Stair Calculator

What the stair calculator does

A flight of stairs is a piece of geometry that has to come out even, the steps all the same and the run fitting the space. This works it out. You give it the total height to climb, and the run, and it returns the number of steps, the riser height, the tread run, the stringer length, and the angle.

It gives you the numbers to set out a stair, with a recommended step and a couple of alternatives to choose from. Below is how it works and how to land on a stair that is both comfortable and to code.

How to use it

1. Choose the run type, entering either a single tread run or the total run of the whole flight.
2. Enter the total rise, the full floor-to-floor height, with its unit.
3. Enter the run to suit, then press Calculate, or Reset to clear it.

How the steps are worked out

The heart of it is dividing the total height into equal steps. The calculator works out how many steps the climb needs, then splits the height evenly between them:

Riser height = total rise ÷ number of steps

From the step count and the run it then works out the rest: the tread run, the length of the stringer that carries the steps, and the angle of the flight. It recommends the step count whose riser lands closest to a comfortable 7 inches, shows a slightly taller and a slightly shorter option alongside it, and checks each one against the code limits.

Rise, run, and the comfortable step

Two measurements define a stair. The rise is the height of each step, the vertical part your foot lifts over, and the run, or tread, is the depth of each step, the flat part your foot lands on. Every step in a flight has to be the same, because the body learns the rhythm from the first step and a single odd one is how people trip.

What makes a stair comfortable is the relationship between the two. A widely used guide pairs a 7 inch rise with an 11 inch run, which climbs easily without feeling like a ladder or a shuffle. A handy cross-check is that one rise plus one run should land between about 17 and 18 inches. Steeper than that and the stair is hard work; shallower and people break stride. The aim is a riser around 7 inches, and the calculator recommends the step count that lands closest to it, with a taller and a shorter option shown alongside for flexibility.

The stringer and the angle

The stringer is the diagonal board that carries the steps, notched to take each tread and riser, and its length is the long side of a right triangle. The two short sides are the total rise and the total run, so the stringer is found the same way you find the hypotenuse, from the square root of the two squared and added. That tells you how long a board to buy before you start cutting.

The angle falls out of the same triangle, and it tells you at a glance how steep the flight is. A comfortable stair sits around 30 to 37 degrees; much steeper starts to feel like a ladder. So the stringer length is what you order, and the angle is the sanity check on whether the flight will feel right to climb.

A worked example: a 9 ft rise

Say the floor-to-floor height is 9 feet, which is 108 inches.

Aiming for a riser near 7 inches, that is about 108 ÷ 7 = 15.4, so 15 steps, giving a riser of 108 ÷ 15 = 7.2 inches. With 14 treads at around 11 inches, the run comes to about 12.8 feet, and the stringer, the diagonal across that rise and run, works out to roughly 16 feet, at an angle near 35 degrees.

So a 9 foot climb wants about 15 steps, and you would order 16 foot stringer boards to cut them from.

Getting it right and to code

Stairs are friendly to plan but unforgiving to get wrong, and they are one of the most closely regulated parts of a building for good reason, since a badly proportioned flight is a real fall risk. The residential code sets firm limits: a riser no taller than about 7 and three-quarter inches, a tread no shallower than 10 inches, and, the one most often missed, every riser within three-eighths of an inch of the others across the whole flight.

So use this to plan the flight: it recommends a comfortable step near a 7 inch riser, shows a couple of nearby alternatives, and flags each against the code limits so you can see at a glance which ones pass. Then measure your total rise carefully from finished floor to finished floor, since an error there spreads across every step, and confirm the riser, tread, headroom, and handrail against your local building code before you cut, or have the design checked by a building professional. That is the sound way to go about it, not a hoop to jump through.

Questions people ask

How do I calculate stairs?

Divide the total rise by the number of steps for the riser height, then work out the tread run, stringer length, and angle. A 108 inch rise over 15 steps gives a 7.2 inch riser.

What is a comfortable stair?

A riser around 7 inches with an 11 inch tread, where one rise plus one run is about 17 to 18 inches, climbing at roughly 30 to 37 degrees.

How do I find the stringer length?

It is the diagonal across the total rise and total run, found like the long side of a right triangle, from the square root of the two squared and added.

What are the code limits for stairs?

The residential code caps the riser at about 7 and three-quarter inches and sets a 10 inch minimum tread, with every riser within three-eighths of an inch of the rest. Confirm against your local code.

References

A quick note on the numbers. The step geometry is arithmetic and the stringer is the Pythagorean theorem, the diagonal of the rise and run. The riser, tread, and uniformity limits, and the comfort guidance, follow the stairway provisions of the International Residential Code, Section R311.7. The unit conversions follow the US National Institute of Standards and Technology guide. This gives a planning estimate; confirm the final dimensions against your local building code or with a building professional.

1. International Code Council (ICC), International Residential Code, Section R311.7 (stairways). https://codes.iccsafe.org
2. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811