How to Calculate Roof Rafters
Calculating rafter length accurately is critical for a square, structurally sound roof. This guide covers the adjusted run formula, plumb cut angle, bird's-mouth geometry, and IRC span compliance — with worked examples for any pitch.
Get your exact rafter length fast. Enter building span, ridge thickness, pitch, and overhang to get rafter length, plumb cut angle, and bird's-mouth heel depth. Use the Roof Rafter Calculator to get exact rafter length and cut angles instantly.
Calculate my rafter length →What is a common rafter?
A common rafter is the structural member that runs from the ridge board at the roof peak down to the wall plate at the top of the exterior wall, then extends further as the tail that creates the eave overhang. It is the primary structural element of a stick-framed roof. Getting rafter length right means every rafter seats flush on the wall plate and meets at the ridge without bowing — getting it wrong means a visually and structurally compromised roof.
A rafter is not simply a diagonal line from wall to ridge. It has three distinct segments: the segment from ridge to wall plate (the structural span), the bird’s-mouth notch where it bears on the wall plate, and the tail that forms the eave overhang. Each segment requires a separate calculation, and they are related through the pitch angle. The roof pitch calculator gives you the angle in degrees you need for all three cuts.
Rafter length formula
The core mistake in rafter calculation is using the full building span instead of the adjusted run. The run is half the span minus half the ridge board thickness. That ridge board deduction is small (typically 0.75 inches for a 1.5-inch ridge) but matters — skip it and every rafter is slightly too long, bowing the ridge board outward and pushing the walls out of plumb.
Adjusted Run
X = (Building Span in inches − Ridge Thickness) ÷ 2
Segment Length (ridge to wall plate)
Lseg = X ÷ cos(θ)
Total Rafter Length
Ltotal = Lseg + (Overhang ÷ cos(θ))
Worked example. Building span = 24 ft (288 inches), ridge = 1.5 inches, pitch = 6:12 (θ = 26.57°), horizontal overhang = 12 inches. Adjusted run: X = (288 − 1.5) ÷ 2 = 143.25 inches. Segment: 143.25 ÷ cos(26.57°) = 160.16 inches. Overhang extension: 12 ÷ cos(26.57°) = 13.42 inches. Total: 173.58 inches (14 feet 5.58 inches). This is the measurement from the upper plumb cut at the ridge to the lower tail cut at the eave. The roof slope calculator cross-references the same pitch in degrees for structural drawings.
Plumb cut and seat cut angles
Every rafter has two primary cuts at the bird’s-mouth. The plumb cut is vertical — parallel to the walls and perpendicular to the roof surface. The seat cut is horizontal — parallel to the top plate and creating the flat bearing surface where the rafter rests on the wall. The angle for both cuts comes directly from the pitch.
Set your circular saw bevel to the pitch angle in degrees. For a 6:12 pitch, the bevel is 26.57 degrees (round to 26.5 for the saw). The plumb cut at the ridge is also this angle — it creates the vertical surface that butts against the ridge board. For the tail cut at the eave, use the same angle oriented to create a vertical plumb surface or a square fascia cut, depending on the design intent.
| Pitch (X:12) | Plumb cut angle | Saw bevel setting |
|---|---|---|
| 3:12 | 14.04° | 14° |
| 4:12 | 18.43° | 18.5° |
| 5:12 | 22.62° | 22.5° |
| 6:12 | 26.57° | 26.5° |
| 8:12 | 33.69° | 33.5° |
| 9:12 | 36.87° | 37° |
| 12:12 | 45.00° | 45° |
Bird’s-mouth notch geometry
The bird’s-mouth is the notch cut in the underside of the rafter where it seats on the wall plate. It transfers the roof load into the wall. IRC R802.7.1 limits the notch depth to 25% of the rafter’s actual depth at the bearing point — violating this limit creates a structural hinge point that can catastrophically fail under snow load or wind uplift.
The heel cut depth is calculated from the seat cut length. For a seat cut of 3.5 inches (resting on a 2×4 plate) at 6:12 pitch: Heel cut = 3.5 × tan(26.57°) = 3.5 × 0.5 = 1.75 inches. For a 2×8 rafter (actual depth 7.25 inches), the 25% maximum is 1.81 inches — just within the limit. Use a deeper rafter if the calculation produces a heel cut that exceeds the 25% threshold. After rafter sizing is confirmed, use the roof area calculator to finalize the sheathing and material takeoff.
Frequently asked questions
What is the formula for calculating rafter length?
Rafter length uses two calculations. First, the adjusted run: (building span in inches minus ridge board thickness) divided by 2. Second, the segment length: adjusted run divided by cosine of the roof pitch angle in degrees. Add the overhang extension (overhang in inches divided by cosine of the pitch angle) to get total rafter length from upper plumb cut to lower tail cut.
Why do I subtract half the ridge board thickness from the run?
The ridge board sits at the roof peak and has physical thickness that each rafter must account for. Each rafter butts against one face of the ridge board, so its run terminates at the ridge centerline, not the face. For a 1.5-inch ridge board, each rafter run is shortened by 0.75 inches. Skip this and the rafters push the ridge board off-center, bowing it and creating a visually and structurally defective peak.
What is a plumb cut on a rafter?
A plumb cut is a cut that is vertical when the rafter is installed — parallel to the exterior walls of the building. The plumb cut at the ridge creates the surface that butts against the ridge board. The plumb cut at the eave creates the vertical face of the tail visible below the fascia. The bevel angle for all plumb cuts equals the pitch angle in degrees (for example, 26.57 degrees for a 6:12 pitch).
What is a bird's-mouth cut?
A bird's-mouth is a two-cut notch in the underside of a rafter at the bearing point where the rafter sits on the wall plate. It consists of a plumb cut (vertical, facing the exterior) and a seat cut (horizontal, resting on the top plate). The seat cut creates the flat bearing surface. The bird's-mouth transfers roof loads into the wall and prevents the rafter from sliding outward.
How deep can I cut the bird's-mouth notch?
The IRC limits the bird's-mouth notch to 25 percent of the rafter's actual depth. For a 2x8 rafter (actual depth 7.25 inches), the maximum notch is 1.81 inches. For a 2x10 (actual 9.25 inches), it is 2.31 inches. Exceeding this creates a dangerous weak point that can crack under snow load or wind uplift. If your seat cut length requires a deeper notch, use a larger rafter size rather than deepening the cut.
How many common rafters do I need for a gable roof?
Rafter count follows the truss count formula: (roof length in inches divided by rafter spacing in inches) plus 1, doubled for both sides of the ridge. For a 32-foot gable at 16 inches OC: (384 divided by 16) plus 1 equals 25 rafters per side, 50 total common rafters. Add ridge board length, plus any hip, valley, or jack rafters separately for more complex roof geometries.
References
International Code Council. (2021). International Residential Code, Section R802.5.2: Rafter Spans and R802.7: Notching and Boring. ICC.
American Wood Council. (2021). Prescriptive Residential Wood Deck Construction Guide (DCA6). AWC. awc.org
National Roofing Contractors Association. (2024). The NRCA Roofing Manual: Steep-slope Roof Systems. NRCA.