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Stair Stringer Calculator

Lay out a cut stringer: how much to drop the bottom, where to mark each notch, how much wood is left under the notches, and the shortest board that will do, drawn to scale.

Stair and board

Units
Finished floor to finished floor.
Nosing to nosing; equals the length of each seat cut.
Actual thickness, e.g. 1 in for 5/4 decking, 1 1/2 in for 2x lumber.
At the top of the stair

13 notches, first riser cut 6 11/16 in, others 7 11/16 in, seats 10 1/2 in, throat 5 1/16 in, shortest board 14 ft 13/16 in. Drawing and details

More options
If the stringer sits on a subfloor or slab and flooring goes down afterwards, enter its thickness.
Only affects the drawing.
Outside to outside of the outer stringers.
On centre. 18 in is the maximum in AWC's DCA 6 deck guide; follow your own design or local rules.

Worked example: edit any value

Stringer layout

First riser cut≈ 6 11/16 inbottom, after the drop
Other riser cuts≈ 7 11/16 intongue of the square
Seat cuts10 1/2 in13 seats, blade of the square
Shortest board14 ft 13/16 innext even length: 16 ft

Throat ≈ 5 1/16 in Mark every ≈ 13 in Pitch 36.3° Top seat to floor ≈ 8 11/16 in Stringers 3

3 stringers for a 36 in wide stair at no more than 18 in apart, outer stringers at the edges.

Cut stringer layoutCut stringer drawn to scale with 13 tread seats. First riser cut 6 11/16 in, other riser cuts 7 11/16 in, seats 10 1/2 in long, marks every 13 in along the board edge, throat 5 1/16 in, shortest board 14 ft 13/16 in.first cut6 11/16 inmark every 13 inthroat 5 1/16 inshortest board 14 ft 13/16 in8 11/16 inupper finished floorlower finished floor
To scale. The dashed outline is the uncut board; copper dots are the marks where the framing square meets the edge. The copper line shows the throat. Treads are ghosted on their seats.

Mark positions along the board edge

Distances from mark 1 (top of the first riser cut) along the top edge. Height and horizontal columns are measured from the bottom of the stringer and the first riser cut.

MarkAlong edgeHeightHorizontal
10 in≈ 6 11/16 in0 in
2≈ 13 in≈ 14 7/16 in10 1/2 in
3≈ 26 1/16 in≈ 22 1/8 in21 in
4≈ 39 1/16 in≈ 29 7/8 in31 1/2 in
5≈ 52 1/8 in≈ 37 9/16 in42 in
6≈ 65 1/8 in≈ 45 5/16 in52 1/2 in
7≈ 78 3/16 in53 in63 in
8≈ 91 3/16 in≈ 60 11/16 in73 1/2 in
9≈ 104 1/4 in≈ 68 7/16 in84 in
10≈ 117 1/4 in≈ 76 1/8 in94 1/2 in
11≈ 130 5/16 in≈ 83 7/8 in105 in
12≈ 143 5/16 in≈ 91 9/16 in115 1/2 in
13≈ 156 3/8 in≈ 99 5/16 in126 in
Layout steps with your numbers
  1. Set the framing square (or stair gauges)tongue (riser) 7 11/16 in · blade (going) 10 1/2 inClamp gauges at these marks on the outside edge of the square so every notch is identical.
  2. Mark one step along the edge, then repeatstep along edge = √(h² + g²) = √(7.7143² + 10.5²) = 13.0292 inMark 13 notches. Measure each mark from the first one (table below) instead of stepping off, so small errors do not add up.
  3. Drop the bottom by the tread thicknessfirst riser cut = h − tread thickness = 7.7143 − 1 = 6.7143 inCut this much off the bottom level cut. Once treads are on, the first step then equals every other step.
  4. Check the remaining depth (throat)throat = board width − h × g ÷ √(h² + g²) = 11.25 − 7.7143 × 10.5 ÷ 13.0292 = 11.25 − 6.2168 = 5.0332 inMeasured square to the board edge, from the inside corner of a notch to the bottom edge.
  5. Top of the stringertop seat to upper finished floor = 8.7143 inOne riser plus one tread thickness. The plumb cut at the top bears against the header or rim; hangers or a ledger are a structural detail to confirm locally.
  6. Shortest board that contains the stringer14 ft 13/16 in (168.7876 in)Measured along the board, from the bottom of the first riser cut to the top corner of the last seat. Add an allowance for trimming and checks.
Cut list and dimensions (table)
ItemValueNote
Risers / tread seats14 / 13
Riser height (finished)≈ 7 11/16 in7.7143 in
First riser cut on stringer≈ 6 11/16 in6.7143 in
Other riser cuts≈ 7 11/16 in
Seat cut (going)10 1/2 in
Step along board edge≈ 13 in13.0292 in
Throat (remaining depth)≈ 5 1/16 in5.0332 in
Pitch (seat cut to board edge)36.30°riser cuts meet the edge at 90° − pitch
Top seat to upper floor≈ 8 11/16 in
Shortest board14 ft 13/16 inlumber is usually sold in 2 ft steps: 16 ft
Stringers3from width and spacing

What this stringer calculator adds

The stair calculator decides the stair: how many risers, how tall, how long. This page turns that stair into a board you can cut. It works out each cut from the actual board width and tread thickness, rather than handing you a diagonal and leaving the rest to you.

