Rafter Calculator
Get exact rafter length, birdsmouth cut dimensions, tail overhang, rafter count, and total board feet — everything you need to frame a roof from scratch.
Roof Framing Inputs
ft
ft
ft
in
Common Rafter Length
14.465 ft
Rafter to Plate13.347 ft
Tail (Overhang)1.118 ft
Run (half span)12.000 ft
Rise (total)6.000 ft
Rafters (each side)31
Total Rafters62
Ridge Board Length40.000 ft
Pitch Angle26.6°
Birdsmouth Cut Dimensions
Plumb cut angle (from vertical)26.6°
Seat cut angle (from horizontal)63.4°
Seat cut width (horizontal)3.5" (standard plate)
Plumb cut depth (vertical)1.75"
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How to Use This Calculator
Enter these values to get complete rafter dimensions:
- Building Width — The outside-to-outside dimension of the building perpendicular to the ridge. The rafter run = half this width minus ridge board thickness (usually ½ inch).
- Roof Pitch — Rise over 12 inches of run (e.g., 6/12). This determines the rafter angle and plumb cut.
- Overhang / Eave — How far the rafter extends beyond the wall plate (horizontal measurement). Typical eaves are 12–24 inches.
- Rafter Spacing — Distance from center to center, typically 16" OC or 24" OC
- Ridge Length — The length of your building parallel to the ridge, for calculating total rafter count
Outputs include: rafter length (plumb to birdsmouth), tail length, total rafter length, plumb cut angle, seat cut depth, and total rafter count with board feet.
The Formula
Run = (Building Width / 2) - (Ridge Thickness / 2)
Pitch Multiplier = √(1 + (Rise/Run)²) = √(1 + (pitch/12)²)
Rafter Length = Run × Pitch Multiplier
Tail Length = Overhang × Pitch Multiplier
Total Rafter = Rafter Length + Tail Length
Plumb Cut Angle = arctan(Rise/12) degrees
Seat Cut Depth = (Plate Width × 12) / Rafter Depth (max 1/3 depth)
Rafter Count = ((Ridge Length × 12) / Spacing) + 1, × 2 sides
Pitch Multiplier = √(1 + (Rise/Run)²) = √(1 + (pitch/12)²)
Rafter Length = Run × Pitch Multiplier
Tail Length = Overhang × Pitch Multiplier
Total Rafter = Rafter Length + Tail Length
Plumb Cut Angle = arctan(Rise/12) degrees
Seat Cut Depth = (Plate Width × 12) / Rafter Depth (max 1/3 depth)
Rafter Count = ((Ridge Length × 12) / Spacing) + 1, × 2 sides
Example: 28 ft Wide House, 6/12 Pitch, 18-inch Overhang
Example: Gable Roof, 28 ft span, 6/12 pitch, 1.5 ft overhang, 16-inch OC, 40 ft long
Run28/2 - 0.5/2 = 13.75 ft
Pitch Multiplier√(1 + 0.25) = 1.118
Rafter Length13.75 × 1.118 = 15.37 ft
Tail Length1.5 × 1.118 = 1.68 ft
Total Rafter17.05 ft (cut from 18-ft lumber)
Plumb Cut Angle26.57° from vertical
Rafters per Side(40 × 12 / 16) + 1 = 31
Total Rafters62 pieces
Order 64 pieces of 2×8×18 lumber (2 extra for waste/mistakes). At 16-inch OC spacing with a 6/12 pitch, 2×8 framing is typically adequate for this span with standard live and dead loads.
Frequently Asked Questions
Rafter length = Run × Pitch Multiplier. Run = half the building width minus half the ridge thickness. For 6/12 pitch, multiplier = 1.118. So a 14-ft run: 14 × 1.118 = 15.65 ft. Add tail length separately (overhang × multiplier).
The seat cut (horizontal cut) of the birdsmouth must not exceed 1/3 of the rafter's total depth. For a 2×8 (actual 7.25 inches), max seat depth = 7.25 / 3 = 2.42 inches. Deeper cuts weaken the rafter at its most critical load point.
Opposing rafters must be nailed together at the ridge — either to a ridge board (structural or non-structural) or face-nailed together. IRC requires collar ties or ridge beams to resist outward thrust at the walls. Toenailing is the traditional method; hurricane clips are superior.
For a 6/12 pitch, the plumb cut angle is 26.57° from vertical (or 63.43° from horizontal). Set your circular saw blade to 26.57°. The tail plumb cut (at the eave) uses the same angle. This calculator shows all cut angles.
Refer to IRC span tables. As a rough guide at 16-inch OC: 2×6 spans up to 12 ft, 2×8 up to 16 ft, 2×10 up to 20 ft, 2×12 up to 24 ft (for standard residential loads with Douglas Fir No. 2). Verify with your local code official or engineer.