Get the rafter length before you cut

Rafter length is the hypotenuse of the run and the rise. Take half the span as the run, multiply the run by the pitch over 12 to get the rise, then take the square root of run squared plus rise squared. A 24 ft span at 6/12 gives a 12 ft run, a 6 ft rise and a line length of about 13 ft 5 inches. Subtract half the ridge thickness and add the overhang to get the length you actually cut.

No, and mixing them up doubles the answer. The span is the full width of the building, wall plate to wall plate. The run is the horizontal distance one rafter covers, which on a symmetrical gable roof is half the span. This calculator takes the span and halves it for you.

Half the ridge thickness, because each rafter meets it from one side — 3/4 inch for a standard 1.5 inch 2x ridge. It is a horizontal measurement, so multiply it by the slope factor before taking it off the rafter rather than deducting 3/4 inch straight.

Overhang is normally specified horizontally, from the outside of the wall, so it has to be multiplied by the slope factor to become length along the rafter. At 6/12 a 16 inch horizontal overhang is about 17.9 inches along the rafter. Cutting 16 inches leaves the eave short — this is the most common source of error.

The length along the rafter for every one unit of horizontal run — the square root of 144 plus the pitch squared, all over 12. At 6/12 it is 1.1180, so every horizontal foot is 1.118 feet of rafter. It is the multiplier behind rafter length, overhangs, ridge deductions and sloped roof area.

A hip or valley rafter runs diagonally across the corner, so its horizontal run is the common run times the square root of two while the rise stays the same. That is where the framing rule of thumb of using 17 instead of 12 comes from — 17 is close to the 16.97 diagonal of a 12 by 12 square.

Divide the building length by the spacing and add one for the closing rafter, then double it for both slopes of a gable. A 40 ft building at 16 inch centres needs 31 per side, so 62 in total. Add rafters for any openings, and check the span tables — this tool gives lengths and counts, not structural sizing.