Stair Calculator

What this calculator does

The Stair Calculator turns a total rise and a tread depth into the main dimensions of a straight staircase. It reports the number of risers and treads, the actual riser height, the total horizontal run, the stringer height, the stringer length, and the stair angle.

You can work two ways. In Fixed rise mode, enter the total rise and a target riser height; the calculator chooses the number of risers that comes closest and then divides the total rise evenly. In Fixed number of steps mode, enter the number of risers you want and the calculator finds the riser height. Both modes use the same tread depth to build the horizontal run.

How to use this calculator

1. Choose Fixed rise or Fixed number of steps.
2. Enter the total rise in inches. This is the floor-to-floor height, not the height of one step.
3. Enter the tread run in inches. This is the depth of one step from nosing to nosing.
4. In Fixed rise mode, enter a target riser height. In Fixed number of steps mode, enter the number of risers.
5. Click Calculate.

The default example uses a 120-inch total rise, a 10-inch tread, and a 7.5-inch target riser. It returns 16 risers, 15 treads, a 7.5-inch riser height, a 12.5-foot total run, a 15.63-foot stringer, and a 36.87-degree stair angle.

Stair formulas

risers = round(total rise ÷ target riser height)
         or the fixed number of steps

riser height = total rise ÷ risers
treads       = risers − 1
total run    = treads × tread depth

stringer height = total rise − riser height
stringer length = √(stringer height² + total run²)
stair angle     = atan(stringer height ÷ total run)

The stringer height subtracts one riser because the stringer is measured from the top of the lowest tread to the top of the highest tread. That is the convention used by the reference calculator. The total run is measured horizontally and does not include a landing.

Assumptions and limitations

• Rise, tread, and target riser values are entered in inches. Total run, stringer height, and stringer length are reported in feet.
• The stair is assumed to be straight. Winders, spirals, and stairs with intermediate landings are not modeled.
• The calculator does not check headroom, floor thickness, handrail height, landing depth, or the thickness of the tread material.
• The angle is based on the stringer triangle, not on the nosing line.
• round() chooses the nearest whole number of risers. A result that is too far from the target means the design needs a different target rise.
• Building codes differ by jurisdiction. Common residential limits are a maximum riser near 7.75 inches and a minimum tread near 10 inches, but confirm local rules.

Frequently asked questions

What is the difference between rise and run?

Rise is the vertical distance from one tread to the next, or from floor to floor. Run, also called tread depth, is the horizontal distance from the front of one tread to the front of the next.

How many steps are in a 10-foot rise?

At a 7.5-inch riser, a 120-inch rise needs 16 risers. That creates 15 treads, because the upper floor serves as the final step. The exact count changes with the target riser height.

Why is the stringer shorter than the total rise plus total run?

The stringer is a diagonal, so its length is the hypotenuse of the rise and run triangle. It also uses the stringer height, which is the total rise minus one riser. The result is shorter than simply adding the two horizontal and vertical measurements.

Reference table

Example stair calculation

A common target is a riser height of about 7–7.75 inches and a tread depth of about 10–11 inches. Local building codes control the allowed range.

Source

Reference: Calculator.net — Stair Calculator.

Use this calculator for planning only. Verify dimensions and code compliance with a qualified builder or inspector before cutting stringers.