  • First riser cut. Treads sit on top of the seat cuts, so if every notch were one full riser high, the first step would end up a tread thickness taller than the rest, and the top step a tread thickness shorter. Cutting the bottom of the stringer down by the tread thickness fixes both. If finished flooring will be laid around the bottom of the stringer later, the first cut grows by that thickness instead.
  • Mark positions. Each notch is one step diagonal, √(riser² + going²), along the board edge. The table gives every mark measured from the first, so a small error at one notch does not accumulate.
  • Throat. The depth of solid wood left between the inside corner of each notch and the bottom edge of the board. Cutting notches removes a triangle of wood with height riser × going ÷ step diagonal, measured square to the edge. What remains is what spans the stair.
  • Shortest board. The cut stringer is projected onto the board's length to find the shortest straight piece that contains it, from the heel of the bottom cut to the top corner of the last seat. It is longer than the pitch-line diagonal most calculators show.

Worked example: 14 risers on a 2x12

The example uses a 108 in rise, 7 3/4 in maximum riser and a 10 1/2 in going, so 14 risers of 7.714 in and 13 tread seats. Treads are 1 in thick and the stringer is a 2x12, which is 11 1/4 in deep.

  • First riser cut: 7.714 − 1 = 6.714 in (about 6 11/16 in). Every other riser cut is 7.714 in.
  • Step along the edge: √(7.714² + 10.5²) = 13.029 in. Thirteen marks span 12 × 13.029 = 156.35 in.
  • Throat: 11.25 − (7.714 × 10.5 ÷ 13.029) = 11.25 − 6.217 = 5.03 in.
  • Top seat to the upper floor: one riser plus one tread, 8.714 in.
  • Shortest board: 168.79 in, about 14 ft 13/16 in. A 14 ft board is just too short, so you would buy 16 ft. The pitch-line diagonal for this stair is 182.4 in, but that line runs through the nosings and is not a board length.

These numbers are part of the automated test fixtures (S1 on the methodology page), and the stringer's area is checked independently against a separate formula.

Laying out and cutting, briefly

  1. Crown the board: sight along it and put any bow upward, so load straightens it.
  2. Clamp stair gauges on a framing square at the riser height (tongue) and going (blade).
  3. Mark the first notch near the bottom, then measure each following mark from the first one using the table. Draw the seat and riser lines at each mark.
  4. Mark the bottom level cut, then move it up by the first-riser drop. Mark the top plumb cut.
  5. Cut the long lines with a circular saw, stopping at the corners, and finish the inside corners with a hand saw or jigsaw. Over-cutting past the corner weakens the throat.
  6. Check the first stringer in place before using it as a pattern for the others.

What it does not decide

Geometry is not structure. This page does not check whether a board can span the stair, how the top is fixed (hangers, ledger, header or flush mount), or what the bottom bears on. AWC's prescriptive deck guide, DCA 6 (2015 edition), for example, calls for stringers of at least 2x12, limits how far they span, asks for at least three when only cut stringers are used, and spaces stringers at no more than 18 in on centre on wider stairs. Those are prescriptive rules for decks, not universal limits. Get spans and connections confirmed by your building department or a qualified professional.

Questions people ask

These are questions Google showed under "People also ask" for related searches (checked 2026-10-24), answered here with the same tested formulas the calculators use.

What is the stringer on stairs?

A stringer is the sloping board that carries the treads. A cut (notched, sawtooth) stringer has notches cut into it for each tread and riser. A solid or housed stringer stays whole, with the treads fixed to its face or set into grooves. Most simple stairs and deck stairs use two or three cut stringers.

What is the formula for stair stringers?

Riser height h = total rise ÷ risers. Each notch is one step along the board edge: √(h² + going²). The first riser cut is h − tread thickness, so the first finished step matches the others. The wood left under each notch (the throat) is board width − h × going ÷ √(h² + going²).

For 14 risers of 7.714 in, a 10 1/2 in going and 1 in treads on a 2x12: marks every 13.03 in, first cut 6.71 in, throat 5.03 in, shortest board 168.8 in. The calculator above works it out for your numbers.

Do I need 2x10 or 2x12 for stair stringers?

For cut stringers, usually a 2x12. Notching removes wood: with 7 11/16 in risers and 10 1/2 in goings, a 2x12 (11 1/4 in deep) keeps about 5 in below each notch, but a 2x10 (9 1/4 in) keeps only about 3 in. AWC's prescriptive deck guide (DCA 6, 2015 edition) calls for stringers of at least 2x12. How far a stringer may span, and whether it needs mid-supports, is a structural question for your plans reviewer.

How long is 2x12 for a 5 step stringer?

It depends on the riser and going. One example: 5 risers of 7 1/2 in (37 1/2 in rise), 10 1/2 in goings and 1 in treads need about 51 in (4 ft 3 in) of board for the cut stringer. If "5 steps" means five tread notches (6 risers, 45 in rise), it is about 64 in (5 ft 4 in). An 8 ft 2x12 covers either. Enter your own numbers above to get the exact shortest board.

What is the 27 rule for stair stringer dimensions?

It is not a building-code rule, and websites describe it inconsistently: some say riser + tread = 27 in, others say 2 × riser + tread = 27 in. The second is a version of the old comfort formula, 2 × riser + going, which this site shows for every layout (25.9 in for the 9 ft example). Use it to compare layouts. The code limits on riser height and tread depth still apply.