Rafter Length
174.4"
Pitch
6:12
Angle
26.6°
Birdsmouth
5.5"
161.0"
72.0"
6:12
26.6°
Seat Cut (horizontal)
5.5"
Plumb Cut (vertical)
5.5"
Rafter length = √(run² + rise²). For a 6:12 pitch with 12 ft run: rise = 6 ft, length = √(144 + 36) = √180 = 13.4 ft, plus overhang.
The birdsmouth is the notch cut into the rafter where it sits on the wall plate. It consists of a seat cut (horizontal) and plumb cut (vertical).
Common choices are 2x6, 2x8, or 2x10 depending on span and load. 2x6 rafters can typically span 10-12 feet with standard spacing.
Roof pitch is the slope expressed as rise over run. A 6:12 pitch means the roof rises 6 inches for every 12 inches of horizontal run.
Inputs
Result
Unit length = sqrt(144 + 36) = sqrt(180) = 13.42". Rafter = 13.42 × 12 ft = 161.0". Overhang tail = sqrt(12² + 6²) = 13.4". Total = 161.0 + 13.4 = 174.4". Ridge height = (144/12) × 6 = 72.0". Angle = atan(6/12) = 26.6°.
Inputs
Result
Unit length = sqrt(144 + 64) = sqrt(208) = 14.42". Rafter = 14.42 × 10 ft = 144.2". Overhang tail = sqrt(18² + 12²) = sqrt(468) = 21.6". Total = 144.2 + 21.6 = 165.9". Ridge height = (120/12) × 8 = 80.0". Angle = atan(8/12) = 33.7°.
Rafter Length = sqrt(12² + Rise²) × Run (ft)Calculates the line length of the rafter (without overhang) using the unit length method.
Where:
Rise= Roof pitch rise per 12 inches of run (e.g., 6 for a 6:12 pitch)Run= Horizontal distance from wall to ridge in feet (half of total span)Total = Rafter Length + sqrt(Overhang² + (Overhang × Rise / 12)²)Adds the overhang tail length to the main rafter length.
Where:
Rafter Length= Main rafter length in inches (from wall plate to ridge)Overhang= Horizontal overhang distance in inchesRidge Height = Run (in) / 12 × Rise | Angle = atan(Rise / 12) × (180 / PI)Calculates the ridge height above the wall plate and the rafter angle from horizontal.
Where:
Run (in)= Horizontal run in inchesRise= Pitch rise per 12 inches of runPlan your building projects
Last Updated: Feb 12, 2026
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