Stair stringer calculator
Stairs are built from a fixed total rise, and everything else follows: divide the floor-to-floor height by a comfortable riser, round up to a whole number of risers, and divide again. That second division is the step most people skip, and it is why finished stairs sometimes have one riser taller than the rest by half an inch — enough to trip on, every time you climb.
Straight runs only. Landings, winders and curved stairs each need their own calculation, and code compliance (headroom, handrail, guard height) should be checked against your local code.
The rule of thumb for comfort is rise plus run equals about 17 to 18 inches, with a riser between 7 and 7.75 inches and a tread of at least 10. A 108 inch floor-to-floor with a 7.5 inch target gives 15 risers at 7.2 inches, 14 treads at 10 inches, a total run of 140 inches and a stringer about 14 feet 9 inches long.
Stringer length is the diagonal — the hypotenuse of the total rise and the total run — plus an allowance for the notches at the top and bottom. Cut from 16 ft stock for that example, not from 14 ft 9 in, because the plumb and level cuts consume the ends. Two stringers for a stair up to about 3 ft wide, three for anything wider.
How the calculation works
Risers = ceil(total rise / target riser height). Actual riser height = total rise / risers. Treads = risers - 1, because the upper floor is the last tread. Total run = treads x tread depth. Stringer length = sqrt(rise² + run²) / 12 feet.
- The total rise is measured between finished surfaces, including the upper floor's thickness — measuring between joists is the most common error.
- A straight run with no landing; a landing splits the stair into two flights, each calculated separately.
- Tread depth is the finished tread including any nosing you intend to add; codes measure the tread depth itself, not the nosing.
- Stringer length excludes the top and bottom plumb cuts; add 12-18 inches when selecting stock.
Sources: Comfort rule: rise + run ~ 17-18 in; typical riser 7-7.75 in, tread 10-11 in (standard practice and IRC limits); Stringer length = sqrt(rise² + run²)
Worked examples
An 8 ft 9 in floor-to-floor (105 in)
105 / 7.5 = 14 exactly, so 14 risers at 7.5 in, 13 treads at 10 in, a run of 130 in and a stringer of 13.9 ft — buy 16 ft stock.
A 6 ft rise to a deck (72 in)
72 / 7.5 = 9.6, so 10 risers at 7.2 in, 9 treads, a run of 90 in and a stringer of 9.6 ft.
Questions
How do I calculate stair stringers?
Divide the total rise by a comfortable riser height, round up to a whole number, then divide again to get the actual riser. Treads are one fewer than risers, and the stringer is the diagonal of rise and run.
How many stairs for a 9 ft ceiling?
Around 15 risers for a typical 108-112 in floor-to-floor, with 14 treads. The floor thickness is what makes the number higher than people expect.
What is a comfortable riser height?
7 to 7.75 inches. Most residential codes cap risers at 7.75 in and require every riser in a flight to be within 3/8 in of the others.
How long should treads be?
Ten to eleven inches of finished tread depth for a comfortable descent, and codes usually require at least 10 in. Deeper treads are easier going down, especially for children and older people.
How many stringers do I need?
Two for a stair up to about 3 ft wide, three for 3-4 ft, and more for wider stairs. Stairs over 30 in above the floor also need a guardrail.
Related calculators
Embed this calculator. Paste this on your own site — it stays in sync with updates here:
<iframe src="https://s06.nl/tools/home/stair-stringer/embed/" width="100%" height="520" style="border:1px solid #ddd" loading="lazy" title="Stair stringer calculator"></iframe><p><a href="https://s06.nl/tools/home/stair-stringer/">Stair stringer calculator</a></p>