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Single-Pitch (Shed) Roof Calculator

Calculate rafter length, bird's mouth cuts, and wall height differences for mono-pitch roofs. Converts between degrees, pitch, and percentage.

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About

A mono-pitch or "shed" roof offers a simplified framing geometry compared to gable or hip roofs, yet precision in rafter length and seat cuts remains non-negotiable. Errors in the Pythagorean calculation of the common rafter lead to uneven fascias or structural misalignment at the top plate. This utility addresses the geometry of the triangle formed by the Run, Rise, and Rafter.

The tool accounts for the Bird's Mouth cut - the notch where the rafter seats on the wall plate - which effectively lowers the rafter's position relative to the roof plane. Correctly calculating the Height Above Plate (HAP) ensures the roof surface remains planar across the span. It also provides instant conversion between the three standard slope definitions: Pitch (x:12), Degrees (θ), and Grade (%), allowing for cross-reference with architectural plans.

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Formulas

The rafter length (L) excluding overhangs is derived from the Pythagorean theorem:

L = √Run2 + Rise2

When the angle (θ) is known, the Rise is calculated as:

Rise = Run × tan(θ)

Reference Data

Pitch (x:12)Angle (°)Slope (%)Common Application
1:124.76°8.3%Industrial / Drainage
2:129.46°16.7%Low Slope / Metal
4:1218.43°33.3%Standard Residential
6:1226.57°50.0%Sheds / Porches
8:1233.69°66.7%Attic Space
12:1245.00°100.0%Steep / Cathedral

Frequently Asked Questions

A Bird's Mouth is a triangular notch cut into the bottom of the rafter to allow it to sit flat on the top wall plate. Without it, the rafter is unstable and relies solely on fasteners for support. The cut consists of a horizontal "seat cut" (usually the width of the wall plate, e.g., 3.5 inches) and a vertical "heel cut".
The core calculation determines the rafter length from wall-to-wall (the span). The overhang is the "tail" of the rafter that extends past the wall. The total rafter length required is the Calculated Length + (Overhang / cos(Angle)).
Yes. While US carpentry standards typically use Pitch (Rise over 12 inches of Run), international standards often use degrees. This tool converts your input automatically.
In a single-pitch roof, the Rise is the difference in height between the low wall and the high wall. This determines the slope.