Rafter Length Calculator

The parts of a rafter

• Span: the building width, outside of wall plate to outside of wall plate.^[5]
• Run: half the span, the level distance from the outside of the wall to the center of the ridge.^[5][6]
• Rise: how far the roof climbs over the run. Pitch is the rise per 12 in of run (6/12 = 6 in per foot).^[7]
• Ridge deduction: a ridge board takes up space at the peak, so each rafter stops at the ridge’s face, half the ridge thickness short of the center.^[5][7]
• Overhang (projection) and tail: the overhang is the level distance from the outside of the wall to the end of the rafter. The tail is the length of rafter that covers it.^[5]
• Plumb cut: the vertical cut at the top that sits against the ridge. The tail end is often cut plumb too, or square across.^[5][6]
• Seat cut and bird’s mouth: the level seat cut rests on the wall plate; together with a short plumb cut (the heel) it forms the notch called the bird’s mouth.^[5][6]

The formulas

Both ends are plumb cuts, and two plumb lines are parallel, so the length between them is the same whether you measure along the top edge, the middle or the bottom of the board.^[8] The ridge is taken off level, half its thickness from each run. Along the rafter that is a little more than half the thickness: 0.84 in at 6/12 for a 1½ in ridge, rather than 0.75 in.^[7] Navy and Swanson tables give the length to the center of the ridge with no overhang, so you add the tail and take off the ridge yourself; the calculator does both.^[5][7]

Example: 6/12, 24 ft wide, 1½ in ridge, 12 in overhang

1. Run: 24 ft ÷ 2 − 1.5 in ÷ 2 = 144 − 0.75 = 143.25 in
2. Slope factor: √(1 + (6 ÷ 12)²) = 1.11803
3. Ridge to wall line: 143.25 × 1.11803 = 160.16 in = 13 ft 4 3/16 in
4. Tail: 12 × 1.11803 = 13.42 in = 1 ft 1 7/16 in
5. Total: 160.16 + 13.42 = 173.57 in (added before rounding) = 14 ft 5 9/16 in
6. Board: both ends are plumb cuts, so on the board the cuts are offset by the rafter depth × pitch ÷ 12 = 7.25 × 6 ÷ 12 = 3.63 in. 173.57 + 3.63 + 1 in to square the ends (our allowance) = 178.20 in, which fits a 16 ft board
7. Plumb cuts: arctan(6 ÷ 12) = 26.57° from square
8. Rise from the wall line to the center of the ridge: 12 ft × 6 ÷ 12 = 72 in (6 ft)

As a check on the method, a 7/12 roof on a 16 ft span with no ridge board or overhang comes to 111.14 in (9 ft 3 1/8 in); the Navy builder’s manual works the same example to 111⅛ in.^[5]

Example: 4/12, 20 ft wide, 18 in overhang, 2×6 rafters on a 2×6 wall

1. Run: 120 − 0.75 = 119.25 in; slope factor 1.05409
2. Ridge to wall line: 119.25 × 1.05409 = 125.70 in = 10 ft 5 11/16 in
3. Tail: 18 × 1.05409 = 18.97 in = 1 ft 7 in
4. Total: 12 ft 0 11/16 in, from a 14 ft board
5. Bird’s mouth on a 5½ in plate: heel 5.5 × 4 ÷ 12 = 1.83 in; notch 1.74 in deep, 32% of the 5½ in rafter. That is over the one-quarter limit, so the calculator warns. A narrower seat or a deeper rafter fixes it; ask your building department which they accept.

Board length to buy

Total rafter length with a 12 in overhang and a 1½ in ridge, and the 2×8 board it comes from. Because both ends are plumb cuts, the board has to be longer than the rafter by its depth × pitch ÷ 12 (the offset between the top and bottom corners of the cuts); the calculator adds that and 1 in for squaring the ends (our allowance), then picks the shortest of 8 to 20 ft in 2 ft steps. Check what your lumberyard stocks.

“Over 20 ft” means a longer piece than common lumber. Use engineered lumber or a splice that has been designed, not a field joint.

