Rafter length calculator
Enter the building span, the pitch, the ridge board thickness and the overhang. You get the rafter length, the total length with overhang and the plumb and seat cut angles, for common or hip and valley rafters.
Enter your measurements
Line length
160 3/16in
Exact geometry
- Total length with overhang
- In the app
- Plumb cut angle
- In the app
- Seat cut angle
- In the app
- Rise
- In the app
- Rafter multiplier
- In the app
Every result is in Truemark
The free web version shows the main result and the drawing. Truemark gives you every mark and measurement, and exports a cut sheet. It is free to download.
How to lay it out
Measure the span
Measure the full width of the building, outside of wall to outside of wall, and enter the roof pitch as rise per 12″ of run.
Mark the plumb cut
Set your speed square or saw to the plumb cut angle and mark the ridge end of the rafter.
Measure the line length
Measure the line length along the rafter from the plumb cut and mark the birdsmouth seat cut at the seat cut angle.
Add the overhang
Measure on past the birdsmouth to the total length with overhang and mark the tail cut.
Cut and test
Cut one rafter, test it on the ridge and wall, and use it as the pattern for the rest.
Good to know
- FabLayout runs the same code as Truemark; the result is exact geometry.
- Source: Plane trigonometry; same calculation as the Truemark app
Method and formula
Roof pitch is given as rise per 12″ of run: a 6/12 roof rises 6″ for every 12″ across. The run is half the span less half the ridge board, and every length follows from it.
- Run = span ÷ 2 − ridge thickness ÷ 2, and rise = run × pitch ÷ 12.
- Rafter multiplier = √(144 + p²) ÷ 12 for a common rafter, √(288 + p²) ÷ 12 for a hip or valley.
- Line length = run × multiplier, and the overhang adds overhang run × multiplier.
- Plumb cut angle = arctan(p ÷ 12) from horizontal; the seat cut is 90° minus that. A hip or valley runs √2 times further, so its plumb cut is flatter.
Worked example
The page defaults: a 288″ span, 6/12 pitch, 1½″ ridge and 12″ overhang. The run is half the span less half the ridge, and the rise is 71.625″. The common rafter multiplier is 1.118, so the line length is 160.1584″ and the total with overhang 173.5748″. The plumb cut is 26.5651° and the seat cut 63.4349°. For a hip at 6/12 the multiplier is √324 ÷ 12 = 1.5.
Questions
Why is the ridge board thickness subtracted?
The rafters meet the faces of the ridge board, not its centre. Each side loses half the board's thickness from its run.
What is the rafter multiplier?
The length of rafter for every inch of run. For a common rafter it is √(144 + p²) ÷ 12, so a 6/12 roof needs 1.118″ of rafter per inch of run.
How are hip and valley rafters different?
They run diagonally across the plan, √2 times as far as a common rafter for the same rise. Their multiplier is √(288 + p²) ÷ 12, which is 1.5 for a 6/12 pitch.
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