Stair Calculator
in
in
Number of Steps13
Riser Height7.38 in
Tread Depth10 in
Stringer Length161.60 in
Angle36.4°
This stair calculator turns a total vertical rise into a workable staircase layout. From the height you need to climb and your preferred riser height, it finds the whole number of steps, the exact riser height that divides evenly, the total run, the diagonal stringer length, and the staircase angle. It uses a standard 10-inch tread depth to lay out the horizontal run for each step.
Formula
steps = round(rise ÷ desired riser) ; riser = rise ÷ steps ; run = steps × 10 ; stringer = √(rise² + run²)
- rise
- Total vertical rise in inches
- desired riser
- Target height of each step in inches
- steps
- Number of risers, rounded to a whole number
- riser
- Actual riser height after dividing rise evenly
- run
- Total horizontal run at 10 in per tread
- stringer
- Diagonal stringer length, √(rise² + run²)
How it works
- Enter the total rise in inches: the vertical distance from the lower finished floor to the upper finished floor.
- Enter your desired riser height in inches (around 7 to 7.5 inches is typical). The calculator divides total rise by this and rounds to the nearest whole number of steps.
- It then recomputes the exact riser height so the steps divide the rise evenly, builds the total run at 10 inches per tread, and uses the Pythagorean theorem for the stringer length plus arctangent for the angle.
Worked example
A total rise of 105 inches with a desired riser height of 7.5 inches.
- Steps: round(105 ÷ 7.5) = round(14) = 14.
- Actual riser: 105 ÷ 14 = 7.5 in.
- Total run: 14 × 10 = 140 in.
- Stringer: √(105² + 140²) = √(11025 + 19600) = √30625 = 175 in; angle = atan(105 ÷ 140) = 36.87°.
14 steps, 7.5-inch risers, a 140-inch run, a 175-inch stringer, and a 36.87° slope.
Frequently asked questions
- What is a comfortable riser height?
- Many residential building codes cap risers around 7.75 inches, and 7 to 7.5 inches is a comfortable, common range. Enter your preferred value and the calculator finds the nearest whole step count that divides the rise evenly.
- What tread depth does this calculator assume?
- It uses a standard 10-inch tread depth to compute the total run and the stringer length. If your treads differ, the riser and step count stay correct, but the run, stringer, and angle would change.
- How is the stringer length calculated?
- The stringer is the diagonal board that supports the steps. The calculator treats the total rise and total run as the two legs of a right triangle and applies the Pythagorean theorem to find the hypotenuse.
- Does this guarantee my stairs meet local code?
- No. It produces dimensions from your inputs, but riser, tread, and headroom limits vary by jurisdiction. Always confirm the final layout against the building code that applies to your project.