Find the length of rafter board needed to span a roof section, from its rise and run.
How it works
The rafter forms the hypotenuse of a right triangle: length = √(rise² + run²). A roof rising 4 feet over a 12-foot run needs a rafter about 12.65 feet long.
What this does not include
This calculates the theoretical rafter length from rise and run alone. Real lumber purchases should add an allowance for the overhang and the ridge and eave cuts, which this calculator doesn’t include.
How to use this calculator
- Enter the rise.
- Enter the run.
A worked example
A roof with 4-in-12 pitch (rise 4, run 12): rafter length = √(4²+12²) = 12.6491 per foot of run.
A 6-in-12 pitch: rafter length = 13.4164 per foot of run — a steeper roof needs a longer rafter to span the same horizontal distance.
What the variables mean
| Variable | Meaning |
|---|---|
| Rise | Vertical rise per unit of run |
| Run | Horizontal run (conventionally 12 inches in roofing) |
Edge cases worth knowing
A steeper pitch always requires a longer rafter for the same horizontal span — the Pythagorean theorem guarantees this, since a bigger rise adds more to the hypotenuse than the run alone would cover.
A rise of zero makes for a flat roof, where rafter length simply equals the run — the calculator declines to show a result for that degenerate case since it’s not really a sloped rafter calculation anymore.
How is this different from this site’s roof pitch calculator?
Roof pitch calculates the slope’s steepness (as a ratio and an angle) from the same rise and run, but doesn’t report the physical board length needed — this calculator answers that separate question.
What’s a typical overhang allowance to add?
Common practice adds 12 to 24 inches beyond the calculated length for the eave overhang, though this varies by design and local building convention.
Does rafter length change with roof pitch?
Yes — for the same run, a steeper pitch (higher rise) means a longer rafter, since the hypotenuse grows as the triangle gets taller.
