Rafter Length Calculator
Enter building span, roof pitch, overhang, and ridge board thickness to calculate rafter run, rafter length, pitch multiplier, ridge height, and birdsmouth seat cut depth.
Estimate only — not professional advice. Always verify results independently before purchasing materials or beginning work. Terms of Use
What is Rafter Length?
A rafter length calculator determines the length of common rafters for a gable or hip roof based on the building span, roof pitch, eave overhang, and ridge board thickness. Common rafters run from the top of the exterior wall plate to the ridge board at the peak of the roof. Accurate rafter calculations are essential for ordering lumber, cutting rafters efficiently, and ensuring the roof structure meets load and span requirements. The rafter run is the horizontal distance from the outside of the wall plate to the center of the ridge. For a simple gable roof, the run equals half the building span minus half the ridge board thickness. A 24-foot wide building with a 1.5-inch ridge board has a run of 12 feet minus 0.0625 feet (0.75 inches), or 11.94 feet. The ridge board deduction is small but important for tight framing. The pitch multiplier (also called the slope factor or secant of the roof angle) converts horizontal run to actual rafter length along the slope. It equals the square root of (1 + (pitch/12) squared). For a 6:12 pitch, the multiplier is sqrt(1 + 0.25) = sqrt(1.25) = 1.1180. This means every foot of horizontal run requires 1.118 feet of rafter. The pitch multiplier is also used to convert roof footprint area to actual sloped surface area for shingle ordering. The total rafter length equals the run multiplied by the pitch multiplier plus the overhang distance. The overhang (also called the eave projection or tail) extends the rafter beyond the wall to protect siding from rain and create shade. Standard overhangs range from 12 to 24 inches for residential construction. The overhang is added directly because it extends along the slope from the wall line. Ridge height is the vertical distance from the top of the wall plates to the top of the ridge board. It equals the rafter run multiplied by the pitch expressed as a decimal (pitch divided by 12). For a 6:12 pitch with an 11.94-foot run, ridge height is 11.94 times 0.5 equals 5.97 feet. Ridge height determines attic space and affects the overall building height for zoning compliance. The birdsmouth is the notch cut into the bottom of each rafter where it sits on the wall plate. The seat cut (horizontal portion of the birdsmouth) should equal the full width of the wall plate, typically 3.5 inches for 2x4 walls. The plumb cut (vertical portion) is determined by the pitch. A properly cut birdsmouth transfers the roof load vertically into the wall and prevents the rafter from sliding outward.
How to Calculate
- Measure the full building span (outside wall to outside wall) in feet
- Determine the roof pitch in rise per 12 inches of run (check existing rafters or plans)
- Decide on the eave overhang distance in feet (1 to 2 feet is typical residential)
- Enter the ridge board thickness in inches (1.5 inches for a 2x ridge, 3.5 inches for a 4x ridge)
- Review the rafter run, pitch multiplier, total rafter length, and ridge height
- Order lumber at least one standard length longer than the calculated rafter length to allow for cutting
Formula
Run (ft) = (Building Span / 2) - (Ridge Thickness / 2 / 12) Pitch Multiplier = sqrt(1 + (Pitch / 12)^2) Rafter Length (ft) = (Run + Overhang) x Pitch Multiplier Ridge Height (ft) = Run x (Pitch / 12) Birdsmouth Seat Cut = 3.5 inches (standard 2x4 wall plate width) Where Pitch is expressed as rise in inches per 12 inches of run. The ridge thickness is converted from inches to feet before subtracting from the half-span.
Example Calculation
A 24-ft building span, 6/12 pitch, 1.5-ft overhang, 1.5-inch ridge board: Run = (24 / 2) - (1.5 / 2 / 12) = 12 - 0.0625 = 11.94 ft Pitch Multiplier = sqrt(1 + (6/12)^2) = sqrt(1 + 0.25) = sqrt(1.25) = 1.118 Rafter Length = (11.94 + 1.5) x 1.118 = 13.44 x 1.118 = 15.02 ft Ridge Height = 11.94 x (6 / 12) = 11.94 x 0.5 = 5.97 ft Birdsmouth Seat Cut = 3.5 in
Frequently Asked Questions
What size lumber do I need for rafters?
Rafter size depends on span, spacing, pitch, and snow/wind loads. For common residential applications with 16-inch spacing and moderate loads: 2x6 rafters span up to 10 feet, 2x8 up to 13 feet, 2x10 up to 16 feet, and 2x12 up to 20 feet. Always check the IRC rafter span tables (Table R802.4) for your specific species, grade, and loading conditions.
Does this calculator account for the overhang pitch?
The overhang length is added directly to the rafter length as a horizontal distance projection. In practice, the overhang measurement is typically specified as the horizontal projection from the wall face. The actual rafter tail length along the slope would be overhang times the pitch multiplier, but since overhangs are specified as horizontal projections in most plans, the calculator adds the stated overhang value directly.
What is the maximum rafter span without support?
Maximum span depends on lumber size, species, grade, spacing, and load. For #2 SPF (spruce-pine-fir) at 16-inch spacing with 20 psf live load and 10 psf dead load: 2x6 spans 10 ft 6 in, 2x8 spans 13 ft 10 in, 2x10 spans 17 ft 8 in, 2x12 spans 21 ft 6 in. Longer spans require purlins, collar ties, or engineered trusses.
Why do I need to subtract the ridge board thickness?
Common rafters rest against the ridge board at the peak. Half the ridge board thickness is on each side of the center line. If you calculate the run as exactly half the building span, the rafters would be too long by half the ridge board thickness (typically 3/4 inch). This small adjustment matters for tight framing and prevents rafters from pushing the ridge board out of alignment.
What is the birdsmouth cut and why is it important?
The birdsmouth is a notch cut at the bottom of the rafter where it bears on the wall plate. It has two parts: the seat cut (horizontal, equal to the plate width of 3.5 inches for 2x4 walls) and the plumb cut (vertical, determined by pitch). The birdsmouth transfers the roof load directly into the wall. IRC Section R802.6 requires that the birdsmouth not cut more than one-third of the rafter depth.