How this instrument works
A common rafter, the horizontal ceiling joist beneath it, and the vertical distance between the ridge and the wall plate form a right triangle: run along the bottom, rise up one side, and the rafter itself as the sloped hypotenuse connecting the two. That is exactly the shape the Pythagorean theorem was built to solve — for a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
This instrument takes the run, the horizontal distance from the outside wall to a point below the ridge, and the rise, how far the roof climbs vertically over that same run, both in feet. It squares each, adds them together, and takes the square root of the total to return the rafter's true length along its slope — the actual board length to measure and cut, not the shorter horizontal run a tape measure would give walking the ceiling joist below it.
Framers have used this relationship for centuries, often via a framing square's rafter tables or the 'stepping off' method rather than raw arithmetic, but the underlying math is identical either way. This instrument skips the tables and steps straight to the number, useful for a quick double-check, an unusual pitch not covered by a standard table, or planning stock length before cutting.
- Enter Run (ft) — the horizontal distance from the outside of the wall's top plate to a point directly below the ridge.
- Enter Rise (ft) — how far the roof climbs vertically over that same run.
- Read Rafter length (ft) beneath both fields — the true sloped board length, recalculated instantly as either input changes.
- This figure is the rafter's theoretical length along the roof slope; add extra stock for the ridge cut, birdsmouth notch and any overhang beyond the wall before cutting.
- For a roof pitch given as 'rise per 12 in of run' rather than matching feet, use this site's roof pitch instrument first to convert it to a rise and run pair.
Worked example — a 12 ft run with a 6 ft rise
Enter 12 into Run (ft) and 6 into Rise (ft) — a roof spanning 12 ft horizontally that climbs 6 ft vertically over that same distance. Squaring and adding gives 12² + 6² = 144 + 36 = 180.
Rafter length (ft) reads 13.4164 — the square root of 180. That is the true board length to measure along the slope for this rafter, nearly a foot and a half longer than the 12 ft horizontal run alone would suggest.
Questions
Why is the rafter longer than the horizontal run?
Because the rafter runs along the roof's slope, not flat like the ceiling joist beneath it — it is the hypotenuse of a right triangle, always the longest side. For a 12 ft run and 6 ft rise, the rafter comes out to about 13.42 ft, roughly 12% longer than the run alone, purely from climbing at an angle rather than running level.
Does this length include the overhang past the wall, or the birdsmouth notch?
No — this is the theoretical rafter length from the wall's top plate to the ridge only, based purely on run and rise. Any eave overhang extends the board beyond that figure, and a birdsmouth notch cut where the rafter sits on the wall plate uses up a bit of length as well, so add both when sizing actual stock to buy.
How do I get run and rise if I only know the roof pitch, like '6/12'?
A '6/12' pitch means 6 in of rise for every 12 in of run, so for any given run in feet, multiply that run by 6/12 = 0.5 to get the matching rise in feet. This site's roof pitch instrument converts a rise-per-12-in figure into a ratio and angle directly if you'd rather not do that step by hand.
Is this the same formula used for stairs or a wheelchair ramp run?
Yes — any straight incline described by a horizontal run and a vertical rise forms the same right triangle, whether it's a roof rafter, a stringer, or a ramp, and the Pythagorean theorem finds the sloped length the same way in every case. Only the typical scale and the building-code minimums differ between applications.
What if my run and rise aren't in the same unit?
Convert both to the same unit before entering them — this instrument expects run and rise both in feet. Mixing feet and inches, or feet and a rise given as a ratio, produces a meaningless hypotenuse, since the Pythagorean theorem only works when both legs of the triangle share one consistent unit.