The physical relationship
Pitch angle is arctangent of rise ÷ run. Rafter length from ridge to wall is the hypotenuse: √(run² + rise²). If an overhang is included, the calculator extends the horizontal run by that amount and calculates the longer hypotenuse at the same slope. It shows geometric line length, not a cut list.
A checked case
With a 3.0 m horizontal run and 1.2 m rise, pitch is arctan(1.2 ÷ 3.0) = 21.8°. The wall-line rafter is √(3.0² + 1.2²) = 3.23 m. A 0.45 m horizontal overhang makes the total run 3.45 m; at the same rise-to-run ratio its line length is about 3.72 m. That is the board line before plumb cuts, birdsmouth, ridge deduction, or stock allowance.
Useful planning use
Use it to understand a measured roof slope, compare a drawing with an existing building, or make an early material-length allowance before a structural design is prepared.
Failure modes in this measurement
A half-span is the run for a symmetrical gable, not the full building width. Measuring rise from finished ceiling instead of from the matching horizontal reference changes the angle. A slope expressed as 4:12 is a ratio, not 4 degrees. Adding a horizontal overhang directly to a sloping board length is also wrong; it must follow the roof angle.
What makes this quantity different
The roofing page turns a known pitch and footprint into roof surface area for covering material. This page derives pitch from rise and run and returns one rafter line length. It does not size rafters, calculate snow or wind load, specify connections, or validate a roof structure.
Field check before acting
Take rise and run from the same roof plane and unit system. Confirm whether a drawing gives clear span, centreline span, or wall-to-ridge run. For repairs, inspect the existing framing rather than assuming a visible fascia is level. Use the displayed length only as a geometry check; cuts and member selection belong on a verified framing plan.
Limits of the model
Roof work has fall and structural hazards. Local building rules, loading, timber grade, spans, supports, openings, and connections require a qualified designer or builder where relevant. This estimate should not be used alone to cut or alter structural framing.