# Stair Stringer Calculator

> Enter the total rise, tread depth, board size and stair width. You get the framing square numbers to mark the board, the shorter first riser, the throat depth left under the deepest notch, the stock board length and how many stringers to cut. A 105 in rise needs 3 stringers of 14 ft.

Canonical: https://receiptscanner.co/tools/stair-stringer-calculator
Updated: 2026-10-28 · Sources re-checked by: 2027-10-28

This is a free interactive calculator that runs in the browser. Nothing you type is stored or sent. Results are estimates.

## How it works

Steps come from the total rise ÷ the riser you want, rounded, so riser = total rise ÷ steps. Mark the board with a framing square at the riser on one blade and the tread on the other. Throat depth = board width − (riser × tread ÷ √(riser² + tread²)); under about 3 1/2 in the stringer is weak at its deepest notch. The bottom riser is cut shorter by the tread thickness, because the tread adds that height back. Board length: the slope line √(rise² + run²), rounded up to the next stock length. Stringers = the stair width less one stringer thickness ÷ the most you allow between them, rounded up, plus 1.

**Throat depth left under the deepest notch (rule of thumb: keep at least 3 1/2 in)**

| Riser and tread | On a 2×10 (9 1/4 in) | On a 2×12 (11 1/4 in) |
| --- | --- | --- |
| 7 in and 11 in | 3.34 in | 5.34 in |
| 7.5 in and 10 in | 3.25 in | 5.25 in |
| 7.75 in and 10 in | 3.12 in | 5.12 in |

**Board length for common rises (7.5 in riser, 10 in tread)**

| Total rise | Steps | Slope length | Stock board |
| --- | --- | --- | --- |
| 60 in | 8 | 7.68 ft | 8 ft |
| 84 in | 11 | 10.88 ft | 12 ft |
| 105 in | 14 | 13.93 ft | 14 ft |
| 120 in | 16 | 16.01 ft | 18 ft |

## Worked example: 105 in rise, 10 in tread, 2×12 board, 36 in wide stairs

1. Steps: 105 ÷ 7.5 = 14 risers of exactly 7 1/2 in. Treads: 13, total run 130 in.
2. Framing square: 7 1/2 in on one blade and 10 in on the other.
3. Throat depth on a 2×12: 11.25 − (7.5 × 10 ÷ 12.5) = 5.25 in. Enough wood remains.
4. Bottom cut: with 1 in treads, the first riser is cut to 6 1/2 in.
5. Board length: slope line √(105² + 130²) = 167.1 in = 13.93 ft, so a 14 ft board. A 36 in stair with stringers no more than 18 in apart needs 3.

## FAQ

### What is a stair stringer?
The sloped board that carries the treads. For cut stringers, notches are cut into a 2×10 or 2×12 so each tread has a flat seat and each riser a vertical face.

### How do I use a framing square to lay out a stringer?
Set the riser measurement on one blade and the tread on the other, so both numbers touch the top edge of the board. Mark the notch, slide the square along and repeat for each step. Stair gauges clamped at those two numbers keep it consistent.

### Why is the bottom riser cut shorter?
Because the treads sit on top of the stringer. Cutting the bottom step short by the tread thickness makes the first step from the ground the same height as all the others once the tread is on.

### What is the throat of a stringer?
The least wood left between the inside corner of a notch and the bottom edge of the board. A thin throat can split under load, so many builders want at least 3 1/2 in left.

### How many stringers do I need?
It depends on the width, the tread material and your local rules. Treads that span a long way need more support. This page lets you enter the most you allow between stringers, and counts them for you.

### Should I use a 2×10 or a 2×12?
A 2×12 leaves more throat, so it suits taller risers and shorter treads. A 2×10 can work with a lower riser and a longer tread. The throat figures above show the difference for your numbers.

## Sources

- [International Residential Code, chapter 3 (R311.7 stairways): riser, tread and headroom limits. Local codes can differ](https://codes.iccsafe.org/content/IRC2021P1/chapter-3-building-planning) (checked 2026-10-28)
- [OSHA 1926.1052: stairways on construction sites (riser and tread uniformity)](https://www.osha.gov/laws-regs/regulations/standardnumber/1926/1926.1052) (checked 2026-10-28)
- [Stairs: rise, run and the 2 x riser + tread comfort rule](https://en.wikipedia.org/wiki/Stairs) (checked 2026-10-28)

This calculator is an estimate for planning. Check the layout on a spare board before you cut, and confirm stringer spacing, lumber grade and fastening with your building department.