How do I calculate stair stringers?

Divide the total rise by 7¾ in and round up for the number of risers; divide the rise by that count for the riser height. Treads are one fewer; total run is treads × the tread run (10 in minimum). The stringer is √(rise² + run²); buy a 2×12 one run longer, rounded up to a stock length.

How many stringers do I need for a 36 inch stair?

Three at 16 in on centre (36 ÷ 16 = 2.25, rounded down, plus one). A 48 in stair needs four. Composite treads often call for 12 in spacing; follow the tread manufacturer.

What size board do I need for a stringer?

A 2×12. After the notches, at least 5 in of throat should remain (AWC DCA 6); with a 7.71 in riser and 10 in run a 2×12 keeps about 5.1 in, a 2×10 would not. Length: stringer length plus one tread run, rounded up to 8–20 ft stock.

What is the maximum riser height and minimum tread depth?

Under the International Residential Code, risers no more than 7¾ in, treads at least 10 in (measured nosing to nosing), and no more than ⅜ in variation between risers in a flight. Local amendments can differ.

How long is a stringer for a 9 ft floor to floor?

With 10 in treads: 14 risers at 7.71 in, 13 treads, 130 in of run, stringer √(108² + 130²) = 169 in, about 14 ft 1 in at 39.7°, cut from a 16 ft 2×12.

Stair Stringer Calculator: From Total Rise to the Board You Cut

This stair stringer calculator starts from the one number you can measure, the total rise from the lower floor to the upper floor, and returns everything a stringer needs: the number of risers and their height, the number of treads and the total run, the stringer length and its angle, the length of 2×12 to buy with the cuts allowed for, and how many stringers the stair width needs.

Calculator

Stair stringer calculator: risers, treads, stringer length and the 2×12 to buy

Total rise (floor to floor)Finished floor to finished floor, not to the subfloor.Tread runNosing not included. IRC R311.7.5.2: at least 10 in.Maximum riserSets the number of risers. IRC R311.7.5.1: at most 7.75 in.Stair widthIRC R311.7.1: at least 36 in clear.Stringer spacing16 in o.c. for 1 in treads; 12 in for thinner or composite treads.

Type the floor-to-floor rise. Risers = rise ÷ 7¾ in, rounded up; treads = risers − 1; stringer = √(rise² + total run²).

Code figures are the 2021 IRC for one- and two-family dwellings (R311.7); decks, commercial stairs and local amendments differ. The throat rule is the AWC deck guide's 5 in. Headroom (6 ft 8 in) and handrails are not checked here. Plain arithmetic, not an AI estimate.

A basement starter plan. Click it to draw the stair footprint (total run × width) in your own layout and check where the bottom step lands.

About

The rules it applies are the ones in the International Residential Code: risers no more than 7¾ in, treads at least 10 in, a stair at least 36 in wide, and no riser in a flight more than ⅜ in different from another, which is why every riser comes out the same height. It is plain arithmetic, not an AI estimate. The floor plan canvas below is for the stair’s footprint, the total run by the width, so you can see where the flight lands in the room.

How the stair stringer calculator lays out the flight

Measure the total rise, finished floor to finished floor, not floor to ceiling. Divide it by the biggest riser the code allows, 7¾ in, and round up: that is the number of risers, and the total rise divided by that count is the height of every riser. A 9 ft floor-to-floor is 108 in; 108 ÷ 7.75 = 13.9, so 14 risers at 7.71 in each. There is one fewer tread than risers because the upper floor is the last tread: 13 treads. At a 10 in run each, the total run is 130 in, 10 ft 10 in, and that is the horizontal distance the stair eats out of the room below.

The stringer length is the hypotenuse: √(108² + 130²) = 169 in, 14 ft 1 in, at 39.7° to the floor. The board has to be longer than that because the top and bottom cuts take a tread’s worth off each end, so the calculator adds one run and rounds up to the next stock length: 169 + 10 = 179 in, which needs a 16 ft 2×12. Three stringers carry a 36 in stair at 16 in on centre; four at 48 in. Change the run to 11 in and the flight gets longer and gentler; set the maximum riser lower and it gets more risers.

