Stair stringer calculator: layout marks, throat and board length
For a 9 ft rise, set the framing square to 7 11/16" × 10" and step it 14 times along a 16 ft 2x12. That leaves 5 1/8" of throat, above the 5" we check for. Enter your rise to get your own cut list.
Layout marks along the board edge
Shopping list
Laying out a stringer with a framing square
The calculator gives you two numbers to set on the square: the riser on the short arm (the tongue) and the run on the long arm (the blade). For a 9 ft rise that is 7 11/16" and 10". Every notch is the same triangle, stepped along the board 14 times.
- Pick a straight 2x12 and sight down its edge. Put the crown (the slight hump) on top, so the notches are cut into the side that will be pushed down under load.
- Clamp stair gauges, or a strip of wood, to the square at the riser mark on the tongue and the run mark on the blade. This keeps every step identical without re-measuring.
- Start near the bottom end. Lay the square on the board with both gauges tight to the top edge and trace along the outside of the tongue and blade. That is one riser line and one tread line.
- Slide the square up so the blade's run mark meets the end of the line you just drew, and trace again. Repeat until you have drawn every riser. The table under the calculator lists the distance of each mark from the first one, measured along the board edge, so you can catch a drift early.
- At the top, extend the last riser line down to the bottom edge. That is the plumb cut that sits against the rim joist or header.
- At the bottom, extend the first tread line backward to make the level cut that sits on the floor. Then shorten the first riser by the tread thickness (next section).
- Cut with a circular saw, stopping at the inside corners. Finish each corner with a handsaw or jigsaw so you do not over-cut into the throat.
- Test-fit the first stringer, check the treads with a level, and only then use it as the template for the others.
Dropping the stringer for tread thickness
The layout marks the top of the stringer, not the top of the tread. Every tread then adds its thickness on top. If nothing is removed at the bottom, the first step grows by one tread thickness while the top step shrinks by the same amount, and the risers are no longer equal.
The fix is to cut the bottom level line one tread thickness lower. With 1" treads on a 7 11/16" riser, the first rise on the stringer measures 6 11/16". With doubled 2x6 deck treads (1 1/2") it is 6 3/16". If the top floor gets new finish flooring later, add that thickness to the total rise before you start, not after.
The throat: how much wood is left
Each notch removes a triangle of wood. What remains between the inside corner of the notch and the bottom edge is the throat, and it carries the stair. The depth of the notch, measured square to the slope, is riser × run ÷ √(riser² + run²). Subtract that from the board width to get the throat.
throat = board width − notch depth
For 7 11/16" × 10" the notch is 6 1/8" deep, so a 2x12 (11 1/4" actual) keeps 5 1/8". The American Wood Council's DCA 6 deck guide checks cut 2x12 stringers assuming about 5.1" of wood left under a 7 3/4" × 10" notch, so this calculator flags any throat under 5". The drawing above marks the throat in blue when it passes and red when it does not.
| Riser × run | Notch depth | 2x10 throat | 2x12 throat |
|---|---|---|---|
| 7" × 11" | 5 7/8" | 3 3/8" thin | 5 3/8" ok |
| 7 1/4" × 10 1/2" | 5 15/16" | 3 5/16" thin | 5 5/16" ok |
| 7 1/2" × 10" | 6" | 3 1/4" thin | 5 1/4" ok |
| 7 1/2" × 11" | 6 3/16" | 3 1/16" thin | 5 1/16" ok |
| 7 3/4" × 10" | 6 1/8" | 3 1/8" thin | 5 1/8" ok |
| 7 3/4" × 11" | 6 5/16" | 2 15/16" thin | 4 15/16" thin |
Two things weaken a throat beyond the numbers: large knots in the bottom third of the board, and saw kerfs that overshoot the inside corner. Choose boards with clear lower edges and stop power cuts short of the corner.
How many stringers to use
The stair width and the span your treads can handle decide the count. Outer stringers sit flush with the stair edges; the rest are spaced evenly between them. For deck stairs, DCA 6 asks for at least three cut stringers on a 36" stair and a maximum spacing of 18" on center; wider stairs can mix cut and solid stringers at the same spacing. Interior stairs with 1" hardwood treads and solid risers are commonly built on three stringers too.
| Stair width | 12" max | 16" max | 18" max |
|---|---|---|---|
| 36" | 4 (11 1/2" o.c.) | 4 (11 1/2" o.c.) | 3 (17 1/4" o.c.) |
| 42" | 5 (10 1/8" o.c.) | 4 (13 1/2" o.c.) | 4 (13 1/2" o.c.) |
| 48" | 5 (11 5/8" o.c.) | 4 (15 1/2" o.c.) | 4 (15 1/2" o.c.) |
| 60" | 6 (11 11/16" o.c.) | 5 (14 5/8" o.c.) | 5 (14 5/8" o.c.) |
Composite and PVC treads are softer than wood and usually call for 12" or even 9" spacing on stairs. The installation guide for the specific board is the authority here, because a tread that flexes will loosen its fasteners over time.
