Calculators · Stair Stringer Calculator

Lumber & Framing

Stair Stringer Calculator

Enter the total rise and tread depth to get the shortest board for the stringer, the notch to mark, the throat and the number of stringers.

Total rise

From the finished lower surface to the finished upper surface.

Riser height you want

Picks the number of risers. Fractions work, like 7 3/4.

Number of risers (optional)

Type a whole number to set it yourself. Leave empty to use the riser height.

Tread depth

The run of one step, from nosing to nosing.

Tread thickness (optional)

The tread board that sits on the stringer. Gives the first riser cut.

Stringer board

Its real depth gives the throat. The depths are minimum dry sizes.

Stair width (optional)

Gives the number of stringers, with the spacing.

Stringer spacing, on center (optional)

The AWC deck guide sets 18 in on center as the maximum when cut and solid stringers are combined on stairs wider than 36 in.

How to lay out a stair stringer

The stair calculator gives you the riser height, the number of treads and the total run. A stringer is the board that carries those steps, and it is laid out from the same numbers. Take the riser r, the vertical part of a step, and the tread t, the horizontal part. The tips of the teeth lie on a straight line, the pitch line, which is the top edge of the board. These formulas give the rest:

What you get	Formula
Riser height r	total rise ÷ number of risers
Treads to cut	number of risers − 1
Step along the top edge, tip to tip	√(r² + t²)
Notch depth, square to the edge	r × t ÷ step length
Throat	depth of the board − notch depth
First riser cut	r − tread thickness
Shortest board	(treads × step length) + r × (r − tread thickness) ÷ step length
Board end to the first tip	r × (r − tread thickness) ÷ step length

To mark the board, set the square so the riser on one leg and the tread on the other both touch the top edge. Draw the two lines. They are the first notch. Every other notch is the same triangle moved along the top edge by one step length. At the bottom the stringer is cut level, where it meets the ground or the landing. At the top it ends in a plumb cut against the header or the rim joist.

Example: a 105 in rise on a 2x12

The total rise is 105 in (8 ft 9 in), the risers are about 7 in and the treads are 10 in deep. The board is a 2x12, which is 11 1/4 in deep in real size. These are the numbers already in the calculator.

Step	Operation	Result
Risers and riser height	105 ÷ 7 = 15, then 105 ÷ 15	15 × 7 in
Treads to cut	15 − 1	14
Step along the top edge	√(7² + 10²) = √149	12.2066 in
Tip to tip, first to last	14 × 12.2066	170.892 in
Board end to the first tip	7 × 7 ÷ 12.2066	4.014 in
Shortest board	170.892 + 4.014	174.906 in (14 ft 6 7/8 in)
Notch depth	7 × 10 ÷ 12.2066	5.735 in
Throat on a 2x12	11.25 − 5.735	5.515 in

If the treads are 1 1/2 in thick and sit on top of the stringer, type 1.5 in the tread thickness box. The first riser cut is 7 − 1.5 = 5 1/2 in, and the shortest board becomes 170.892 + 7 × 5.5 ÷ 12.2066 = 174.046 in, or 14 ft 6 1/16 in. Compare it with the straight line from floor to floor that the stair calculator gives, √(105² + 140²) = 175 in. They are close, but they are different measures, and the board length above is the one that counts for the lumber.

Stringer board length by number of risers

This chart uses 7 in risers and 10 in treads, with no tread thickness. For other numbers, use the calculator above.

Risers	Total rise	Treads	Total run	Shortest board	In feet and inches
3	21 in (1 ft 9 in)	2	20 in	28.43 in	2 ft 4 7/16 in
4	28 in (2 ft 4 in)	3	30 in	40.63 in	3 ft 4 5/8 in
5	35 in (2 ft 11 in)	4	40 in	52.84 in	4 ft 4 13/16 in
6	42 in (3 ft 6 in)	5	50 in	65.05 in	5 ft 5 1/16 in
7	49 in (4 ft 1 in)	6	60 in	77.25 in	6 ft 5 1/4 in
8	56 in (4 ft 8 in)	7	70 in	89.46 in	7 ft 5 7/16 in
9	63 in (5 ft 3 in)	8	80 in	101.67 in	8 ft 5 11/16 in
10	70 in (5 ft 10 in)	9	90 in	113.87 in	9 ft 5 7/8 in
11	77 in (6 ft 5 in)	10	100 in	126.08 in	10 ft 6 1/16 in
12	84 in (7 ft)	11	110 in	138.29 in	11 ft 6 5/16 in
13	91 in (7 ft 7 in)	12	120 in	150.49 in	12 ft 6 1/2 in
14	98 in (8 ft 2 in)	13	130 in	162.70 in	13 ft 6 11/16 in

Throat: how much wood is left

Cutting the notches takes wood out, and the throat is what remains under the deepest point of each notch. It is the depth of the board minus the notch depth, and the notch depth depends only on the riser and the tread. For 7 in risers and 10 in treads the notch is 5.73 in deep. The real depths below are the minimum dry sizes of PS 20-25 (January 2025, table 3, checked October 2026).

