How to Lay Out Deck Stair Stringers (With the Math)

Stair stringers scare a lot of people, but the layout is just a few lines of arithmetic and a framing square. In this Instructable I'll walk through the whole calculation for a short deck stair (38" from the landing to the deck surface), then show how to mark and cut the stringers so every step comes out the same height.

The numbers here follow the US residential code (IRC R311.7): risers no taller than 7 3/4", treads at least 10" deep, and no more than 3/8" difference between any two steps. Check your local code before you build.

2x12 lumber for the stringers (pressure-treated for outdoor use). An 8 ft board is enough for this example.

Framing square and a pair of stair gauges (the small clamps that lock onto the square)

Tape measure, pencil, level and a long straight board

Circular saw, plus a handsaw or jigsaw to finish the notch corners

2x6 boards for the treads, and exterior-rated screws

Measure from the top of the deck surface straight down to where the bottom of the stair will land (a concrete pad or compacted gravel). If the ground slopes, hold a long straight board level off the deck and measure down from it at the spot where the stair will end, not at the rim joist.

Our example: total rise = 38".

Divide the total rise by the maximum riser height (7 3/4") and round UP to a whole number:

38 / 7.75 = 4.9, so 5 risers

Then divide the total rise by that number to get the actual riser height:

38 / 5 = 7.6" (just under 7 5/8")

Every step will be exactly the same height, which is what the code (and your ankles) care about.

There is always one less tread than risers, because the deck itself is the top step. 5 risers means 4 treads.

With a 10" run per tread: 4 x 10" = 40" total run (3' 4"). That tells you how far out from the deck the stair will land.

A quick comfort check is 2 x riser + tread, which should land around 24" to 25 1/2":

2 x 7.6 + 10 = 25.2", which is comfortable.

Two 2x6 boards with a 1/4" gap make an 11 1/4" deep tread, which gives you a 1 1/4" nosing over a 10" cut.

The stringer is the hypotenuse of the rise and the run:

square root of (38 x 38 + 40 x 40) = 55.2" (about 4' 7 3/16")

Add some extra for the cuts at each end, and an 8 ft 2x12 is plenty.

Also check how much wood is left under the notches (the "throat"). With a 7.6" riser and a 10" run, the notch takes about 6" out of the 11 1/4" wide 2x12, leaving roughly 5 3/16". Aim for at least 3 1/2".

To save doing this by hand every time, I built a free stair calculator that runs all of these numbers and draws the stair to scale: https://carpentrymath.com/stair-calculator/

Clamp the stair gauges on the framing square at 7 5/8" on the tongue (short arm) and 10" on the blade (long arm). Lay the square on the 2x12 so both gauges touch the top edge, trace the outline, then slide the square along until the blade mark lines up with the end of your last line. Repeat for all five risers.

If you prefer to measure, here are the marks along the stringer from the bottom (height from the floor / run from the start):

Step 1: 7 5/8" / 0"

Step 2: 1' 3 3/16" / 10"

Step 3: 1' 10 13/16" / 1' 8"

Step 4: 2' 6 3/8" / 2' 6"

Step 5: 3' 2" / 3' 4"

Here's the step most people miss. The treads add thickness on top of every notch, but the ground doesn't get a tread. If you don't compensate, the bottom step ends up taller than the rest.

Cut the thickness of one tread off the bottom of the stringer. With 2x6 treads that's 1 1/2". Now all five steps measure the same once the treads are on.

Cut the notches with a circular saw, stopping at the line, and finish the inside corners with a handsaw or jigsaw so you don't over-cut and weaken the stringer. Set the first stringer in place and check it with a level on the treads. If it's right, use it as a template to trace the others.

For a 36" wide stair, use three stringers. Fasten them to the deck rim with stringer hangers or a hanger board, and set the bottom on a solid, level base.

Screw the 2x6 treads to each stringer with two exterior-rated screws per board, leaving a 1/4" gap for drainage. Check that each riser measures 7 5/8" from tread top to tread top. You're allowed 3/8" of variation, but aim for zero.

That's it: measure, divide, check the comfort rule, mark with the square, and drop the bottom. The math is the same for any height; only the numbers change.