Rafter Length Calculator
Calculate common, hip, or valley rafter line length from run and rise. Includes sloped overhang, plan run, and cut-angle guidance.
Dimensions
Rafter Length
14.53 ft
line length + sloped overhang
Rafter Angle
26.6°
common-rafter angle
Overhang Length
1.12 ft
along rafter slope
Cutting Geometry
- • Minimum stock length before cut allowances: 14.53 ft
- • Main line length, wall plate to ridge: 13.42 ft
- • Plan run along this rafter line: 12.00 ft
- • Line angle above horizontal: 26.6°
💡 Formula: Common line length = √(rise² + run²). A 45° hip or valley uses plan run = common run × √2 before applying the same theorem.
💡 Cut allowance: This is geometric line length, not a cut list. Adjust for ridge-board thickness, birdsmouth position, fascia, and the details on your approved framing plan.
Estimates only. See how this calculator works — the formulas, assumptions, and sources behind it.
Understanding Rafter Calculations
A rafter is the structural beam that forms the slope of a pitched roof. Calculating rafter length accurately is critical for proper framing.
A common rafter uses the Pythagorean theorem: line length = √(rise² + run²). The run is the horizontal distance from the wall to the center of the roof (half of total span). The rise is the vertical height from the top plate to the ridge board.
A hip or valley that runs at 45° in plan has a horizontal plan run of common run × √2. The calculator applies that diagonal plan run while keeping the same ridge rise, then converts the horizontal overhang to length along the hip or valley line.
Plumb cut is the angled cut at the top where the rafter meets the ridge board.Seat cut (or birdsmouth) is the notch at the bottom where the rafter sits on the wall plate.
Common Rafter Lengths by Pitch and Span
Pre-calculated rafter lengths for standard spans. These assume a simple common rafter from wall plate to ridge (half the total span as the run), not including overhang.
| Span (ft) | 4:12 | 6:12 | 8:12 | 10:12 | 12:12 |
|---|---|---|---|---|---|
| 10 | 5.3 ft | 5.6 ft | 6.0 ft | 6.5 ft | 7.1 ft |
| 12 | 6.3 ft | 6.7 ft | 7.2 ft | 7.8 ft | 8.5 ft |
| 14 | 7.4 ft | 7.8 ft | 8.4 ft | 9.1 ft | 9.9 ft |
| 16 | 8.4 ft | 8.9 ft | 9.6 ft | 10.4 ft | 11.3 ft |
| 20 | 10.5 ft | 11.2 ft | 12.0 ft | 13.0 ft | 14.1 ft |
| 24 | 12.6 ft | 13.4 ft | 14.4 ft | 15.6 ft | 17.0 ft |
Values calculated as rafter length = sqrt((span/2)² + (span/2 × pitch/12)²), rounded to one decimal. Add overhang length separately.
Birdsmouth Cut Depth
The birdsmouth cut (also called a bird's mouth or seat cut) is the notch where the rafter sits on the wall plate. The permitted notch geometry depends on the adopted code, member size, notch location, cantilever conditions, and any engineered framing details. A line-length result alone cannot determine a compliant birdsmouth depth.
Cutting too deep weakens the rafter and may not pass inspection. Always verify birdsmouth depth against your local building code and any engineered plans for your project. If in doubt, consult a structural engineer or your local building department.
Rafter Length FAQ
- How do I calculate rafter length?
- Use the Pythagorean theorem for the plate-to-ridge line length, then convert a horizontal overhang to its sloped length. With a 12 ft run, 6 ft rise, and 18-inch horizontal overhang, the main line is 13.42 ft and the sloped overhang is 1.68 ft, for about 15.09 ft before ridge-board and cut allowances.
- What is a plumb cut vs a seat cut?
- A plumb cut is the vertical angled cut at the top of the rafter where it meets the ridge board. A seat cut (also called a birdsmouth) is the notch at the bottom where the rafter sits on the wall’s top plate. Both angles are determined by the roof pitch.
- How much overhang should a roof have?
- Most residential roofs have 12 to 24 inches of overhang (eave). A 12-inch overhang is the minimum for reasonable weather protection. In rainy climates, 18-24 inches is preferred. Overhangs beyond 24 inches may need additional structural support.
- Does this calculator select a rafter lumber size?
- No. Line length is geometry; lumber sizing also depends on species, grade, spacing, roof assembly, design loads, and the locally adopted code. Use an approved span table or engineered plan rather than selecting lumber from length alone.