Board	Real depth	Notch depth	Throat
2x8	7 1/4 in	5.73 in	1.52 in
2x10	9 1/4 in	5.73 in	3.52 in
2x12	11 1/4 in	5.73 in	5.52 in

We did not find a minimum throat in a source we could read, so the calculator reports it and leaves the judgment to your plans, your supplier and your building department. It does tell you when the notch is as deep as the board, because then there would be no wood left.

What the deck guide says about stringers

For stairs on a residential wood deck, the American Wood Council guide DCA 6 (2015 edition, based on the 2012 IRC, checked October 2026) says:

All stringers shall be a minimum of 2x12.
If only cut stringers are used, a minimum of three are required.
For stairs wider than 36 in, a mix of cut and solid stringers can be used, at a maximum spacing of 18 in on center.
Stairs shall be at least 36 in wide.
If the total vertical height of a stairway exceeds 12 ft, an intermediate landing is required.

The guide also limits how far a stringer can span, in a figure we could not read as text, and it allows a post to shorten the span. A later edition of the guide may differ, and your local code can add rules, so check both before you build. For the riser, tread and handrail limits of the IRC, and for stairs with a landing, use the stair calculator. For the deck itself, see the deck calculator.

Frequently asked questions

How long of a 2x12 do I need for a stair stringer?

Enter your rise and tread depth and read the board length at the top of the result. For a 105 in rise with 7 in risers and 10 in treads it is 14 ft 6 7/8 in. That is the least a straight board can measure and still hold the whole stringer, so buy the next length your supplier sells above it. The American Softwood Lumber Standard says standard lengths come in multiples of 1 or 2 feet, but each yard stocks its own. The calculator does not assume any.

How do I calculate stair stringers?

Divide the total rise by the riser height you want and round to a whole number of risers. Divide the rise by that number to get the exact riser. There is one tread fewer than risers. Each step is √(riser² + tread²) long along the top edge of the board, and the notch is the same triangle repeated. The board must reach from the foot, where the first riser is cut, to the plumb cut at the top. The calculator does it and gives the board length, the notch and the throat.

Should stair stringers be 2x10 or 2x12?

The American Wood Council deck guide, DCA 6 in its 2015 edition, says all stringers shall be a minimum of 2x12 for residential wood deck stairs. The depth matters because the notch takes wood out. With 7 in risers and 10 in treads the notch is 5.73 in deep. A 2x12, which is 11 1/4 in deep in real size, leaves a throat of 5.52 in. A 2x10, at 9 1/4 in, leaves 3.52 in. Check your local code and your plans before you choose.

What is the throat of a stair stringer?

The throat is the wood left under the inside corner of a notch, measured square to the edge of the board. It equals the depth of the board minus the depth of the notch. The notch depth is riser × tread ÷ the length of one step. We did not find a minimum throat in a source we could open, so this calculator shows it and does not judge it. Ask your supplier, your plans or your building department.

How many stair stringers do I need?

The AWC deck guide says a minimum of three cut stringers when only cut stringers are used. For stairs wider than 36 in it allows cut and solid stringers at a maximum spacing of 18 in on center. The calculator rounds the width ÷ spacing up and adds one, and never shows fewer than three. A 48 in wide stair at 16 in on center needs 4. The guide also asks for stairs at least 36 in wide.

Why is the first riser cut shorter?

The treads sit on top of the stringer, and each one adds its thickness to the step. At the bottom, the ground is where the first step starts, so there is no tread below to add. If the first riser cut were a full riser, the first step would be taller than the rest by the thickness of the tread. The first cut is the riser minus the tread thickness. Type the thickness and the calculator shows that cut.

Does this check the span of the stringer?

No. The span a stringer can safely cover, the footing, the way it attaches to the deck and the railing are structural questions. The deck guide shows the maximum stringer spans in a figure, which we could not read as text, and it points to a post or an intermediate landing when the span is too long. Use the guide, your local code or an engineer.