Slope length, rise, and pitch angle
Use geometric length to understand the triangle and estimate stock. It is not a finished cut length. Ridge board thickness, fascia details, birdsmouth geometry, heel height, and plumb cuts can change the required piece.
For converting measured rise and run into pitch, the Roof Pitch Calculator provides the rise-per-twelve value.
The formula
A common rafter follows the hypotenuse of the run-and-rise triangle. Overhang is entered horizontally, not as a sloped tail length. The result is a geometric reference measured to the ridge center, before framing cut deductions.
Worked example
A 12 ft run plus a 1 ft horizontal overhang at a 6:12 pitch gives 13 ft of total run and 6.5 ft of rise across that distance. The corresponding slope length is 14.5344 ft and the angle is 26.5651 degrees.
How to use this calculator
- Enter horizontal run to ridge center, horizontal eave overhang using the units shown.
- Set rise per 12 horizontal inches.
- Calculate and review geometric rafter length alongside the supporting quantities.
Run is different from total building span
For a symmetrical gable, the horizontal run to the ridge center is usually half the relevant span. Enter that run directly rather than entering the entire width. The overhang is added to it. If the ridge is off center or the roof has unequal slopes, each common rafter side requires its own calculation.
Prepare a framing cut layout
Actual cut marks depend on the framing arrangement and how measurements are referenced. A ridge board can require a deduction, and the tail may terminate against a fascia or other detail. Hip, valley, and jack rafters use different geometry. Structural member size, support, connections, and loads must be determined separately from this right-triangle calculation.
Assumptions & limitations
What this calculation assumes
- A straight common rafter follows one constant roof pitch.
What to keep in mind
- Excludes cut deductions, hip and valley rafters, member sizing, and load checks.
Common questions
Is overhang measured along the rafter?
No. Enter the horizontal projection. The calculator converts it into sloped length with the rest of the run.
Is this the length I should cut?
It is the geometric reference length. Apply the framing details and cut allowances from the actual layout before cutting.
Can I enter the entire building width as run?
For a symmetrical gable, use the horizontal distance from one support to the ridge center, usually half the relevant span.
Sources & further reading
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