Rafter Calculator: 13.42 ft Rafter for a 24 ft Span

What does rafter length 13.42 ft mean?

It means each rafter on a 24 ft span at 6/12 pitch is 13.42 feet long, measured along the slope. The run is half the span, 12 feet, and the rise is the run times the pitch over 12, which is 6 feet; the rafter is the hypotenuse of that right triangle, the square root of 144 plus 36, which is the square root of 180, or 13.42 feet. The overhang is zero on the defaults, so nothing is added past the wall plate; with a 2 ft overhang the same rafter would be 15.65 feet, since overhang adds slope length, not flat length.

Output · formula · meaning

Three things to check before you trust the number

First, check the span you measured: it is wall plate to wall plate, and the run is half of it, not the whole span — using the full span as the run nearly doubles the rafter. Second, read the pitch off the roof, not off a habit: 6/12 means 6 inches of rise per foot of run, and the roof pitch chart converts slope to angle and rise. Third, judge the overhang honestly: it adds slope length at the pitch factor, about 1.12 ft per foot at 6/12, not one flat foot per foot.

Worked example

24 ft span, 6/12 pitch, 0 ft overhang. Run: 24 ÷ 2 = 12 ft. Rise: 12 × 6 ÷ 12 = 6 ft. Rafter: √(12² + 6²) = √180 = 13.42 ft. In practice that means cutting each rafter 13.42 ft long along the slope, and trimming the birdsmouth on site rather than shortening the plan length. If the same span carried an 8/12 pitch instead, the rise would be 8 ft and the rafter 14.42 ft — the span alone would be identical.

Every branch, checked

With a 30 ft span instead of 24 ft, the run rises to 15 ft, the rise to 7.5 ft, and the rafter to 16.77 ft. With an 8/12 pitch, the run stays 12 ft but the rise rises to 8 ft and the rafter to 14.42 ft. With a 4/12 pitch, the rise falls to 4 ft and the rafter to 12.65 ft. With a 2 ft overhang, the run and rise stay 12 ft and 6 ft but the rafter rises to 15.65 ft, since overhang adds slope length. Span, pitch and overhang each move the length on their own, so a wrong pitch is as costly as a wrong span.

The reverses, worked backwards

The span behind 13.42 ft is 24 ft: at 20 ft the rafter is 11.18 ft (10 ft run, 5 ft rise, 6/12 pitch, 0 ft overhang); at 30 ft it is 16.77 ft (15 ft run, 7.5 ft rise, 6/12 pitch, 0 ft overhang). The pitch behind 13.42 ft is 6 in per ft: at 4 the rafter is 12.65 ft (12 ft run, 4 ft rise, 4/12 pitch, 0 ft overhang); at 8 it is 14.42 ft (12 ft run, 8 ft rise, 8/12 pitch, 0 ft overhang). Each reverse moves one input and holds the rest, so the step is exactly one span or one pitch change. The overhang has no lower neighbor on the defaults, since it already sits at zero — its branch above shows the upward step instead.

What the defaults assume

The defaults assume a gable roof spanning 24 ft from wall plate to wall plate, a 6/12 pitch, and no overhang past the plate. They do not assume a ridge board, birdsmouth cuts, collar ties or fasteners — a rafter cut on site is trimmed at the birdsmouth, and the ridge board is bought by the length, not by the rafter.

Who uses this

• A homeowner sizing rafters for a shed: the 13.42 ft length settles the lumber order before the first rafter is cut.
• A DIY builder framing a garage: the same maths on the span alone gives the rafter, not a whole house.
• A contractor quoting a roof: span, pitch, overhang — the quote follows the same three steps, and the overhang line shows the client why.
• A landlord budgeting a porch roof: the span off the plans, halved for the run, gives the rafter line on the roof budget.

Accuracy & limitations

The arithmetic is exact for the inputs entered; the judgement is the span measurement and the pitch. Real rafters are cut with a birdsmouth that shortens the effective bearing length slightly, and the lumber on the shelf overrides any planning figure; a span measured outside the plates over-orders, and a pitch read off a different roof under-orders length. Treat 13.42 ft as the planning length for a 24 ft span at 6/12 pitch, and cut long, trimming on site.

Cite this calculator

Bright Side Kit, “Rafter Calculator: 13.42 ft Rafter for a 24 ft Span”, https://brightoolbox.com/rafter-calculator/, accessed 3 November 2026. Students and researchers: cite the calculator name, the page URL and the date you used it, and quote the defaults (24 ft span, 6/12 pitch, 0 ft overhang) so the 13.42 ft result can be checked.

Frequently asked questions