Sixteenth
Stair Calculator
Enter the floor-to-floor height. You get the number of risers, the exact riser height, the total run, the stringer length and the marks for a framing square, checked against the IRC.
Type feet, inches and fractions like a tape: 9' 1-1/2", 109.5, or 2.78 m. Plain numbers are inches.
How the stair math works
The calculator divides the total rise by your maximum riser and rounds up to get the number of risers, then splits the rise evenly between them. There is one less tread than risers, because the upper floor is the top step.
risers = ⌈total rise ÷ max riser⌉ · riser = total rise ÷ risers
total run = (risers − 1) × tread · stringer = √(rise² + run²)
Framing square: set stair gauges at the riser height on the tongue and the tread run on the body, and step off one notch per riser. The step length is the distance between marks along the top edge of the stringer.
Drop the stringer: cut the tread thickness off the bottom so the first step is the same height as the others once the treads are on.
Headroom opening: how long the hole in the upper floor must be so you keep the headroom you entered, measured from the top riser.
Questions
How do I calculate the number of stairs?
Divide the total rise (finished floor to finished floor) by the tallest riser you allow, and round up. For a 9' 0" rise (108") and a 7-3/4" maximum, 108 ÷ 7.75 = 13.9, so you need 14 risers of 7-23/32" each. There is always one less tread than risers, because the upper floor is the last step.
What is the maximum riser height and minimum tread depth?
For homes, the IRC (R311.7.5) allows risers up to 7-3/4" and treads no shallower than 10", with no more than 3/8" difference between the tallest and shortest step. Headroom must be at least 6' 8". Check your local code, because some areas are stricter.
How long should a stair stringer be?
The stringer runs along the hypotenuse: √(total rise² + total run²). Buy a board at least one step longer than that so you have room for the bottom seat cut and the top cut. A 2×12 is usual for notched stringers, since you want at least 5" of solid wood (the throat) left below each notch.
What is a comfortable stair?
A common rule is 2 × riser + tread = 24" to 25-1/2". A 7-1/2" riser with a 10" tread gives 25", which feels natural. Steeper stairs save space but are harder to climb.