Calculating the length of a common rafter involves a few key steps based on a right-angled triangle:

1. Determine the Roof Span and Run: The 'span' is the total width of the building from wall to wall. The 'run' is half of the span, representing the base of our right triangle.
2. Determine the Pitch and Total Rise: The 'pitch' is the amount of vertical rise for every 12 inches of horizontal run. The calculator uses this ratio to find the 'total rise'—the full vertical height from the wall plate to the ridge, which is the height of our right triangle.
3. Calculate Line Length (Pythagorean Theorem): With the run (a) and total rise (b) known, the calculator finds the rafter's line length (c) using `a² + b² = c²`.
4. Add the Overhang: The calculator performs a second, smaller Pythagorean calculation to find the diagonal length of the overhang and adds it to the line length for the final cut length.

• Rafter: The angled structural members of a roof that support the roof sheathing.
• Span: The total horizontal distance from the outside of one supporting wall to the other.
• Run: Half of the span. It's the horizontal distance a single rafter covers.
• Rise: The vertical increase in height of a roof for every 12 inches of run. A '6/12 pitch' means the roof rises 6 inches for every 12 inches it runs horizontally.
• Line Length: The diagonal measurement along the top of the rafter from the ridge cut to the plumb cut at the wall plate.
• Overhang: The portion of the rafter that extends beyond the supporting wall, creating the eave.
• Bird's Mouth: A notch cut into a rafter that allows it to sit securely on top of the wall's top plate.

"This calculation gives you the theoretical length. Remember to account for the thickness of the ridge board when you make your first cut. A common practice is to subtract half the thickness of the ridge board from your rafter's run before calculating, or simply shorten the first rafter by that amount after cutting." - Master Roofer

"Always cut one rafter first as a pattern. Test fit it to make sure your calculations and cuts are perfect. Once you have a confirmed 'master rafter,' you can use it to trace and cut all the others, which ensures every single one is identical."