Stair Stringer Calculator

Enter your total rise and total run below to calculate the exact board length you need to cut a stair stringer, plus how many stringers your staircase requires.

Total rise (in)

Total run (in)

Stair width (in)

Stringer length (in)

142.1 in

Stringer length (ft)

11.84 ft

Board to buy

12 ft

Stringers needed

3

Minimum stringers by stair width

Stair width	Minimum stringers
Up to 36 in	3
36–48 in	3–4
Over 48 in	4+, no more than 16" apart

Board length is rounded up to the nearest standard stock size (8, 10, 12, 14, 16, 18, or 20 ft) so there's enough extra length for the top and bottom notch cuts.

Need to figure out your riser and tread count first? Use our stair calculator instead. This page assumes you already know those numbers and is about cutting the actual board.

What a Stringer Is (and Why the Math Is Different Here)

A stringer is the diagonal board with notches cut into it that the treads sit on. Once you know your total rise and total run, finding the board length is a straightforward right-triangle problem. The stringer is the hypotenuse.

The Formula

Stringer Length = √(Total Rise² + Total Run²)

This is the Pythagorean theorem: the rise and run form the two legs of a right triangle, and the stringer is the diagonal connecting them.

Example: A staircase with a total rise of 90 inches and a total run of 110 inches (12 risers at 7.5“, 11 treads at 10“). See our stair calculator for how to get these numbers.

√(90² + 110²) = √(8,100 + 12,100) = √20,200 = 142.1 inches ≈ 11.85 feet

Since lumber comes in standard lengths, you’d order a 12-foot 2×12 for each stringer, which leaves enough length for the top and bottom notch cuts.

How Many Stringers Do You Need?

Stringers shouldn’t be spaced more than 16 inches apart on center, the same spacing convention used for floor joists, and for the same reason: wider spacing lets the tread flex too much underfoot.

Stair Width	Minimum Stringers
Up to 36 inches	3 (both edges + 1 center)
36–48 inches	3–4
Over 48 inches	4+, spaced no more than 16“ apart

Most standard residential stairs (36–42 inches wide) use 3 stringers: one at each outer edge and one down the center.

Laying Out the Cuts

Once you have your board and know your riser height and tread depth, the notches get marked using a framing square set to those two measurements: riser height on one arm, tread depth on the other. Walk the square down the board, tracing each notch, until you’ve marked out your full riser count.

Fit a pair of stair gauges, the small brass clamps that lock onto the square’s edges, at your riser and tread dimensions before you start. They turn the square into a fixed template, so every notch is identical without re-reading the scale each time. Marking fourteen notches by eye against the scale is how a flight ends up failing the ⅜-inch uniformity rule despite every individual measurement looking right.

Mark the whole board before cutting anything, then check the last notch lands where it should. An error of a sixteenth per notch is invisible on any single step and is a full inch out by the bottom of the flight.

The Bottom Cut: Where Most Stringers Go Wrong

This is the single most common stringer error, and it produces a flight that fails inspection on uniformity while every notch is cut perfectly.

When you walk the framing square down the board, every notch you mark is a full riser height. But the bottom riser is different: the treads sit on top of the stringer notches, so every step in the flight gains the tread thickness, except the bottom one, which starts from the floor.

The fix is called dropping the stringer: trim the bottom of the stringer by exactly one tread thickness.

Bottom cut = Riser height − Tread material thickness

With 7.5-inch risers and 1-inch treads, the bottom cut is 6.5 inches. Skip it and your bottom riser is 8.5 inches, an inch taller than the rest, well past the ⅜-inch allowance, and precisely the kind of inconsistency that catches a foot.

Two adjustments layer on top of this:

• Finished floor at the bottom. If tile or hardwood is going down after the stairs are built, the bottom riser shrinks by that thickness too. Account for the finished floor level, not the subfloor.
• Finished floor at the top. The same logic applies in reverse at the landing.

Both are covered in more detail in our stair code requirements guide, since the uniformity rule they violate is the one that fails the most inspections.

What’s Left of the Board After Notching

Cutting notches removes a substantial amount of material, and what remains, the throat, is what actually carries the load.

Throat = Board width − (Riser × Tread) ÷ √(Riser² + Tread²)

Board	Riser / Tread	Remaining Throat
2×12 (11.25 in)	7.5 / 10	5.25 in
2×12	7.75 / 10	5.12 in
2×12	7 / 11	5.34 in
2×10 (9.25 in)	7.5 / 10	3.25 in
2×10	7.75 / 10	3.12 in

This is the real reason 2×12 is the standard stringer stock. A notched 2×12 keeps over five inches of continuous material along its back; the same cuts in a 2×10 leave barely three, and many jurisdictions set a minimum throat of 3½ or 5 inches. Check your local requirement before substituting a narrower board. The saving is small and the consequence is a stringer that flexes or splits along the notch corners.

Note that a deeper tread increases the throat slightly while a taller riser decreases it, which is one more reason a comfortable 7/11 stair is structurally easier than a steep 7¾/10 one.

Cut Stringers and Solid Stringers

There are two ways to support treads, and only one of them involves the notching above.

Cut (open) stringers are the notched boards described here. The tread ends are visible from the side, and this is the standard approach for deck stairs, basement stairs, and most utility flights.

Solid (housed) stringers are uncut boards with shallow tapered mortises routed into the inside face. Treads and risers slide into the mortises and are wedged tight from behind. Nothing is notched away, so the board keeps its full depth and stiffness, and the stair edge reads as a clean diagonal line. This is the traditional approach for finished interior staircases, and it needs a router and a jig rather than a circular saw.

For a deck or a basement, cut stringers from 2×12 stock are the right choice. If you are building a feature staircase in a finished space, a housed stringer is what gives it the finished appearance, and it is worth pricing a stair builder, since the jig work is where the cost sits.