Rafter Length Calculator
Calculate exact rafter length from run and rise measurements. Includes overhang, plumb cut angle, and seat cut angle for framing.
Dimensions
Half of total span
Ridge height above top plate
Eave extension beyond wall
Rafter Length
14.53 ft
hypotenuse + overhang
Roof Angle
26.6°
3.5:12 pitch approx
Overhang Length
1.12 ft
along rafter slope
Cutting Info
- • Order rafters at least 15' long (round up for safety)
- • Main rafter length (run to ridge): 13.42 ft
- • Plumb cut angle (top, where rafter meets ridge): 26.6°
- • Seat cut angle (bottom, where rafter meets wall): 63.4°
💡 Formula: Rafter length = √(rise² + run²) — the Pythagorean theorem applied to roof framing.
💡 Ridge board allowance: Subtract half the ridge board thickness from the rafter length for an accurate cut (typically 0.75-1.5 inches).
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.
The calculation uses the Pythagorean theorem: rafter 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.
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. Common framing guidance often limits the seat cut depth to around one-third of the rafter depth — for example, roughly 2.4" on a 2×8 (actual depth 7.25") or 3.1" on a 2×10 (actual depth 9.25"). However, exact limits vary by IRC version, notch location (end vs mid-span), cantilever conditions, and local code amendments.
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: rafter length = √(run² + rise²). Then add the overhang length. For example, with a 12 ft run, 6 ft rise, and 18-inch overhang, the rafter is √(144 + 36) + 1.5 = 13.42 + 1.5 = about 14.92 ft. Always round up when buying lumber.
- 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.
- What size lumber do I need for roof rafters?
- Rafter size depends on span, spacing, and load. Common sizes: 2×6 for spans up to 10 ft, 2×8 for up to 14 ft, 2×10 for up to 18 ft, and 2×12 for up to 22 ft — all at 16-inch on-center spacing. Check local building codes for your area’s snow and wind load requirements.