Roof pitch formula
Pitch X:12 = 12 × rise ÷ horizontal run. The roof angle in degrees is arctan(rise ÷ run) × 180 ÷ π. The slope percentage is 100 × rise ÷ run. The pitch multiplier for converting horizontal run to sloped distance is √(1 + (rise ÷ run)²).
Worked example: 6:12 pitch
When the vertical rise is 6 inches for a horizontal run of 12 inches, the pitch is 6:12, the angle is approximately 26.57°, the slope is 50%, and the multiplier is approximately 1.1180. The resulting line from this measured rise and run is about 13.42 inches. You can also enter a horizontal eave overhang to add its sloped length.
What is a run?
Run is the horizontal distance from the starting point to the roof point being measured, not the distance along the sloping surface. In a typical symmetric gable roof, the run to the ridge is often half the building span, but the geometry depends on the roof configuration.
Structural and installation limits
Calculated rafter line length excludes cuts, birdsmouth geometry, ridge details and structural loads. Roof pitch does not determine permissible roofing materials or structural design. Check local building requirements and use a qualified roof professional for design.