🪜 Stair Stringer Calculator

Enter your total rise, target riser height and tread run to find the number of steps, actual riser height, and stringer length.

Total Rise (in)

Target Riser Height (in)

Tread Run (in)

How the steps are laid out

Your target riser height is a wish, not an instruction. The total rise is divided by it and rounded to the nearest whole number of risers, then the rise is divided back out so every step is identical. Treads come to one fewer than risers, because the top riser lands on the floor above rather than on a tread. The stringer is the hypotenuse of the whole flight.

risers        = round(total rise / target riser)
actual riser  = total rise / risers
treads        = risers - 1
total run     = treads x tread run
stringer      = sqrt(total rise^2 + total run^2)

A 108 in rise - a typical 9 ft floor to floor - with a 7.5 in target gives 14 risers at 7.71 in each, 13 treads, a total run of 130 in and a stringer of 14.08 ft. Ask for 7.25 in instead and you get 15 risers at 7.2 in, a gentler stair that eats another 10 in of floor.

Cutting it out of real timber

Buy stock longer than the diagonal. That 14.08 ft stringer comes out of a 16 ft board: the plumb cut at the top, the seat cut at the bottom and a squared end all need length beyond the geometry, and a stringer cut short is firewood.
Notching removes a lot of wood. Cut a 2x12 for 7.7 in risers and 10 in treads and only about 5 in of solid throat is left behind the notches. That remaining depth is what carries the stair, which is why stringers are 2x12 rather than 2x10.
Count the stringers, then the boards. A 36 in wide stair usually takes three, so the 16 ft board becomes three 16 ft boards - and a mis-cut on the third one costs a full length, not an offcut.

Two details decide whether the finished stair feels right. Drop the bottom of the stringer by the thickness of one tread before you set it, or the first step ends up a tread thicker than every other one. And check the total run against the room: 130 in is nearly 11 ft of floor before you add landing space at the bottom.

This page flags an actual riser above 7.75 in, which is the common residential maximum, but the real limits are whatever your local building rules say. Maximum riser, minimum tread, headroom, handrails and the requirement that risers within one flight match to within a small tolerance are all set by code and inspected. They override the numbers here - work backwards from them if the result lands close to a limit.

Frequently asked questions

How many stairs for a 108 inch rise?

14 risers at 7.71 in each, with 13 treads. Fifteen risers would give a more comfortable 7.2 in step but stretches the run from 130 in to 140 in, so the floor space you have often settles it.

Why is there one fewer tread than riser?

Because the last riser brings you up to the floor above, and that floor is the final walking surface. Building a tread there as well would put an extra step in - and leave the top one short by a tread thickness.

What size lumber do I need for a stair stringer?

A 2x12 for a standard flight, since the notches for treads and risers leave only around 5 in of uncut depth. Buy the length above the calculated stringer - a 14.1 ft stringer needs a 16 ft board.