Stair calculator

What is a stair calculator?

A stair calculator is a free online tool that turns a single vertical measurement — the total rise from one finished floor to the next — into a complete set of stair dimensions. You give it the floor-to-floor height and the riser height you are aiming for, and it works out how many steps you need, how tall each step actually ends up, how deep each tread should be, how far the staircase reaches horizontally, how long the stringer boards must be, and the angle the whole flight makes with the floor. It replaces the trial-and-error arithmetic that carpenters otherwise do by hand and helps you check a design before you cut a single board.

How does it work?

You provide two measurements: the total rise (the vertical distance between the two finished floor levels) and a target riser height (the step height you would like, typically around 7 inches for a comfortable interior stair). Because a staircase must be divided into a whole number of equal steps, the calculator first decides how many steps fit best, then divides the rise back across that count so every step is exactly the same height. From the riser height it derives a matching tread depth using a well-known comfort rule, multiplies the tread depth across the runs to get the horizontal reach, and finally uses the rise and run as the two legs of a right triangle to find the stringer length and the pitch angle.

Everything downstream depends on the step count being a whole number, which is why the actual riser height usually differs slightly from the target you asked for. The tool computes each value in inches internally and then converts it to whichever unit you select for display, so you can mix a metric rise with imperial outputs without the numbers drifting.

Formula

The number of steps is the total rise divided by the target riser, rounded to the nearest whole number:

$N = \operatorname{round}\!\left(\frac{\text{rise}}{\text{target riser}}\right)$

The actual riser height spreads the rise evenly across those steps:

$R = \frac{\text{rise}}{N}$

The tread depth comes from the common comfort rule that twice the riser plus the tread should equal about 25 inches:

$T = 25 - 2R$

A flight of $N$ steps has $N - 1$ treads between the floors, so the total horizontal run is:

$\text{run} = T \cdot (N - 1)$

The stringer is the hypotenuse of the right triangle formed by the rise and the run:

$L = \sqrt{\text{rise}^2 + \text{run}^2}$

And the stair angle is the arctangent of rise over run:

$\theta = \arctan\!\left(\frac{\text{rise}}{\text{run}}\right)$

Worked example

Suppose the finished-floor-to-finished-floor rise is 108 inches and you would like a riser height near 7 inches.

• Number of steps: $N = \operatorname{round}(108 / 7) = \operatorname{round}(15.43) = 15$.
• Actual riser height: $R = 108 / 15 = 7.2$ inches, a touch taller than the 7-inch target because the rise had to divide evenly.
• Tread depth: $T = 25 - 2 \times 7.2 = 10.6$ inches.
• Total run: $\text{run} = 10.6 \times (15 - 1) = 148.4$ inches, or about 12 feet 4 inches of floor space.
• Stringer length: $L = \sqrt{108^2 + 148.4^2} \approx 183.5$ inches.
• Stair angle: $\theta = \arctan(108 / 148.4) \approx 36.1^\circ$.

Notes

The 25-inch comfort rule (2R + T = 25) is a rule of thumb that produces treads and risers that feel natural to climb; some builders use the related “riser plus tread equals 17 to 18 inches” guideline instead, which can give slightly different tread depths. Local building codes set hard limits on the maximum riser height and minimum tread depth, and they often require every riser and tread in a flight to be within a small tolerance of each other, which is why equal steps matter so much.

This calculator sizes the treads and risers only; it does not account for the thickness of the tread material, the nosing overhang, headroom clearance, or the landing. Treat its output as a starting design that you confirm against your local code and the actual materials before cutting.

FAQs

Why is the actual riser height different from my target?

Because a staircase must be split into a whole number of equal steps. The calculator rounds the rise divided by your target to the nearest whole step count, then divides the rise back across that count. Unless your target divides the rise evenly, the actual riser will be a little taller or shorter than what you asked for.

What is a comfortable riser height and tread depth?

For interior stairs, risers around 7 to 7.75 inches paired with treads of at least 10 to 11 inches are widely considered comfortable and are common code targets. The 2R + T = 25 rule keeps the pair balanced: a taller riser is matched with a shallower tread and vice versa.

What does the stair angle tell me?

The angle is the pitch of the flight measured from the horizontal. Everyday stairs usually fall between about 30 and 37 degrees; steeper angles save floor space but are harder and less safe to climb, while shallower angles are gentler but need a longer run.