Rafter Length
174.4"
Pitch
6:12
Angle
26.6°
Birdsmouth
5.5"
161.0"
72.0"
6:12
26.6°
Seat Cut (horizontal)
5.5"
Plumb Cut (vertical)
5.5"
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Rafter length = √(run² + rise²). For a 6:12 pitch with 12 ft run: rise = 6 ft, length = √(144 + 36) = √180 = 13.4 ft, plus overhang.
The birdsmouth is the notch cut into the rafter where it sits on the wall plate. It consists of a seat cut (horizontal) and plumb cut (vertical).
Common choices are 2x6, 2x8, or 2x10 depending on span and load. 2x6 rafters can typically span 10-12 feet with standard spacing.
| Lumber Size | Max Span (16" OC) | Max Span (24" OC) | Cost/ft |
|---|---|---|---|
| 2×6 | 12 ft | 10 ft | $0.80–$1.20 |
| 2×8 | 16 ft | 14 ft | $1.20–$1.80 |
| 2×10 | 20 ft | 17 ft | $1.60–$2.40 |
| 2×12 | 24 ft | 20 ft | $2.20–$3.50 |
Roof pitch is the slope expressed as rise over run. A 6:12 pitch means the roof rises 6 inches for every 12 inches of horizontal run.
| Pitch | Angle | Rise/ft | Common Use |
|---|---|---|---|
| 4:12 | 18.4° | 4" | Low-slope, modern homes |
| 6:12 | 26.6° | 6" | Most common residential |
| 8:12 | 33.7° | 8" | Colonial, Cape Cod |
| 12:12 | 45.0° | 12" | A-frame, steep gable |
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Inputs
Result
Unit length = sqrt(144 + 36) = sqrt(180) = 13.42". Rafter = 13.42 × 12 ft = 161.0". Overhang tail = sqrt(12² + 6²) = 13.4". Total = 161.0 + 13.4 = 174.4". Ridge height = (144/12) × 6 = 72.0". Angle = atan(6/12) = 26.6°.
Inputs
Result
Unit length = sqrt(144 + 64) = sqrt(208) = 14.42". Rafter = 14.42 × 10 ft = 144.2". Overhang tail = sqrt(18² + 12²) = sqrt(468) = 21.6". Total = 144.2 + 21.6 = 165.9". Ridge height = (120/12) × 8 = 80.0". Angle = atan(8/12) = 33.7°.
Rafter Length = sqrt(12² + Rise²) × Run (ft)Calculates the line length of the rafter (without overhang) using the unit length method.
Where:
Rise= Roof pitch rise per 12 inches of run (e.g., 6 for a 6:12 pitch)Run= Horizontal distance from wall to ridge in feet (half of total span)Total = Rafter Length + sqrt(Overhang² + (Overhang × Rise / 12)²)Adds the overhang tail length to the main rafter length.
Where:
Rafter Length= Main rafter length in inches (from wall plate to ridge)Overhang= Horizontal overhang distance in inchesRidge Height = Run (in) / 12 × Rise | Angle = atan(Rise / 12) × (180 / PI)Calculates the ridge height above the wall plate and the rafter angle from horizontal.
Where:
Run (in)= Horizontal run in inchesRise= Pitch rise per 12 inches of runThe unit length method calculates rafter length by finding the hypotenuse for each foot of horizontal run. For a 6:12 pitch, the unit length is √(12² + 6²) = √180 = 13.42 inches per foot of run. A 12-foot run at 6:12 pitch produces a rafter line length of 13.42 × 12 = 161.0 inches (13.42 ft) before adding the overhang tail.
Overhang adds a separate triangle calculation: tail length = √(overhang² + (overhang × rise/12)²). A 12-inch overhang at 6:12 pitch adds √(144 + 36) = 13.4 inches, bringing the total rafter to 174.4 inches. Carpenters typically add 6–12 inches to the lumber length for the ridge cut and birdsmouth, meaning this rafter needs a 16-foot board.
