Stair Stringer Calculator
Enter the total rise and your tread depth to get everything you need to mark and cut the stringer: the framing-square settings, the stringer length and board to buy, the throat left under the notches, the bottom drop, how many stringers, and a check against the US and UK stair rules.
Finished surface to finished surface. You can type 8' 9" or 2 m 67 cm.
Rounded to a whole number of equal risers. Typical 7–7½ in (175–190 mm).
The notch's level cut: nosing to nosing, without the overhang. Typical 10–11 in (250–280 mm).
Face of the first riser to the face of the top (header), measured flat.
Actual width, typical sizes. 2×12 is the usual pick for cut stringers.
Outside of one stringer to the outside of the other.
Sets the typical stringer spacing and tread thickness.
Centre to centre. Use your tread maker's figure.
One step down (usual): treads = risers − 1. Flush: the top tread is level with the floor or deck.
Cut off the bottom of the stringer so the first step isn't taller.
Tile or boards laid after the stringer goes in. 0 if the floor is finished.
Its height above the lower floor.
Measured flat. Blank: we show how far back it must stay.
Your stringer, to scale
On the board
How your stringer is worked out
Split the rise into equal risers, set the square to riser and going, step it along the board, and keep enough wood under the notches.
- 1
Count the risers
105 ÷ 7.5 = 1414 × 7 1/2 in
- 2
Set the square
tongue 7 1/2 inblade 10 instep 12 1/2 in
- 3
Check the throat
11.25 − 7.5×10÷12.5= 5 1/4 in ✓
- 4
Board to buy
13 × 12.5 = 162.5buy 14 ft
Read more: the formula, a worked example, cutting steps and the US and UK figures
A stringer is the sawtooth board that carries the treads. The total rise is split into equal risers. Each notch is a right triangle with the riser and the going as its short sides, so each step along the board's edge is the long side, √(riser² + going²). The solid wood left under the notches is the throat, and the stringer is dropped by the tread thickness so the first and last steps come out the same as the rest.
The formula
risers = total rise ÷ riser height wanted, rounded to a whole number
riser height = total rise ÷ risers
treads = risers − 1 (one step down at the top) or = risers (top tread flush)
tread depth = your going, or total run ÷ treads
step along the board = √(riser² + going²) · stringer length = treads × step
angle = arctan(riser ÷ going) · tread cut at the angle to the board edge, riser cut at 90° − angle
notch depth = riser × going ÷ step · throat = board width − notch depth
drop = tread thickness − floor finish still to come · first riser cut = riser − drop
plumb cut at the top = board width × step ÷ going − riser
seat cut at the bottom = (board width × step ÷ going − riser + drop) × going ÷ riser
stringers = (stair width − stringer thickness) ÷ largest spacing, rounded up, + 1
headroom = ceiling height − (riser + (distance from the first riser + nosing) × riser ÷ going)
Worked example
The deck is 105 in above the patio and you would like 7½ in risers: 105 ÷ 7.5 = 14 risers of exactly 7½ in. The top step goes onto the deck, so there are 14 − 1 = 13 treads. With a 10 in going the total run is 13 × 10 = 130 in (10 ft 10 in). Each step along the board is √(7.5² + 10²) = √156.25 = 12½ in, so set the square to 7½ in on the tongue and 10 in on the blade and step it 13 times: the stringer is 13 × 12.5 = 162½ in (13 ft 6½ in) along its edge. The angle is arctan(7.5 ÷ 10) = arctan(0.75) = 36.87°. Each notch is 7.5 × 10 ÷ 12.5 = 6 in deep, so a 2×12 (11¼ in) keeps a throat of 11.25 − 6 = 5¼ in, more than both 3½ in and 5 in. The treads are 1½ in thick and the patio is finished, so the drop is 1½ in and the first riser on the board is cut to 7.5 − 1.5 = 6 in. The plumb cut at the top is 11.25 × 12.5 ÷ 10 − 7.5 = 14.0625 − 7.5 = 6 9/16 in long and the seat cut at the bottom is (14.0625 − 7.5 + 1.5) × 10 ÷ 7.5 = 10¾ in. The cut piece is 161.6 in end to end; with 2 in spare for the ends, buy 14 ft (168 in) boards. For a 36 in wide stair with 2× treads at most 18 in apart: (36 − 1.5) ÷ 18 = 1.92, so 2 spaces and 3 stringers 17¼ in apart. The comfort check 2 × 7.5 + 10 = 25 in (635 mm) is in the usual 24–25½ in.
