Rafter Length Calculator
Reviewed by the My Roof Pitch editorial team · Updated · Free, no sign-up, works offline after first load
Rafter length is the hypotenuse of the rise and run triangle: √(rise² + run²). For a 24 ft span at 6:12, the run is 12 ft, rise is 6 ft, and the line length is 13.42 ft. Add the overhang along the same slope to get the cut length.
Your measurements
Enter the values you know — results update live.
Outside-to-outside width of the building at the wall plates.
Enter 6 for a 6:12 roof.
Horizontal projection past the wall. The tool converts it to slope length for you.
Analysis
Live results from your measurements.
Show the working
- Run:
24 ÷ 2 − 0.125 ÷ 2= 11.938 ft - Rise:
11.938 × (6 ÷ 12)= 5.969 ft - Line length:
√(11.938² + 5.969²)= 13.347 ft - Overhang along slope:
1.5 × 1.118= 1.677 ft - Total rafter:
13.347 + 1.677= 15.024 ft - Plumb cut:
90° − 26.57°= 63.43°
What this calculator does
A common rafter runs from the wall plate straight up to the ridge, perpendicular to both. Its line length is measured from the outside face of the wall plate to the centre of the ridge, along the top edge of the rafter. That line length plus the sloped overhang gives the piece you actually cut. Two cuts define it: the plumb cut at the ridge, which is vertical when the rafter is in place, and the birdsmouth seat cut that lands flat on the wall plate. Both angles come from the same roof pitch.
How to use it
- Measure the building span from outside face to outside face of the wall plates.
- Halve the span to get the run, then subtract half the ridge board thickness.
- Multiply the run by the pitch ratio (rise ÷ 12) to get the total rise.
- Take the square root of run squared plus rise squared for the line length.
- Multiply the horizontal overhang by the pitch multiplier and add it for the total cut length.
- Set the plumb cut to 90 minus the roof angle and the seat cut to the roof angle.
The formula
Rafter line length
line length = sqrt(run^2 + rise^2)
Pythagoras on the run and rise of one roof plane.
Shortcut using the multiplier
line length = run × sqrt(rise^2 + 144) / 12
The pitch multiplier converts run straight into rafter length.
Ridge deduction
run = span / 2 - ridge thickness / 2
The rafter stops at the face of the ridge board, not its centreline.
Worked example
A 28 ft span at 8:12 with a 2 ft overhang and a 1.5 in ridge board.
- Run: 28 ÷ 2 − 0.0625 = 13.9375 ft
- Rise: 13.9375 × 0.6667 = 9.2917 ft
- Line length: √(13.9375² + 9.2917²) = 16.75 ft
- Overhang along slope: 2 × 1.2019 = 2.404 ft
- Total: 16.75 + 2.404 = 19.154 ft
Cut each common rafter at 19 ft 1 7/8 in overall; buy 20 ft stock.
Reference chart
| Pitch | Length per ft of run | 12 ft run | 16 ft run | Angle |
|---|---|---|---|---|
| 3:12 | 1.0308 | 12.37 | 16.49 | 14.04° |
| 4:12 | 1.0541 | 12.65 | 16.87 | 18.43° |
| 5:12 | 1.0833 | 13 | 17.33 | 22.62° |
| 6:12 | 1.118 | 13.42 | 17.89 | 26.57° |
| 7:12 | 1.1577 | 13.89 | 18.52 | 30.26° |
| 8:12 | 1.2019 | 14.42 | 19.23 | 33.69° |
| 9:12 | 1.25 | 15 | 20 | 36.87° |
| 10:12 | 1.3017 | 15.62 | 20.83 | 39.81° |
| 12:12 | 1.4142 | 16.97 | 22.63 | 45° |
Maximum common rafter span for No. 2 Douglas fir-larch, 40 psf roof load
| Rafter size | 16 in on centre | 24 in on centre |
|---|---|---|
| 2×6 | 12 ft 6 in | 10 ft 3 in |
| 2×8 | 16 ft 6 in | 13 ft 6 in |
| 2×10 | 20 ft 2 in | 16 ft 6 in |
| 2×12 | 23 ft 5 in | 19 ft 1 in |
Common mistakes
- Using the full span as the run. The run is half the span on a symmetrical gable.
- Skipping the ridge board deduction, which leaves every rafter about 3/4 in too long.
- Adding the overhang horizontally rather than along the slope.
- Cutting the birdsmouth deeper than one third of the rafter depth, which the IRC does not allow.
- Measuring the line length along the bottom edge instead of the top edge of the rafter.
- Using a common rafter length for a hip or valley rafter — those run on a 17-unit base, not 12.
Assumptions and limits
- A symmetrical gable with both plates at the same height.
- The rafter is a straight, uniform-depth member with a standard birdsmouth.
- Span tables shown are indicative and not a structural design.
- The overhang is a level projection past the wall face.
Frequently asked questions
How long is a rafter for a 24 foot span at 6/12?
The run is 12 ft and the rise is 6 ft, so the line length is √(144 + 36) = 13.42 ft, or 13 ft 5 inches. Add the sloped overhang to get the length you cut.
What is the plumb cut angle for a 6/12 roof?
The roof angle is 26.57 degrees, so the plumb cut is 63.43 degrees from the rafter edge — set a circular saw bevel to 26.57 degrees off square to make it.
Do I subtract the ridge board from the rafter length?
Yes. Subtract half the ridge thickness from the run before calculating. A 1.5 inch ridge board means the run drops by 0.75 inches on each side.
What is rafter line length?
It is the distance from the outside face of the wall plate to the centreline of the ridge, measured along the top edge of the rafter. Overhang and ridge deduction are handled separately.
How do I calculate a hip rafter length?
A hip rafter runs diagonally, so its run per foot is 16.97 inches rather than 12. Use √(rise² + 16.97²) ÷ 16.97 as the multiplier against the hip run.
How deep can a birdsmouth cut be?
The seat cut should not remove more than one third of the rafter depth. On a 2×8, which is 7.25 inches deep, that limits the seat cut to about 2.4 inches.
Related guides
- How to Calculate Roof Pitch: 6 Methods That Actually WorkSix field-tested ways to find the pitch of a roof — from the ladder, from the attic, from a photo — plus the arithmetic that turns any measurement into X:12, degrees and percent.
- Shed and Lean-To Roof Pitch: How to Choose and Calculate ItSingle-slope roofs use the whole building depth as run, which changes every calculation. Here is the geometry, the wall-height math and the pitch to pick for a shed, lean-to or carport.
Last updated 2026-08-05. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.