Stair Calculator
Enter the total rise from the lower floor to the upper floor. The calculator divides it into equal risers no taller than your maximum and returns the tread count, total run, stringer length and angle.
Result
- Number of treads
- 13
- Total run
- 133.25 in
- Total run in feet
- 11.1 ft
- Stringer length
- 171.52 in
- Stringer length in feet
- 14.29 ft
- Stair angle
- 37°
- 2 × riser + tread
- 25.68 in
Stringer length is the straight-line distance from the bottom of the first riser to the top of the last. Buy stock longer than this to allow for end cuts. Always confirm stair dimensions with your local building code.
Formula
- Risers = total rise ÷ maximum riser height, rounded up
- Riser height = total rise ÷ number of risers
- Treads = risers − 1
- Total run = treads × tread depth
- Stringer length = √(total rise² + total run²)
- Angle = arctan(riser height ÷ tread depth)
How the Stair Calculator works
Every riser in a flight must be the same height. Divide the total rise by the tallest riser you will accept and round up to a whole number of risers. Dividing the total rise by that count gives the exact riser height.
A straight flight has one fewer tread than risers, because the upper floor acts as the last tread. The stringer is the hypotenuse of the triangle formed by total rise and total run.
The International Residential Code limits risers to 7 3/4 inches and requires treads of at least 10 inches. A comfortable stair also keeps twice the riser plus the tread between 24 and 25 inches.
Worked example
For a total rise of 108 in and a 7.75 in maximum riser: 108 ÷ 7.75 = 13.9, so 14 risers of 108 ÷ 14 = 7.714 in. There are 13 treads. At 10.25 in each the total run is 133.25 in, the stringer is √(108² + 133.25²) = 171.52 in, and the angle is 37.0°.
Frequently asked questions
How do I calculate the number of stairs I need?
Measure the total rise in inches, divide by your maximum riser height, and round up. For 108 inches and 7.75 inch risers that is 14 risers and 13 treads.
What is the standard rise and run for stairs?
A common residential target is a 7 to 7 3/4 inch rise with a 10 to 11 inch run. The International Residential Code sets 7 3/4 inches as the maximum rise and 10 inches as the minimum tread depth.
How long a board do I need for a stair stringer?
Use the stringer length shown and round up to the next stock length. A 171.5 inch stringer is 14.3 feet, so a 16 foot board is needed.
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