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Roof pitch calculator: slope, angle, and rafter line

Convert a rise-over-run roof pitch into degrees and a slope factor, and see the sloped rafter length across half a span.

Direct answer

Roof pitch is rise divided by run over a fixed run, usually 12. The angle from horizontal is arctan(rise / run), and the slope factor sqrt(1 + (rise / run)^2) converts any horizontal distance into its sloped length.

Interactive tool

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Formula

Angle = arctan(rise / run) in degrees; slope factor = sqrt(1 + (rise / run)^2); sloped rafter line = (span / 2) x slope factor.

Worked example

A 6-in-12 pitch is a ratio of 0.5. The angle is arctan(0.5) = 26.565 degrees and the slope factor is sqrt(1.25) = 1.118. Across a 28 ft span, one side runs 14 ft horizontally, so the sloped rafter line is 14 x 1.118 = 15.653 ft before overhang, ridge thickness, birdsmouth, and bearing detail are added.

Assumptions

  • Both roof planes share one symmetrical pitch about a central ridge.
  • Rise and run are entered in the same unit.
  • The span is the horizontal distance across the building, not a distance along the slope.

Caveats

  • The result is a geometric line length, not a cut list or a rafter size.
  • Minimum pitch depends on the roof covering and its manufacturer instructions.
  • Snow, wind, seismic, and dead loads determine member sizes and require a qualified designer.

Primary references

Understand and continue

Planning quantity, not construction directionThis calculator does not verify codes, specifications, structure, utilities, product suitability, purchasing, pricing, installation, or safety. Verify the result and all project decisions with qualified local professionals.