Rafter Angle Calculator

Rafter Cut-Angle Lookup Table (3/12 through 12/12)

Angles for the common residential pitch family, computed with plumb = atan(X/12) × 180 / π and seat = 90 − plumb. Use it as a rafter angle calculator offline, or to sanity-check the generator output before you cut. The saw-bevel column is the number you dial into the circular saw for the plumb face.

Plumb-cut = atan(X/12) × 180 / π. Seat-cut = 90 − plumb. At 12/12 both cuts are 45° because rise equals run, so the plumb and seat faces become mirror images.

How to Calculate Roof Pitch Degrees (and Why It Equals the Plumb Cut)

The plumb-cut angle and the pitch-in-degrees are the same number, which is the key insight behind how to calculate roof pitch degrees. The equation is degrees = atan(X/12) × 180 / π: a 4/12 pitch is 18.43°, a 6/12 is 26.57°, an 8/12 is 33.69°, and a 12/12 is exactly 45°. Because the plumb face of a rafter is vertical, its tilt from horizontal is the roof angle itself — so when you compute the pitch in degrees you have already computed the plumb-cut angle. That is why a rafter angle calculator starts from the same equation as a pitch-to-degrees tool but then extends it into the seat cut and the birdsmouth, which is the part a plain pitch calculator does not cover.

To work the equation in reverse (from degrees back to a pitch), use X = 12 × tan(angle). A 30° roof gives X = 12 × tan(30°) = 6.93, which is roughly a 7/12 pitch. That inverse is useful when a plan or a truss spec states the pitch in degrees and you need the X/12 form to look up the cut angles in the table above. Whichever direction you convert, the plumb cut and the pitch angle stay the same number, and the seat cut is always 90° minus that number.

Roof Rafter Dimensions: Where the Cut Angles Fit

Roof rafter dimensions describe the full board: the sloped length from ridge plumb cut to birdsmouth, the plumb-cut angle, the seat-cut angle, and the birdsmouth depth (HAP). The cut angles are what this rafter angle calculator owns — they are derived from the pitch and they define how the rafter meets the ridge and seats on the plate. The sloped length is a separate dimension computed from the run and the pitch angle (length = run ÷ cos(pitch angle)), and it lives on the main rafter calculator. Splitting the dimensions across the two tools keeps each page focused: this page answers what angle to cut; the rafter length calculator answers how long to cut the board.

A practical consequence is that the cut angles do not change with the span — a 6/12 rafter is plumb-cut at 26.57° whether the building is 24 feet or 40 feet wide. Only the sloped length changes with span; the angles are a function of pitch alone. That is why the lookup table on this page is indexed by pitch and not by span, and why you can cut a stack of plumb cuts at one saw setting for an entire run of common rafters as long as the pitch is constant. For the hip, valley, and jack rafters on a hip roof the angles are different (they run diagonally), so use the Hip and Valley guide for those.

Rafter Plumb Cut, Figuring Rafter Angles & Angle-Rafter Terminology

Three searches bring people to this page beyond the tool itself: understanding the rafter plumb cut precisely, figuring rafter angles by hand, and decoding the term "angle rafter." This section covers all three — the vocabulary, the manual methods, and where the calculator fits.

The Rafter Plumb Cut in Detail: One Angle, Three Locations

A plumb cut is any cut on a rafter whose face ends up vertical (plumb) once the rafter is installed — and it is always cut at the pitch angle, atan(X/12). The same angle appears in three places on one rafter:

• Ridge plumb cut: the top end that meets the opposing rafter or the ridge board. On a gable without a ridge board the two plumb faces meet flush — a "double plumb cut" when both rafters are cut as one pair.
• Heel plumb cut: at the birdsmouth, the vertical face that sits against the wall's edge (on a flush-eave detail) — this is the same 90° face as the seat cut's complement.
• Tail plumb cut: the fascia end of the rafter overhang, cut plumb so the fascia board nails on flat and vertical.

Because every plumb face is vertical in the finished roof, one saw-bevel setting serves all three locations: dial the pitch angle (26.57° for a 6/12) and the blade sweeps the plumb face wherever it appears. That is why the lookup table above carries a single plumb column — cut angles are a function of pitch alone, not of where along the rafter the cut lands.

Figuring Rafter Angles: Manual Layout vs. Calculator

Figuring rafter angles without electronics is a century-old skill, and every manual method is just a physical implementation of the same atan(X/12) math this page runs. Pick the method that matches what is in your hand:

• Framing square (the classic): hold the square to the rafter edge with the rise on the tongue and 12 on the body — for a 6/12, 6 on the tongue, 12 on the body — and the tongue edge traces the plumb line. The seat line comes from the body edge. No numbers beyond the pitch itself.
• Speed square (the fast one): pivot the square's lip on the board edge and rotate until the pitch number on the "common" scale lines up with the board edge; scribe along the pivoting edge for an instant plumb line. Fast, but the printed scale is typically whole degrees, so it trades precision for speed.
• Angle finder on an existing roof: for repairs, lay a digital protractor or a torpedo level on the exposed rafter or roof plane and read the angle directly, then convert back to pitch with X = 12 × tan(angle).
• Calculator (this page): enter the pitch once and get the plumb cut, seat cut, and saw bevel to two decimals — plus the birdsmouth walkthrough. Best when the pitch is odd (a 5.5/12 shed addition) or when you need the bevel and the seat cut together.

The manual methods and the calculator agree to within saw tolerance (about ±0.5° on a bevel scale, tighter on a square's scribed lines). In practice most framers lay out with a square and use the calculator to verify the first rafter before batching the run — the two approaches are complementary, not competing.

What Is an "Angle Rafter"? Terminology Explained

"Angle rafter" is not a separate rafter type — it is shorthand for rafters defined by the angles they are cut at. In standard framing vocabulary, every rafter in the roof gets its name from its position and its angle geometry:

• Common rafter: runs perpendicular from wall plate to ridge at the roof pitch — the rafter this page's angles apply to directly.
• Hip rafter: runs along the 45° diagonal corner where two roof planes meet, so its cuts (cheek cuts and backing bevel) differ from the common rafter's.
• Valley rafter: the diagonal where two roof planes meet in a trough — same diagonal-angle problem as the hip, opposite direction.
• Jack rafter: a shortened common rafter that lands on a hip or valley instead of the ridge, needing cheek cuts at the compound angle.

So when a plan says "angle rafter," read it as "which rafter, cut at which angle" — and for common rafters, the answer is always the pitch angle on every plumb face and its complement on the seat. The hip, valley, and jack variants carry their own diagonal geometry, which the Hip and Valley Rafter guide linked below handles in full.