What it works out
Use this for one common rafter. Choose two values you know, such as run and pitch, and you get the rise, the rafter length along the slope, the pitch angle and the rise per 12. Run is the horizontal distance from the outside of the plate to the ridge centre line, so half the span of an even roof. The length is an ideal centre line with no ridge, seat or overhang added.
The formula
- Rafter
- √(rise² + run²)
- Rise
- run × rise per 12 ÷ 12
In words: Rafter = the square root of rise squared plus run squared; rise = run times rise per 12 divided by 12
Worked example
A 6 in 12 roof over a 12 ft run
- Pitch 6 in 12
- Run 12 ft
- Rise = 12 × 6 ÷ 12 = 6 ft
- Rafter = √(6² + 12²) = √180 = 13.42 ft
- Pitch angle = atan(6 ÷ 12) = 26.57°
That length is an ideal centre line, before any ridge, seat cut or overhang.
Good to know
- One common rafter. Hip, valley and jack rafters need their own cuts.
- Run is measured from the outside of the plate to the ridge centre line.
- No ridge, birdsmouth or overhang is added.
- A calculator, not a building-code check: confirm local rules with your building authority.
Questions
What is run?
The horizontal distance from the outside of the plate to the ridge centre line, which is half the span of an even roof.
Is the answer the board length to buy?
No. It is the ideal centre-line length. Add overhang and trim allowances yourself.