CARPENTRY
Calculate stair stringer length, stock-board length, angle and estimated stringer count. Enter your measurements below and the estimate updates instantly.
Formula, validation and worked example reviewed November 12, 2026. See our calculation methodology.
4 stringers · 15 risers at 7.2 in · Step slope 35.8°
15.23 ft diagonal plus allowance; not a finished stringer or cut length.
14 treads; count assumes two outer stringers across entered width.
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Cut planning and safety
To estimate stair stringer length, use total rise and total run as the legs of a right triangle. This calculator finds that diagonal, adds your stock allowance, chooses the next common board length, and estimates stringer count from stair width and maximum spacing.
A stair stringer forms the hypotenuse of a right triangle whose legs are the total vertical rise and the total horizontal run. Using the Pythagorean theorem, we compute the geometric diagonal and then add your layout stock allowance:
where:
Rise/run diagonal = square root of (total rise squared + total run squared)Stock-length estimate = rise/run diagonal + allowance; actual cut geometry is not modeledStringer count = round(stair width / maximum spacing) up + 1Stock length = next common board length at or above required stockShows geometric diagonal and next common 2×12 stock length (8, 10, 12, 14, 16, 18, 20 ft).
| Total Rise | Risers / Treads | Diagonal Length | Recommended 2×12 Stock |
|---|---|---|---|
| 42 in (6 risers) | 6 risers / 5 treads | 5.30 ft | 8 ft board |
| 60 in (8 risers) | 8 risers / 7 treads | 7.68 ft | 10 ft board |
| 84 in (12 risers) | 12 risers / 11 treads | 11.58 ft | 14 ft board |
| 96 in (13 risers) | 13 risers / 12 treads | 12.81 ft | 14 ft board |
| 108 in (15 risers) | 15 risers / 14 treads | 14.73 ft | 16 ft board |
Find the total rise and total run, then use them as the two legs of a right triangle. The diagonal is a geometric planning reference, not the finished stringer length. Top and bottom cuts, tread thickness and connection details require a separate layout.
You must cut off the thickness of one tread material from the bottom of the stringer. When you install treads, the bottom tread rests on top of the stringer, restoring the exact uniform riser height.
A 36-inch stair with standard 2x lumber treads uses 3 stringers (spaced ~16" OC). A 48-inch stair uses 4 stringers. If using composite decking, use 4 stringers for 36" (12" OC) and 5 stringers for 48".
No. It is the diagonal plus your allowance rounded to a common board length. Actual cuts and connections depend on the full stair detail.
No. Notch depth and remaining wood must be checked against the board, span, species, grade, loads, and applicable design requirements.
The tool divides stair width by your maximum spacing, rounds up, and adds one outer stringer. Treat this as planning guidance only.
Yes. Span, lumber properties, notching, loads, and the governing design can require support or a landing before the full diagonal length.
Verify finished rise, tread layout, board size and quality, throat, span, spacing, attachments, bearing, landings, guards, handrails, and local approval.
Use the calculator to plan material, then verify the complete stair geometry, remaining throat, support and connections before cutting.
The right-triangle diagonal comes from total rise and total run. It is a geometry reference, not a finished cut length.
The calculator adds your allowance and rounds up to a common board length. Top and bottom cuts still require a full layout.
Count is based on stair width and entered maximum spacing. Tread material, loads, lumber, notching and local requirements can change the design.
When cutting the bottom of the stringer, subtract one full tread thickness from the bottom riser cut so your finished first step height matches all others.
Standard 2x dimensional wood treads span up to 16 inches on center. Composite decking treads (Trex, TimberTech) are more flexible and often require 12 or 9 inches on center.
Method references: American Wood Council stair stringer guidance · Simpson Strong-Tie installer guidance