Rafter Length Calculation: Pitch, Run, and Overhang Made Simple
October 21, 2026
A common rafter runs from the top plate of an exterior wall up to the ridge, and its length depends on the horizontal run and the roof pitch. Pitch is expressed as rise over 12 inches of run: a 6/12 pitch rises 6 inches for every 12 inches of horizontal distance. The sloped length of a rafter is the hypotenuse of the right triangle formed by its run and rise, which means it is the run multiplied by a pitch factor.
For a 6/12 pitch, the factor is √(6² + 12²) ÷ 12 = 1.118. A building 24 feet wide has a run of 12 feet per side (half the span), so the rafter length before overhang is 12 × 1.118 = 13.42 feet.
Skip the math and get your answer instantly:
Open the Roofing Calculator →The Basic Formula
Rafter length = run × √(rise² + 12²) ÷ 12, where rise is the pitch numerator. For common pitches the multiplier (called the rafter length factor per foot of run) is 1.054 for 4/12, 1.118 for 6/12, 1.202 for 8/12, 1.302 for 10/12, and 1.414 for 12/12. Multiply by the run in feet to get the length in feet along the slope.
The rise of the roof at the ridge is run × rise ÷ 12. For a 12-foot run at 6/12, the ridge sits 6 feet above the top plate.
| Pitch | Length factor | Rafter length for 12 ft run | Ridge rise above plate |
|---|---|---|---|
| 4/12 | 1.054 | 12.65 ft | 4.0 ft |
| 6/12 | 1.118 | 13.42 ft | 6.0 ft |
| 8/12 | 1.202 | 14.42 ft | 8.0 ft |
| 12/12 | 1.414 | 16.97 ft | 12.0 ft |
Adding the Overhang
Most roofs extend past the wall to shed water and shade the walls. The overhang is measured horizontally. For a 12-inch overhang at 6/12, the added sloped length is 1 ft × 1.118 = 1.12 ft. The total rafter length is then 13.42 + 1.12 = 14.54 feet before the ridge adjustment, so you need a 16-foot board.
Overhang dimensions are usually 12 to 24 inches for typical homes, with more in sunny or rainy climates. Check how your design handles the fascia and soffit before finalizing.
Adjusting for the Ridge Board
A ridge board has thickness, usually 1½ inches. The rafters butt against its sides, so each rafter's run is reduced by half the thickness of the ridge, which is ¾ inch. The adjustment along the slope is 0.75 × 1.118 = 0.84 inches. Subtract that from the length measured to the theoretical center line to get the actual cut length.
If you use a structural ridge beam with rafters resting on top, no reduction is needed, but the height changes by the beam's depth.
Cuts: Plumb, Seat, and Birdsmouth
The top of the rafter is cut at a plumb angle matching the pitch. For 6/12, the plumb cut angle is arctan(6 ÷ 12) = 26.57° from vertical. The bottom has a birdsmouth notch that sits on the top plate. The seat cut is horizontal, and the heel cut is plumb. The depth of the birdsmouth should not remove more than a third of the rafter's depth, so you do not weaken it.
Cut one rafter, test it, and use it as a pattern for the rest. Check that the first fits at both the ridge and the plate.
Engineering and Code
Rafter size, spacing, and span depend on the species and grade of lumber, the loads for snow and wind where you live, and the roof covering. Span tables in building codes or prescriptive guides give the allowable spans. For example, 2×8 rafters at 16 inches on center might span around 12 to 14 feet horizontally in typical conditions, but you must use the tables for your region. For complex roofs, trusses engineered by the manufacturer are often simpler and stronger.
Frequently Asked Questions
How do I calculate rafter length?
Multiply the horizontal run by the pitch factor, which for rise/12 is √(rise² + 144) ÷ 12.
What is the run of a rafter?
Half the building span, measured horizontally from the wall to the center of the ridge.
How do I add overhang?
Multiply the horizontal overhang by the pitch factor and add it to the rafter length.
What is a birdsmouth cut?
A notch cut into a rafter so it sits flat on the wall's top plate.
Do I need an engineer?
For unusual spans, heavy snow loads, or complex roofs, yes. Always check local code and span tables.