Stair Stringer Calculator

One board, three numbers

A cut stringer is a 2x12 with triangles taken out of one edge. Three numbers describe it: the total rise you measured, the riser height you divide it into, and the tread depth you walk on. Measure the rise finished surface to finished surface — decking to pad, not framing to dirt — or the bottom step comes out short by the thickness of a board.

Tread depth is the walked depth, nosing excluded. A nosing widens the board the treads are cut from and changes nothing about the run, so that field adds to the tread stock only.

The riser count is a division, not a lookup

Nothing is looked up here. The count is the rise over your target riser, rounded to the nearest whole number rather than up: 57 inches at a 7 inch target is 8.143, so 8 risers of 7 1/8 in — not 9 of 6 5/16 in, a flatter, longer stair nobody asked for. Half-way rounds up, the smaller riser being the safer miss, and the risers come out exactly equal because the rise is divided back by the count.

The tread count depends on where the stair lands. On a deck or a floor the top surface is the last step, so the stringer carries one tread fewer than it has risers — 8 and 7 here. A stringer carrying a tread at the top has the same number of each: 8 treads and 6 ft 8 in of run. It is a select, not an assumption made for you.

Risers     n  =  floor( rise / target + 0.5 )   nearest, not a ceiling
Riser      r  =  rise / n
Treads     t  =  n - 1  (top step is the deck)  or  n
Run        R  =  t x tread
Diagonal   D  =  sqrt( R^2 + rise^2 )           straight length of board
Layout     L  =  t x sqrt( r^2 + tread^2 )      the stepped line
Throat     Th =  11.25 - ( r x tread ) / sqrt( r^2 + tread^2 )
Stringers  S  =  max( 3, ceil( width / 18 ) + 1 )

The layout line, the diagonal, and the board you buy

Two lengths run up a stringer. The diagonal, √(run² + rise²) = 7 ft 6 1/4 in here, is the board length: the figure that decides what you buy. The layout line is the stepped line a framing square walks, the treads times √(riser² + tread²), 7 ft 1 15/16 in. They differ by one riser, and marking a board to the wrong one puts every step out.

The sheet picks the shortest listed 2x12 the diagonal fits inside — 8 ft for the default stair. No allowance is added for the top and bottom connections: the board still has to carry them, and how much it takes is the detail you are building.

A steeper division buys run, a shallower one spends it: that trade is what this sheet hands back instead of a limit.

The throat, and where its limit lives

The throat is the wood left behind the notch, measured square to the layout line: 11.25 in — the actual width of a nominal 2x12, a milled dimension and not a code figure — less (riser × tread) / √(riser² + tread²). At 7 1/8 in and 10 in that is 11.25 − 71.25 ÷ 12.2787 = 5.4473 in. Deepen the riser and it thins fast: at a 7¾ in riser on the same tread, 5.1243 in. What a throat has to be is DCA 6 Figure 28, a drawing: this sheet prints what yours is and links the figure.

How many stringers a width needs

Two sentences of AWC DCA 6-2015 decide the count, quoted rather than summarised: If only cut stringers are used, a minimum of three are required. and For stairs greater than 36" in width, a combination of cut and solid stringers can be used, but shall be placed at a maximum spacing of 18" on center. The sheet reads them as ceil(width ÷ 18) + 1, never fewer than 3.

The spacing is a field, so a stair built to a tighter one counts from yours. Two more DCA 6 sentences raise warnings here rather than numbers: If the total vertical height of a stairway exceeds 12'-0", then an intermediate landing shall be required. — above 144 in the sheet takes off one flight at a time — and All stairs with 4 or more risers shall have a handrail on at least one side, from 4 risers up, not in this takeoff.

Frequently asked

How do you calculate stair stringers?

Divide the total rise by the riser height you work to, round to the nearest whole number, then divide the rise back by that count. Treads are one fewer than risers when the top step is the deck, and the run is treads times tread depth: 57 in over 7 in gives 8 risers of 7 1/8 in, 7 treads, 5 ft 10 in of run.

How long is a 2x12 for a 5 step stringer?

Five risers at these defaults is 2 ft 11 in of rise and 4 treads, so a diagonal of √(40² + 35²) = 53.15 in, 4 ft 5 1/8 in. The shortest listed board it fits inside is 8 ft, with nothing added for the top and bottom connections.

What is the 7-11 rule for stairs?

It names two code figures — a maximum riser and a minimum tread — and this sheet prints neither: you type the riser and the tread you work to. DCA 6 is a prescriptive guide based on the IRC. The code your jurisdiction has adopted governs, and it is the document to check before you cut.

What is the 27 rule for stringers?

A live search on 2026-09-20 returned no authoritative definition of the "27 rule" for stringers, so this sheet does not state one.

Limits of this sheet

This sheet prints no maximum riser height, no minimum tread depth, no nosing limit, no headroom and no guard or handrail height. Those live in a figure or a table of the code, they are linked here, and you type the riser and the tread you are working to.

S-301 cuts one flight: it does not size a landing, design a guard, count hardware, check a stringer span or price labour. The deck it lands on goes through sheet A-301. Quantities are for ordering, not engineering.

Sheet S-301 prepared by TakeoffMetric Editorial; no author, credential or field measurement is claimed.