Code figures: United States (IRC R311.7)
| Riser height | 7¾ in max (R311.7.5.1); tallest and shortest within ⅜ in |
|---|---|
| Tread depth | 10 in min (R311.7.5.2) |
| Nosing | ¾–1¼ in with solid risers when treads are under 11 in (R311.7.5.3) |
| Headroom | 6 ft 8 in from the line of the nosings (R311.7.2) |
| Width | 36 in min (R311.7.1) |
| One flight | 151 in max rise (R311.7.3) |
| Landings | Top and bottom, at least 36 in deep (R311.7.6) |
| Open risers | No 4 in ball through, when the total rise is over 30 in (R311.7.5.1) |
Source: International Residential Code, section R311.7. States and cities adopt different editions and add their own rules.
Code figures: United Kingdom (Approved Document K, private stair)
| Rise | 150–220 mm |
|---|---|
| Going | 220–300 mm |
| Pitch | 42° max |
| 2 × rise + going | 550–700 mm |
| Headroom | 2.0 m (a loft conversion may accept 1.9 m at the centre) |
| Landings | Top and bottom, at least as long as the stair is wide |
| Open risers | No 100 mm ball through, treads overlap at least 16 mm |
Source: Approved Document K (England). Wales, Scotland and Northern Ireland have their own rules. These figures are a summary; always check with your local building office before you build.
Cutting the stringer, step by step
- Check the board: straight, with no big knots near the bottom edge. Crown up.
- Clip stair gauges to the framing square at the riser height on the tongue (short arm) and the going on the blade (long arm).
- Start at the bottom: draw the first riser and tread, then the level seat cut square to the first riser.
- Slide the square along so the tongue mark meets the last blade mark, and draw the next notch. Repeat once for each tread.
- Draw the plumb cut at the top end, then take the drop off the bottom, square to the first riser.
- Cut with a circular saw up to the lines and finish the corners with a handsaw, so you don't over-cut into the throat.
- Try the first stringer in place, then use it as a pattern for the rest.
Typical stringer spacing
- 2× solid wood treads (1½ in, 38 mm): stringers up to about 18 in (450 mm) apart.
- 5/4 wood decking (1 in, 25 mm): about 16 in (400 mm).
- Composite or PVC decking: often 12 in (300 mm) or closer on stairs.
These are typical figures, not rules: always use your tread maker's span table and your local deck guide. The 3½ in throat is a common rule of thumb; the 5 in figure is from the US deck guide AWC DCA 6 (awc.org), which also limits how far a cut stringer may span without support. The US IRC and UK Approved Document K figures here are summarised from the codes and have not yet been checked line by line against the official text (12 October 2026).
Common questions
How do I lay out a stair stringer with a framing square?
Clip stair gauges to the square: the riser height on the tongue and the tread depth (going) on the blade. Lay the square on the board with both gauges against the top edge, draw along the tongue and blade, slide it along to the last mark and repeat once for each tread. For 7½ in risers and 10 in treads each step moves 12½ in along the board.
How long should a stair stringer be?
Each step along the board is √(riser² + going²). Multiply by the number of treads to get the layout length: 13 treads of 7½ in by 10 in give 13 × 12.5 = 162.5 in. Add a little for the ends and buy the next typical board length, here 14 ft (168 in).
What is the throat of a stair stringer?
The throat is the solid wood left between the inside corner of each notch and the bottom edge of the board. It is the board width less the notch depth, riser × going ÷ √(riser² + going²). A 2×12 with 7½ in by 10 in notches keeps 11.25 − 6 = 5.25 in. A common rule is at least 3½ in; the US deck guide AWC DCA 6 asks for 5 in.
Why do you cut the bottom of a stringer shorter?
The treads sit on top of the notches, so they make every step higher by the tread thickness. The steps in the middle still come out equal, but the first one would be too tall. Cutting the tread thickness off the bottom (the drop) fixes that. With 1½ in treads and 7½ in risers the first riser on the board is cut to 6 in.
How many stringers do I need for stairs?
Divide the stair width, less one stringer thickness, by the largest spacing your treads allow, round up and add one. A 36 in stair with 2× treads at up to 18 in apart needs (36 − 1.5) ÷ 18 = 1.92, so 2 spaces and 3 stringers. Composite deck boards usually need closer stringers; check the maker.
What are the code limits for stair risers and treads?
In the US the IRC allows risers up to 7¾ in, treads of at least 10 in and 6 ft 8 in of headroom. In England, Approved Document K allows private stairs a rise of 150–220 mm, a going of 220–300 mm, a pitch up to 42° and 2 × rise + going of 550–700 mm. Check with your local building office.
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