The bird’s mouth

The seat is level and as wide as the bearing on the wall; the heel is a short plumb cut at the outside of the wall. For a seat of width w at pitch X/12:

One quarter of the actual depth is 0.88 in for a 2×4, 1.38 in for a 2×6, 1.81 in for a 2×8, 2.31 in for a 2×10, 2.81 in for a 2×12.^[2] The IRC has no rule that names the bird’s mouth, so whether the end-notch limit applies to it is your building department’s call. The Navy manual says to leave at least 2 in of wood above the seat cut.^[5] The seat must still give the bearing the code asks for: at least 1½ in on wood or metal and 3 in on masonry or concrete (R802.6).^[1]

Laying out a rafter

With a Speed Square

1. Lay the square on the face of the board with its lip (the T bar) over the top edge. Pivot it on the pivot point until the pitch number on the COMMON scale lines up with the same edge, and mark along the square from the pivot point. That is the plumb line at the ridge.^[8]
2. Swanson’s instructions then move that line toward the tail by half the ridge thickness, because the table length runs to the center of the ridge.^[8] The calculator’s “ridge to wall line” length already has the ridge taken off, so with it you skip this step. Don’t deduct the ridge twice.
3. Measure the ridge-to-wall-line length along the top edge and mark a second plumb line the same way.^[8] This is the heel of the bird’s mouth, at the outside of the wall.
4. Measure the heel height up this line from the bottom edge and draw the seat line square to it. It runs level to the bottom edge, and its length equals the seat width.
5. From the heel line, measure the tail length along the top edge toward the low end and mark the tail plumb cut the same way as the ridge cut.^[8] The Army carpentry manual notes the tail is often cut square across instead.^[6]
6. Cut one rafter, test it on the building at both ends, then use it as the pattern for the rest.^[8]

With a framing square

Hold the square with the rise (for example 6) on the tongue, the narrow arm, and 12 on the blade, both on the same edge of the board. A line along the tongue is a plumb cut and a line along the blade is a level seat cut.^[5] Many framing squares also have a rafter table stamped on them: under the number 6 it reads 13.42, the inches of rafter per foot of run.^[5][9] Multiplying 13.42 by the run in feet gives the length to the ridge center. The exact figure is 13.416, so over a 12 ft run the rounded one comes out 0.04 in long (161.04 in instead of 161.00 in); the calculator works with the full figure.^[10]

If you cut with the board lying flat on a miter saw, the plumb cut is a miter of 26.57° at 6/12 (the pitch angle; 18.43° at 4/12, 33.69° at 8/12).

How many rafters

A 40 ft building at 16 in on center: 480 ÷ 16 = 30 spaces, + 1 = 31 per side, 62 for the roof. The count does not include rafters for a gable overhang (rake), doubled rafters beside skylights or chimneys, or anything else your plans add. The spacing comes from the span table, not from this count.

Before you cut

• A ridge board must be at least 1 in nominal thick and no shallower than the cut end of the rafter. A 2×8 rafter at 6/12 has a plumb cut 8.1 in tall, more than the 7.25 in of a 2×8, so it needs a 2×10 ridge board. Without ceiling joists or rafter ties to hold the walls together, the ridge must be supported by a wall or a ridge beam (R802.3).^[1]
• Collar ties near the top of the attic do not replace rafter ties or ceiling joists near the bottom (R802.4.6); ceiling joists or rafter ties set above the lower third of the attic take the roof outside the simple tables (the ridge designed as a beam, or engineered connections; R802.5.2 and its tables), and even within the lower third, the higher they sit, the shorter the allowed rafter span (the adjustment factors in Table R802.4.1(9)).^[1]
• Rafters must be attached to the wall with connections that resist wind uplift (R802.11); plain nailing is allowed only in limited cases.^[1]
• Rafters on opposite sides of the ridge should line up; the IRC allows them to be offset by no more than 1½ in (R802.4.2).^[1]
• An overhang notched where it sits on the wall needs at least 3½ in of rafter left above the notch, and the overhang can be no more than 24 in (R802.7.1.1). Hip and valley rafters must be at least 2 in nominal thick (R802.4.3).^[1]
• Hip and valley rafters are longer per foot of run than common rafters; the roof pitch calculator gives both.

Related calculators

• Roof pitch calculatorFind the pitch, angle and multiplier
• Roofing calculatorRoof area, squares and shingle bundles
• Square footage calculatorPlan area of rooms and odd shapes
• Project materials listPrint everything you added from each calculator

Prepared by the Yard & Build editors. The formulas behind this calculator are checked against hand-worked answers every time the site is built. Rafter tables and code sections checked October 5, 2026.