Risers = total rise ÷ maximum riser, rounded up; riser height = total rise ÷ risers.
Treads = risers − 1; total run = treads × run; stringer = √(rise² + run²).
Board = stringer + one run, rounded up to 8, 10, 12, 14, 16 or 20 ft.
Stringers = width ÷ spacing, rounded down, + 1: three for 36 in at 16 in o.c.

The throat: why a 2×12 is the smallest board that works

When you notch a stringer for the risers and treads, what is left between the inside corner of the notch and the back edge of the board is the throat, and that is all the wood that carries the stair. The calculator takes the board depth (11¼ in for a 2×12) and subtracts the depth of the notch, which is riser × run ÷ √(riser² + run²): with a 7.71 in riser and a 10 in run the notch is 6.11 in deep and 5.14 in of throat remain. The American Wood Council’s deck guide (DCA 6) wants at least 5 in; a 2×10 with the same cuts would leave about 3 in, which is why the calculator flags it. A steeper stair cuts deeper and leaves less.

The old carpenter’s check, two risers plus one tread between 24 and 25 in, is shown as a hint: 2 × 7.71 + 10 = 25.4 in is on the steep side of comfortable, and lengthening the run to 10½ or 11 in brings it into the band at the cost of about a foot of floor.

Decks, basements and the landing below

Deck stairs use the same arithmetic with the total rise measured from the deck surface to the pad or the ground, and the pad has to be where the total run says it is: a 130 in run from a 9 ft deck puts the bottom step nearly 11 ft out. For a basement stair the question is usually the other way round, whether the run fits between the wall and the furnace; draw the footprint on the canvas, total run by width, and move it until the bottom step clears the door swing. The canvas is a schematic, rule-checked drawing, not an AI.

What this stair stringer calculator does not do

It does not check headroom (6 ft 8 in under every point of the flight), handrail height (34 to 38 in), guard height, landings at doors or the maximum 12 ft 7 in of rise between landings; those are in IRC R311.7 and your inspector will check them. It does not size the stringer for span, which for long flights means a mid-span support or a third stringer, and it does not know your lumber’s actual dimensions: measure the board. Local amendments apply: some jurisdictions allow a 8¼ in riser and a 9 in tread.

Frequently asked questions

How do I calculate stair stringers?: Divide the total rise by 7¾ in and round up for the number of risers; divide the rise by that count for the riser height. Treads are one fewer; total run is treads × the tread run (10 in minimum). The stringer is √(rise² + run²); buy a 2×12 one run longer, rounded up to a stock length.
How many stringers do I need for a 36 inch stair?: Three at 16 in on centre (36 ÷ 16 = 2.25, rounded down, plus one). A 48 in stair needs four. Composite treads often call for 12 in spacing; follow the tread manufacturer.
What size board do I need for a stringer?: A 2×12. After the notches, at least 5 in of throat should remain (AWC DCA 6); with a 7.71 in riser and 10 in run a 2×12 keeps about 5.1 in, a 2×10 would not. Length: stringer length plus one tread run, rounded up to 8–20 ft stock.
What is the maximum riser height and minimum tread depth?: Under the International Residential Code, risers no more than 7¾ in, treads at least 10 in (measured nosing to nosing), and no more than ⅜ in variation between risers in a flight. Local amendments can differ.
How long is a stringer for a 9 ft floor to floor?: With 10 in treads: 14 risers at 7.71 in, 13 treads, 130 in of run, stringer √(108² + 130²) = 169 in, about 14 ft 1 in at 39.7°, cut from a 16 ft 2×12.

Sources

Where the numbers come from

Local amendments apply; check your own jurisdiction.