How do I calculate rafter length?
A common rafter is the hypotenuse of a right triangle. The run is half the building span, less half the ridge board. The rise is the run times the pitch. Framers use the length per foot of run, which is √(pitch² + 12²), the same number printed on a framing square's rafter table.
Rafter length = run (ft) × √(pitch² + 144) ÷ 12 × 12 in, plus the overhang × the same factor
A 24 ft wide building with a 6/12 roof, a 1.5 in ridge board and a 12 in overhang: the run is 144 − 0.75 = 143.25 in. Each foot of run takes √(36 + 144) = 13.42 in of rafter, so the rafter is 143.25 × 13.42 ÷ 12 = 160.2 in, or 13 ft 4 3/16 in, from the ridge to the outside of the wall. The 12 in overhang adds 13 7/16 in, for 14 ft 5 9/16 in in total. Buy 16 ft boards.
The plumb cut at the ridge is 26.6°, which is 6 on the common scale of a speed square. The birdsmouth seat on a 2×4 wall is 3 1/2 in level and 1 3/4 in deep.
Roof rafter calculator: pitch table
| Pitch | Plumb cut angle | Common rafter per foot of run | Hip or valley per foot of common run |
|---|---|---|---|
| 3/12 | 14.0° | 12.37 in | 17.23 in |
| 4/12 | 18.4° | 12.65 in | 17.44 in |
| 5/12 | 22.6° | 13.00 in | 17.69 in |
| 6/12 | 26.6° | 13.42 in | 18.00 in |
| 7/12 | 30.3° | 13.89 in | 18.36 in |
| 8/12 | 33.7° | 14.42 in | 18.76 in |
| 9/12 | 36.9° | 15.00 in | 19.21 in |
| 10/12 | 39.8° | 15.62 in | 19.70 in |
| 12/12 | 45.0° | 16.97 in | 20.78 in |
Multiply the run in feet by the figure for your pitch to get the rafter length in inches. These are the same numbers on the rafter table of a framing square.
Hip rafter calculator
A hip or valley rafter runs at 45° to the walls in plan, so it covers 16.97 in of run for every 12 in of common run. Its length per foot of common run is √(pitch² + 288). For the 24 ft, 6/12 example, the hip line length is 12 ft of run × 18 in = 216 in, or 18 ft, plus 18 in of overhang.
The calculator gives the hip's theoretical line length to the center of the ridge. A common method is to shorten it by half the 45° thickness of the ridge, measured level, and then cut the side cuts. How much depends on how your hip meets the ridge, so lay out one hip and check it before cutting the rest.
Birdsmouth and seat cut
The seat cut sits level on the wall plate, and its depth is the seat length times the pitch ÷ 12. A common rule is to keep the seat cut no deeper than about a third of the rafter's depth so enough wood is left above the wall. The calculator warns you when it's deeper. The height above plate is the plumb distance from the seat to the top of the rafter, which you'll want the same on every rafter.
Rafter calculator free, no app
This page works in any phone browser, with no app to install and no sign-up. Your last inputs are saved in your browser, so the numbers are still there when you come back from the cut station.
Layout, not engineering
The calculator does layout math only. Rafter size, spacing, ridge type and connections depend on snow load, wind, span and your local code. Take them from your plans or the span tables your building department uses. Under the IRC, a roof pitched below 3/12 needs its ridge, hips and valleys designed as beams, and rafters need ceiling joists or rafter ties unless a structural ridge carries the load. Check with your building department.
Questions
How do you calculate rafter length?
Multiply the run in feet by the square root of pitch squared plus 144. That gives the length in inches. For a 6/12 roof, each foot of run takes 13.42 inches of rafter.
What is the plumb cut angle for a 6/12 roof?
26.6 degrees. On a speed square, pivot to 6 on the common scale.
How long is a hip rafter?
The common run in feet times the square root of pitch squared plus 288. For a 6/12 roof that's 18 inches per foot of common run, before the ridge deduction.
How deep should a birdsmouth cut be?
A common rule is no more than about a third of the rafter's depth. Follow your plans and local code.