Rafter Calculator

A rafter calculator takes roof pitch, horizontal run, and overhang and turns them into the exact board length a carpenter needs to cut, along with the plumb cut angle at the ridge and the birdsmouth notch angle at the wall plate. This page explains how the rafter calculator works, walks through the formula with a real worked example, lists common rafter lengths by pitch and run, and covers the mistakes that waste lumber on a framing job.

What the Rafter Calculator Finds

A common rafter runs from the ridge board down to the top plate of an exterior wall, and its length depends entirely on roof pitch and horizontal run. The rafter calculator on this page returns the theoretical rafter length along the top edge of the board, the plumb cut angle where it meets the ridge, the seat cut angle at the birdsmouth, and the tail length if you want an overhang past the wall. Getting these numbers right the first time matters because rafters are structural, cut from full-length stock, and expensive to redo once a roof deck is partially sheathed.

How to Use the Rafter Calculator

Enter the roof pitch as x:12 or in degrees, then enter the horizontal run measured from the center of the ridge to the outside face of the wall plate. Add the overhang distance you want the rafter tail to extend past the wall, typically 12 to 24 inches on a residential roof. The rafter calculator instantly returns total rafter length, the plumb cut angle, and the birdsmouth depth needed at the seat cut. If your roof uses a ridge board rather than a ridge beam, subtract half the ridge board thickness from the run before entering it, since the rafter calculator assumes run is measured to the ridge centerline by default.

Rafter Length Formula and Worked Example

The core formula is the Pythagorean theorem: rafter length = √(run² + rise²), where rise = run × (pitch ÷ 12). For a roof with an 8:12 pitch and a run of 10 feet (120 inches), rise = 120 × (8/12) = 80 inches. Rafter length = √(120² + 80²) = √(14,400 + 6,400) = √20,800 ≈ 144.2 inches, or about 12 feet before adding the overhang. Add an 18-inch tail and the total board length needed is roughly 13 feet 6 inches, which the rafter calculator rounds up to the nearest standard lumber length so you order 14-foot stock. Doing this arithmetic by hand for every rafter on a roof is slow and error-prone, which is exactly why a rafter calculator exists.

Common Rafter Lengths by Pitch and Run

Pitch	Run (ft)	Rafter Length (approx.)
4:12	10	10' 6"
6:12	10	11' 2"
8:12	10	12' 0"
6:12	14	15' 8"
8:12	14	16' 10"
10:12	14	18' 3"

These figures assume the rafter calculator's default measurement from ridge centerline and do not include overhang, so add your planned tail length to each value before ordering lumber.

Birdsmouth Cuts and Overhang

The birdsmouth is a notch cut where the rafter crosses the top plate, and it has two cut lines: the seat cut, which sits flat on the plate, and the heel cut, which runs perpendicular to the rafter's length. The rafter calculator derives both angles directly from the pitch, since the seat cut angle equals 90 degrees minus the roof's angle in degrees. Overhang length is a separate design choice rather than a structural requirement, and it affects how much rain runoff clears the exterior wall as well as how much shade the eave provides in summer. Keep the birdsmouth notch depth to no more than a third of the rafter's total depth, since cutting deeper weakens the rafter at its most loaded point.

Mistakes to Avoid

A rafter calculator's output is only as accurate as the pitch and run you enter, so the most common mistake is guessing the pitch instead of measuring it with a level or the roof pitch calculator first. Cutting the first rafter as a pattern and test-fitting it before cutting the rest of the batch catches measurement errors before they cost an entire pack of lumber. Forgetting to account for ridge board thickness shifts every rafter length by a consistent amount, which is easy to miss until the roof deck does not sit flush. Finally, ignoring species and grade when selecting rafter stock can leave a roof under-spanned even if every length from the rafter calculator is technically correct, so check span tables for your specific lumber grade separately.

Tools for Cutting Rafters Accurately

A speed square set to the roof's angle in degrees makes marking the plumb cut and birdsmouth fast and repeatable across every rafter in a run. A circular saw with a sharp blade keeps cuts clean on the seat and heel lines, and a rafter calculator paired with a printed cut list prevents mixing up lengths between different roof sections. Framing squares with rafter tables etched into the blade were the traditional tool before digital calculators, and they still work as a manual cross-check against what the rafter calculator returns.

Related Calculators

Before cutting rafters, confirm the roof's pitch with the roof pitch calculator to make sure your rise-and-run inputs are accurate. For the rest of the framing and finishing project, the stair calculator and stair stringer calculator handle interior and exterior stairs, while the concrete yard calculator sizes footings for any posts supporting the roof structure. Keeping every measurement consistent across these calculators, starting with the rafter calculator, reduces the chance of a mismatch once framing is underway.