How to Lay Out Stair Stringers: Rise, Run and Framing Square Steps

Find the riser height and tread count first, then set a framing square to the riser on one leg and the tread on the other and step the marks along the board. The diagonal is √(rise² + run²), not the board length.

For a 108 in total rise: 14 risers of 7.714 in, 13 treads of 10 in, a 130 in run and a 169.0 in diagonal. The board you cut from is longer than that figure.

What numbers do you need before you lay out a stringer?

Three numbers decide every mark on the board: the number of risers, the riser height and the tread depth. They come from the total rise, measured from finished floor to finished floor (or deck surface to finished grade). The stair rise and run guide explains how to measure the rise and why a 9 ft ceiling is not a 9 ft rise.

The riser limit of 7-3/4 in and the 10 in minimum tread used below are the values printed in the 2015 and 2018 IRC text, as reproduced in AWC’s DCA 6 deck guide and in county and city handouts. Your jurisdiction may have adopted another edition or amended them, so confirm the figures with your local building department before you cut.

What is the layout math?

risers n     = ceil( total rise ÷ 7.75 )
riser r      = total rise ÷ n                   (every riser equal)
treads       = n − 1                            (upper floor is the top step)
run          = treads × tread depth
diagonal   = √( total rise² + run² )

Use the stair calculator to get these values from your total rise. The diagonal here is the straight distance across the rise-and-run triangle, a starting figure for the length of the board and not a cut length.

How do you lay out a stair stringer with a framing square?

A framing square has two legs at 90 degrees. Placed on the edge of the board, one leg runs plumb (the riser) and the other level (the tread). The steps below are the geometry only; the board, its size and how it connects come from your plans.

1. Write down the numbers. Riser r to the nearest thousandth of an inch, tread depth d, number of risers n and treads n − 1.
2. Choose the two marks on the square. The riser height goes on one leg and the tread depth on the other. Both marks must sit on the same edge of the board, so the square is held at a fixed angle.
3. Trace the first step. Draw along the outside of both legs. This gives one riser line and one tread line.
4. Slide the square along and repeat. Move the square along the edge until the riser leg touches the end of the tread line you just drew, with both marks again on the board edge, and trace the next riser and tread. Repeat until you have n − 1 treads.
5. Check the count and the total. You should have n risers in all, counting the one formed at the top by the upper floor, and a combined rise of n × r equal to the total rise. Your square may not have a marking at 7.714 in. Take the closest mark you can read, then check the total: 14 risers at 7-11/16 in come to 107.625 in, which is 3/8 in short of 108 in.
6. If the total is off, mark by position. Instead of repeating a rounded step, measure each riser line from the first mark at k × r: 7.714, 15.429, 23.143 in, and so on, and check that the tread lines are d apart.
7. Mark the top and bottom cuts. The bottom of the stringer meets the lower floor and the top meets the upper structure. How these ends are cut and connected depends on the plans, and it is not covered here.
8. Test the layout. Cut one stringer, hold it in place against the opening, and check that the first and last riser heights match the others before using it as a pattern.

Equal risers and equal treads matter. The code text quoted in the rise and run guide lets the tallest riser exceed the shortest by no more than 3/8 in in one flight, and the same for treads. That includes the first and last step, so account for floor finish and tread thickness at the ends.

How long is a stair stringer?

The diagonal length is the hypotenuse of the rise-and-run triangle. All rows use a 7.75 in maximum riser and a 10 in tread, with the upper floor as the top step.

The arithmetic for the 8 ft row: 96² = 9,216 and 120² = 14,400, which sum to 23,616, and √23,616 = 153.7 in. These rows assume the total rise is measured finished floor to finished floor.

The actual board is longer than the diagonal. The top plumb cut and the bottom level cut, the stock left for the connection and the thickness of the stringer below the notches all add length, and this guide does not put a number on them. Lay the stringer out full size or on a framing square, as above, and measure the board from the layout. Stringer size and span are not computed.

Worked example: a 9 ft floor-to-floor rise

• Total rise: 108 in, finished floor to finished floor.
• Risers: 108 ÷ 7.75 = 13.94, rounded up to 14.
• Riser height: 108 ÷ 14 = 7.714 in (about 7-11/16 in on a tape).
• Treads: 14 − 1 = 13, each 10 in deep.
• Run: 13 × 10 = 130 in (10 ft 10 in).
• Diagonal: 108² = 11,664 and 130² = 16,900, so √(11,664 + 16,900) = √28,564 = 169.0 in (14 ft 1 in).
• Angle of that diagonal: atan(108 ÷ 130) = 39.7° (the roof pitch guide explains the rise-over-run-to-degrees step). The slope of the stair itself is atan(7.714 ÷ 10) = 37.6°, because the diagonal starts at the lower floor, one riser below the first nosing, so it is steeper than the stair.

The layout positions for the riser lines are 7.714 in, 15.429 in, 23.143 in and so on up to 14 × 7.714 = 108 in. If you build a top tread, treads become 14, the run 140 in and the diagonal √(108² + 140²) = 176.8 in.

Do you adjust the bottom riser for tread thickness?

The equal-riser layout above assumes every riser is measured to a finished surface. Where the tread boards sit on top of the stringer, the bottom riser cut is usually adjusted by the tread thickness so that the first step matches the others. Whether the adjustment applies, and by how much, depends on your tread material and how it is attached. Follow the instructions for the treads, or the plans, and do not guess a number. This guide does not give one.

Assumptions, common errors and limits

• The limits are quoted from 2015 and 2018 IRC text as reproduced in DCA 6 and local handouts. Check the code edition adopted where you build.
• Starting from the ceiling height. Measure floor to floor instead.
• Rounding the riser instead of checking the total. A riser of 7-11/16 in repeated 14 times is 3/8 in short.
• Using the diagonal as the board length. The board is longer.
• Forgetting the ends. Floor finish at the top and bottom and the tread thickness change the first and last riser.
• Counting treads wrong. The count is n − 1 when the upper floor is the top step and n when a top tread is built.
• This guide does not choose the stringer size or material, spans, number of stringers, connections, fasteners, handrails or guards, landings, winders or headroom. Use the code adopted locally and a qualified professional.

Common questions