Roof Rafter Calculator

Calculate precise common rafter cutting length, ridge board deductions, bird’s mouth seat cuts, and overhang dimensions.

Building Span (Total Width Ft) Outside of wall to outside of wall

Roof Pitch (Rise / 12)

Ridge Board Thickness (Inches) 1.5" for standard 2x lumber

Eave Overhang (Horiz. Inches) Horizontal tail overhang

Rafter Lumber Size

Line Length (Ridge to Wall)

13' 4-3/8"

160.4 inches true line length

Overhang Tail Length 17.9 in Along rafter slope

Total Board Cut 16 ft Stick Line length + Tail

Bird's Mouth Maximum Depth: Building code (IRC) mandates that the vertical heel cut of a bird's mouth seat notch must never exceed 1/3 of the total rafter depth (e.g. maximum 2.4" deep on a 2x8) to prevent split failures.

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How Common Rafter Length Is Calculated

Rafter geometry follows the Pythagorean theorem:

Run to Ridge = (Building Span / 2) - (Ridge Board Thickness / 2)
Rafter Line Length = Run to Ridge × √(1 + (Pitch / 12)²)
Tail Length = Horizontal Overhang × √(1 + (Pitch / 12)²)

Line length is measured from the long point of the top plumb cut (at the ridge) to the heel point of the bird's mouth notch (plumb face of the exterior wall top plate).

Frequently Asked Questions

Why do you subtract half the ridge board thickness?

The ridge board sits centered between opposing rafters. Half its thickness (typically 3/4" for a 2x board) must be subtracted from the total half-span run so the roof fits the building exactly.

What is a bird’s mouth cut?

A notch cut into the rafter consisting of a level seat cut (resting on the wall top plate) and a plumb heel cut (bearing against the outside face of the wall stud).

What angle is the plumb cut on a framing square?

Align the pitch rise (e.g. 6") on the square tongue and 12" on the body. Scribing along the rise tongue marks the plumb cut; scribing along the 12" body marks the level seat cut.