the shape of each step, or left uncut so they conceal the tread edges.
Common building code figures
Codes differ locally and anyone building a staircase should work to the ones in force where they are. These are the figures most often quoted.
| Measurement | Common requirement | Metric |
|---|---|---|
| Tread depth | at least 10 inches | 25.4 cm |
| Riser height | no more than 7.75 inches | 19.7 cm |
| Nosing | between 0.75 and 1.25 inches | 1.9 to 3.2 cm |
| Headroom | at least 6 feet 8 inches | 203.2 cm |
| Stair width | at least 36 inches | 91.44 cm |
| Guard height | at least 34 inches | 86.36 cm |
| Handrail height | between 34 and 38 inches | 86.36 to 96.52 cm |
| Handrail diameter | between 1.25 and 2.675 inches | 3.18 to 6.79 cm |
Guards are generally required where the total rise is more than 30 inches above the floor, and their height is measured from the top of the treads.
One distinction worth knowing: residential and commercial codes are not the same. Dwelling stairs in the United States are typically allowed a 7.75 inch riser with a 10 inch tread, while commercial stairs are usually held to a 7 inch riser and an 11 inch tread. A staircase that passes at home can fail in a shop.
There is also a tolerance rule that catches more retrofits than any maximum does. The largest riser in a flight may exceed the smallest by no more than 3/8 of an inch, about 9.5 mm, and the same applies to tread depth. Uneven risers are a trip hazard precisely because people stop looking at stairs after the first two steps.
Rules of thumb for a comfortable staircase
Codes set the outer limits; they do not describe a stair that feels right. Three relationships have been used by builders for centuries, all describing the same trade-off between rise and run:
- Two risers plus one tread should come to between 24 and 25 inches
- One riser plus one tread should come to between 17 and 18 inches
- Riser times tread should come to between 71 and 74 square inches
They are worth checking against whatever the calculator returns. The default example here, a 20 cm rise with a 25 cm run, gives 7.87 and 9.84 inches, so two risers plus a tread is 25.59 inches. That is marginally steeper than the comfortable band, which is exactly the sort of thing worth knowing before the timber is cut rather than after.
The reason these formulas work is that a person's stride shortens as they climb. A tall riser with a deep tread forces an awkward stretch; a shallow riser with a shallow tread makes people shuffle. The band between them is narrow.
Standard and flush stringer mounts
How the stringer meets the upper floor changes the numbers, which is why the detailed calculator asks.
With a standard mount the stringer sits against the face of the upper floor framing, and the top tread is one riser below the finished floor. The stringer therefore spans the total rise less one riser, which is why the stringer height here comes out at 330 cm for a 350 cm total rise with a 20 cm rise.
With a flush mount the stringer is hung from the header so its top finishes level with the upper floor, and it carries the full total rise. Same staircase, different cut, different stringer length.
The first step is rarely the same as the others
Total rise almost never divides evenly by a chosen riser height, and the remainder has to go somewhere. This calculator puts it in the first step, which is why a 350 cm rise with a 20 cm riser reports 17 steps of 20 cm and a first step of 10 cm.
In practice a builder has two options: absorb the remainder at the bottom as shown here, or adjust the riser height slightly so every step is identical. The second is usually preferable, because of the 3/8 inch tolerance rule above, and it is what the fixed-number-of-steps mode does.
Tread thickness feeds into the same problem. Where treads sit on top of the stringer, the bottom of the stringer is cut down by the tread thickness so the finished first step matches the rest. Miss that cut and every step in the flight is right except the first, which is the one people trip on.
Fraction to decimal conversion
Tape measures are marked in sixteenths and calculators work in decimals. This table covers the conversions needed for stair work.
| 16th | 8th | 4th | 2nd | Decimal |
|---|---|---|---|---|
| 1/16 | 0.0625 | |||
| 2/16 | 1/8 | 0.125 | ||
| 3/16 | 0.1875 | |||
| 4/16 | 2/8 | 1/4 | 0.25 | |
| 5/16 | 0.3125 | |||
| 6/16 | 3/8 | 0.375 | ||
| 7/16 | 0.4375 | |||
| 8/16 | 4/8 | 2/4 | 1/2 | 0.5 |
| 9/16 | 0.5625 | |||
| 10/16 | 5/8 | 0.625 | ||
| 11/16 | 0.6875 | |||
| 12/16 | 6/8 | 3/4 | 0.75 | |
| 13/16 | 0.8125 | |||
| 14/16 | 7/8 | 0.875 | ||
| 15/16 | 0.9375 | |||
| 16/16 | 8/8 | 4/4 | 2/2 | 1 |
Common mistakes
The first is counting treads instead of risers. A flight has one more riser than it has treads, and using the wrong count puts the rise per step out by several millimetres on every single step.
The second is forgetting the finished floor. Total rise is measured between finished floor levels, so tile, carpet or underlay at either end changes it. Measuring to a bare subfloor and then laying 20 mm of flooring at the top makes the top step short by 20 mm.
The third is treating the total run as the sum of the treads when there is nosing. The overhang repeats on every step, so the error grows with the flight.
The fourth is designing to the code maximum. A 7.75 inch riser paired with a 10 inch tread is legal in a house and steep to use; dropping the riser an inch usually costs less floor space than people expect.
Common questions
Frequently asked questions
Divide the total rise by a target riser height and round to a whole number of risers, then divide the total rise by that count to get the exact rise per step. Remember there is always one more riser than there are treads, since the last riser lands on the upper floor.
Total rise is the whole vertical distance between finished floor levels. Rise is the height of one step, measured from the top of one tread to the top of the next. Total rise divided by the number of risers gives the rise.
On a standard mount the stringer sits against the upper floor framing and its top tread is one riser below the finished floor, so it spans the total rise less one rise. A flush mount hangs from the header instead and carries the full total rise.
It is the pitch of a single step: the arctangent of the rise divided by the run. For a 20 cm rise on a 25 cm run that gives 38.66 degrees. A comfortable domestic staircase usually lands between about 30 and 37 degrees.
The commonly quoted figures are a maximum riser of 7.75 inches, a minimum tread of 10 inches, headroom of at least 6 feet 8 inches and a width of at least 36 inches. Commercial stairs are usually held tighter, to a 7 inch riser and an 11 inch tread. Local codes govern.
A comfort check: twice the riser height plus the tread depth should come to between 24 and 25 inches. Related versions are riser plus tread between 17 and 18 inches, and riser times tread between 71 and 74 square inches.
Because the total rise rarely divides evenly by the chosen riser height, and this calculator puts the remainder in the first step. A 350 cm rise with a 20 cm riser gives 17 steps of 20 cm and a first step of 10 cm. Adjusting the riser slightly so every step matches is usually the better build.
Effectively yes. Codes allow the largest riser in a flight to exceed the smallest by no more than 3/8 of an inch, about 9.5 mm. People stop looking at stairs after a step or two, so an odd riser is a genuine trip hazard.
Where treads sit on the stringer, the bottom of the stringer is cut down by the tread thickness so the finished first step matches the others. Skip that and every step is correct except the first one.
Nosing is the tread overhang past the riser below, usually between 0.75 and 1.25 inches, and it gives the foot extra room without lengthening the staircase. It counts in the tread length but must be subtracted when totalling the run, since the overhang repeats on every step.