Ridge height is calculated as (run in inches / 12) × rise. For a 12 ft run at 6:12: (144 / 12) × 6 = 72 inches (6 ft) above the wall plate. The rafter angle from horizontal is arctan(6/12) = 26.6°, which determines both the plumb cut angle at the ridge and the seat cut angle at the birdsmouth.
The birdsmouth notch seats the rafter on the wall top plate using two cuts: a horizontal seat cut and a vertical plumb cut. Per IRC R802.6, the seat cut depth must not exceed one-third of the rafter depth for structural integrity—on a 2×6 rafter (5.5” actual), the maximum seat cut is 1.83 inches.
The plumb cut angle matches the roof pitch: 26.6° for 6:12, 33.7° for 8:12, and 45° for 12:12. Framers mark these angles using a framing square with the pitch value on the tongue (short side) and 12 on the blade (long side). For a 6:12 pitch, align 6 inches on the tongue and 12 inches on the blade against the rafter edge.
Cutting accuracy matters—a 1/8-inch error at the birdsmouth can translate to 1/2 inch or more at the ridge over a 12-foot run. Use a circular saw for the straight cuts and finish the inside corner with a sharp hand saw. Pre-drill any fastener holes to prevent splitting at the notch.
| Pitch | Plumb Cut Angle | Unit Length/ft | Ridge Height (12 ft run) |
|---|---|---|---|
| 4:12 | 18.4° | 12.65" | 48" |
| 6:12 | 26.6° | 13.42" | 72" |
| 8:12 | 33.7° | 14.42" | 96" |
| 10:12 | 39.8° | 15.62" | 120" |
| 12:12 | 45.0° | 16.97" | 144" |
2×8 SPF #2 rafters at 16-inch on-center spacing can span up to 16 feet under a 20 psf live load and 10 psf dead load—the most common residential rafter choice per the IRC span tables. Increasing to 24-inch spacing reduces the maximum span by approximately 15%, to about 14 feet for the same lumber grade.
Snow load areas requiring 40+ psf live load ratings often mandate upsizing by one lumber dimension. A 12-foot span that works with 2×6 at 20 psf needs 2×8 at 40 psf. At $1.20–$1.80 per linear foot for 2×8 versus $0.80–$1.20 for 2×6, the material cost increase for a 30-rafter roof is $240–$360.
For spans exceeding 20 feet, engineered lumber (LVLs or I-joists) becomes cost-effective compared to oversized dimensional lumber. A 24-foot LVL rafter costs $4–$6 per foot but eliminates the need for intermediate bearing walls. Check with a structural engineer for any span that pushes the limits of the beam size calculator.
Always verify rafter sizing against IRC Table R802.4 or local amendments. Ceiling-attached rafters (cathedral ceilings) have reduced spans compared to standard attic rafters due to the combined bending and tension loads.
A complete rafter calculation starts with measuring the horizontal run from the outside of the wall plate to the center of the ridge board. For a gable roof on a 24-foot-wide building, the run is 12 feet (half the span). The ridge board thickness (typically 1.5 inches for dimensional lumber) shortens the actual rafter run by 0.75 inches.
The roof pitch calculator converts between pitch notation (6:12) and angle degrees (26.6°). Pair it with the roofing calculator to estimate shingle bundles after determining the actual roof area from the rafter dimensions and roof length.
Determine run and pitch
Measure horizontal distance from wall plate to ridge center. Half the building span minus half the ridge board thickness. Select pitch based on architectural style and local snow/wind requirements.
Calculate rafter line length
Use unit length method: √(12² + rise²) × run in feet. For 6:12 pitch, 12 ft run: √(180) × 12 = 161.0 inches.
Add overhang tail
Overhang tail = √(overhang² + (overhang × rise/12)²). For 12" overhang at 6:12: √(144 + 36) = 13.4". Total rafter = 174.4".
Select lumber and mark cuts
Choose lumber that exceeds total length by 6–12". Mark birdsmouth at wall plate location: seat cut ≤33% of rafter depth (1.83" max for 2×6). Mark plumb cuts at ridge and tail.
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Last Updated: Mar 26, 2026
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