Quick answer
To find a rafter's length, multiply the run, which is half the building width, by the slope factor for your pitch. The slope factor is the square root of 144 plus the rise squared, divided by 12. For a 24 ft span the run is 12 ft, and at a 6 in 12 pitch the slope factor is 1.118, so the rafter is 12 x 1.118 = 13.42 ft, or 13 ft 5 in, before the overhang.
How to use the rafter length calculator
- Enter the span (the full building width) or the run (half the span) directly.
- Enter the pitch as rise over 12, for example 6 for a 6 in 12 roof.
- Add the overhang if the rafter extends past the wall.
- Read the rafter length, the total length with overhang, the pitch angle, and the plumb and seat cut angles.
- Enter the span in feet or metres; the pitch stays as rise in 12 either way.
Worked example
A building is 24 ft wide with a 6 in 12 pitch and no overhang.
- 1.Run: 24 / 2 = 12 ft
- 2.Slope factor: square root of (144 + 36) / 12 = 1.118
- 3.Rafter length: 12 x 1.118 = 13.42 ft, or 13 ft 5 in
- 4.Pitch angle: 26.57 degrees. Plumb cut 26.57 degrees, seat cut 63.43 degrees
When to use this
The formula
The rafter length is the run times the slope factor:
slope factor = square root of (144 + rise squared) / 12, then rafter length = run x slope factor.
The pitch angle is the angle whose tangent is rise over 12. The plumb cut matches the pitch angle, and the seat cut is 90 degrees minus the pitch angle. The overhang is multiplied by the same slope factor and added to the length.
Slope factor and pitch angle by roof pitch
Multiply the run by the slope factor to get the rafter length.
| Pitch | Slope factor | Pitch angle |
|---|---|---|
| 3 in 12 | 1.031 | 14.04 deg |
| 4 in 12 | 1.054 | 18.43 deg |
| 5 in 12 | 1.083 | 22.62 deg |
| 6 in 12 | 1.118 | 26.57 deg |
| 7 in 12 | 1.158 | 30.26 deg |
| 8 in 12 | 1.202 | 33.69 deg |
| 9 in 12 | 1.250 | 36.87 deg |
| 10 in 12 | 1.302 | 39.81 deg |
| 12 in 12 | 1.414 | 45.00 deg |
Swipe sideways to see all columns
Turning the length into an order
The calculator gives the length of one rafter along the slope. To order timber, round each rafter up to the next length you can buy, since boards come in fixed sizes, so a 13 ft 5 in rafter is cut from a 14 ft board and leaves a short offcut. If the roof has an overhang, measure to the end of the tail, not the wall, so one board covers the birdsmouth and the tail in a single piece. For the number of rafters, divide the roof length by the spacing, usually 16 or 24 inches (400 or 600 mm) on centre, then add one for the final rafter. Order a few spares for knots and mistakes.
Common mistakes
Frequently asked questions
Multiply the run, half the building width, by the slope factor for your pitch. At a 6 in 12 pitch the slope factor is 1.118, so a 12 ft run gives a 13.42 ft rafter before the overhang.
The pitch sets the slope factor, which is the square root of 144 plus the rise squared, divided by 12. A steeper pitch gives a larger slope factor and a longer rafter for the same run.
The run is the horizontal distance from the outside wall to the centre of the ridge. For a simple gable roof it is half the building width.
The overhang is the horizontal distance the rafter extends past the wall, multiplied by the same slope factor. The calculator adds it to the length and shows the total.
The plumb cut is the vertical cut where the rafter meets the ridge, at the pitch angle. The seat cut is the horizontal cut of the birdsmouth that rests on the wall, at 90 degrees minus the pitch angle.
References. The formulas and figures here follow standard construction references. See our Methodology for how we check them. Rafter geometry uses the standard slope-factor method.
Related calculators
Estimates only. Check supplier specs and local codes before you order or build.