Board length to buy
The layout line from the bottom nosing to the top nosing is shorter than the board you need. The board also has to reach the floor at the bottom and the header at the top, which adds about one more step diagonal. The calculator rounds that up to the next stock length.
| Total rise | Risers | Layout line | Board needed | Buy |
|---|---|---|---|---|
| 2' 6" | 4 | 3' 1 1/2" | 4' 2" | 8 ft |
| 4' 0" | 7 | 6' 3/4" | 7' 7/8" | 8 ft |
| 6' 0" | 10 | 9' 2 7/8" | 10' 3 1/4" | 12 ft |
| 8' 0" | 13 | 12' 5 3/16" | 13' 5 5/8" | 14 ft |
| 9' 0" | 14 | 13' 8 3/16" | 14' 8 13/16" | 16 ft |
| 10' 0" | 16 | 15' 7 1/2" | 16' 8" | 18 ft |
| 12' 0" | 19 | 18' 9 7/8" | 19' 10 3/8" | 20 ft |
Above roughly 16 ft of board, straight 2x12s get expensive and hard to find. That is also about where a stair passes 120" of rise, so a landing is worth considering for both structure and comfort.
Fastening the top and bottom
Top. On decks, the usual method is an adjustable galvanized stair-stringer connector for each stringer, nailed or screwed to the rim joist with the fasteners its maker specifies. Indoors, stringers often hang from a 2x hanger board nailed to the header, or bear on a ledger. Either way, the top plumb cut must sit fully against the framing, not on a shim.
Bottom. Outdoors, DCA 6 has the stringers bear on a 2x4 bearing block fastened to posts, and the posts sit on footings at least 12" below undisturbed ground or below the frost line, whichever is deeper. The guide does not allow stringers to bear on a concrete pad or patio unless the pad is founded that deep. Indoors, the stringers sit on the subfloor with a kicker or blocking fastened down.
Long stringers can bounce in the middle. DCA 6 limits how far a stringer may span (its Figure 28). Past that limit, add a 4x4 post notched and bolted to the stringer with two 1/2" through-bolts, standing on a 12" round or 10" square footing 6" thick, or break the flight with a landing.
Precut, metal and other stringers
Home centers sell precut treated stringers in 3, 4 and 5-step lengths. They save time on small deck stairs, but their rise and run are fixed. Check the tag against your total rise before buying: if your calculated riser differs from theirs by more than a fraction of an inch, the top or bottom step will be off. Steel and aluminum stringers suit modern interiors or commercial work; they are sized by the maker and are not notched on site, so this calculator's throat check does not apply to them.
Frequently asked questions
How long a stringer do I need for 8 feet of rise?
For 96" of rise with 10" treads: 13 risers of 7 3/8", a layout line of 12' 5 3/16", and about 13' 5 5/8" of board once the top and bottom cuts are included. Buy 14 ft boards.
Should I use 2x10 or 2x12 for stair stringers?
Use 2x12 for cut stringers. After notching a 7 3/4" × 10" step, a 2x12 keeps about 5 1/8" of solid wood, while a 2x10 keeps about 3 1/8". The AWC DCA 6 deck guide requires 2x12 as the minimum for all stair stringers.
How far apart should stair stringers be?
The AWC DCA 6 deck guide sets 18" on center as the maximum and asks for at least three cut stringers on a 36" stair; with that spacing, 5/4 deck boards or 2x4s work as treads on cut stringers. Composite treads often need closer spacing, and the tread maker's installation guide gives the exact span.
What is the throat of a stair stringer?
The throat is the narrowest band of wood left under the notches, measured square to the bottom edge. It carries the load after the cuts are made, so it decides whether the stringer is strong enough.
Why do you drop the stair stringer?
Treads add thickness on top of every notch. If the stringer is not shortened at the bottom by one tread thickness, the first step ends up taller than the rest by that amount and the top step shorter.
How do I attach a stair stringer to a deck?
At the top, hang each stringer from the rim joist or a hanger board with an adjustable stair-stringer connector, fastened with the screws or nails the connector maker lists; ordinary deck screws are not rated for hanger loads. At the bottom, DCA 6 has the stringers bear on a 2x4 block fastened to posts that sit on footings.