How to calculate stair stringer length

Step 1: measure the total rise correctly

Total rise is the vertical distance from the finished surface at the bottom of the stair to the finished surface at the top. For a deck it is deck surface to the landing pad or grade where the stringer will sit. For an interior stair it is finished floor to finished floor, including flooring thickness on both levels.

Measure at the exact spot the stringer will land, not at the top. A yard that slopes 2 inches over the projected run changes the bottom riser by 2 inches, which is more than the 3/8 inch variation the code allows. Use a level and a straight board or a laser to project the top surface out to the landing point, then measure down.

Write the rise in inches with fractions converted to decimals. 9 feet 1 1/2 inches is 109.5 inches. Every later number depends on this one, so measure it twice.

Step 2: find the number of risers and the exact riser height

The International Residential Code caps riser height at 7 3/4 inches. Divide total rise by 7.75 and round up to the next whole number; that is the minimum number of risers. Then divide the total rise by that number to get the actual riser height. For 109.5 inches: 109.5 divided by 7.75 is 14.13, so 15 risers, and 109.5 divided by 15 is 7.3 inches per riser.

Many builders prefer a riser near 7 inches for comfort. Try one more riser and compare: 16 risers gives 6.84 inches. Both pass code, but 16 risers adds a tread and 10 to 11 inches of run, which may not fit the space. The calculator on myCarpentry and similar tools work this way, adjusting the step count until the riser height and tread depth both look right.

Remember the count is risers, not treads. A stringer with 15 risers has 14 treads because the top surface (deck or floor) serves as the last step. Cutting 15 treads by mistake is one of the most common layout errors.

Step 3: choose the tread run and compute total run

Tread run is the horizontal cut on the stringer for each step. Code requires a finished tread depth of at least 10 inches measured nosing to nosing, with a 3/4 to 1 1/4 inch nosing, or at least 11 inches with no nosing. On a deck, two 5 1/2 inch boards give an 11 inch run and no nosing is needed. For an interior stair with a 1 inch nosing, a 10 inch run on the stringer yields an 11 inch finished tread.

Total run is tread run multiplied by the number of treads. With 14 treads at 10 inches, total run is 140 inches. This is the horizontal distance the stair will occupy on the floor, and it determines whether the stair fits the room and where the bottom of the stringer will land.

Keep the riser and run in proportion: a tall riser with a short run feels steep, and a short riser with a long run feels like a ramp. A 7.3 inch riser with a 10 inch run is a comfortable, code compliant pairing for a house or deck.

Step 4: stringer length with the Pythagorean theorem

The total rise and the total run form the two legs of a right triangle, and the stringer is the hypotenuse. Stringer length equals the square root of (total rise squared plus total run squared). This gives the length of the line from the bottom corner to the top corner of the notched stringer.

Worked example. Total rise 109.5 inches, 15 risers, 14 treads at 10 inches, total run 140 inches. Rise squared is 11,990.25. Run squared is 19,600. The sum is 31,590.25, and its square root is 177.7 inches, which is 14 feet 9.7 inches. A second example from the spikevm calculator: 109.5 inch rise, 14 risers, 9 5/8 inch run gives 13 feet 5 1/4 inches of stringer.

This is the length of the cut stringer, not the board you buy. Add a few inches at each end for the plumb cut at the top and the level cut at the bottom, then round up to a stock length. Stringers are cut from 2 by 12 lumber, sold in 2 foot increments from 8 to 20 feet, so the 177.7 inch example needs a 16 foot 2 by 12 (192 inches). A 14 foot board at 168 inches would be short.

Step 5: drop the stringer and check the lumber

Every riser is measured from tread surface to tread surface. The bottom step sits on the floor, so if you cut every riser at the calculated height and then add a 1 inch tread on top of each notch, the bottom riser ends up 1 inch too tall and the top riser 1 inch too short. The fix is to cut the tread thickness off the bottom of the stringer, called dropping the stringer, so every finished riser matches.

Also confirm the throat, the uncut depth of the board that remains below the notches. After notching a 7.3 inch riser and 10 inch run from a 2 by 12, check that enough solid wood is left to carry the load over the span; local building departments publish a minimum throat depth, and a very deep run with a tall riser can leave too little wood. If so, add a riser or use a solid stringer with cleats.

Lay out with a framing square: set the tongue at the riser height and the blade at the run, using stair gauges so every step repeats exactly. Mark all steps before any cut, count the risers, and compare the marked total run and total rise with your numbers. Benchlet's stair calculator draws the stringer with the cut lines and the throat dimension from the same inputs, which is a convenient cross check of a hand layout before the saw comes out.

Common errors and how to catch them

Forgetting the finished floor: if the total rise was measured to the subfloor and 3/4 inch hardwood goes on later, the top riser shrinks by 3/4 inch, breaking the 3/8 inch uniformity rule. Measure to finished surfaces or add the flooring thickness.

Using the tread count instead of the riser count in the division: 109.5 divided by 14 gives 7.82, which is over the 7 3/4 inch maximum and would fail inspection, while 109.5 divided by 15 passes.

Buying lumber by the diagonal alone: the cut stringer is the hypotenuse, but the top plumb cut and bottom level cut extend beyond it, so buy the next stock length up. When in doubt, lay out the stringer on the board before cutting and confirm the last riser lands with room to spare.

Frequently asked questions

Sources

• Decks.com Stair Stringer Calculator (rise, run, Pythagorean stringer length, 2x12 stringers)
• spikevm.com Length of a Stair Stringer Calculator (109 1/2 in rise worked example)
• myCarpentry Stair Calculator (IRC limits: 7 3/4 in riser, 10 in tread, 3/8 in variation)
• City of Boise IRC Code Handout #437: R311.7.5 Stair Treads and Risers