Rafter length for a 24 ft wide building with a 6/12 roof

Short answer

A 24 ft wide gable roof at 6/12 pitch with a 12 inch overhang needs rafters about 173-9/16 inches (14 feet 5-9/16 inches) long along the top edge, or 160-3/16 inches (13 feet 4-3/16 inches) from ridge to wall line. With 2×8 rafters buy 16 ft boards; a 24 ft long building at 16 inches on center takes 38 rafters.

How to work it out

  1. Run = 24 ft ÷ 2 − ½ × 1.5 in ridge = 143.25 in
  2. Slope factor √(1 + (6/12)²) = 1.118 → 143.25 in × 1.118 = 160.16 in
  3. + overhang 12 in × 1.118 = 13.42 in → 173.57 in = 173-9/16 in (14 ft 5-9/16 in)
  4. Board: 173.57 + 3.63 plumb-cut allowance (7.25 in × 6/12) = 177.20 in, + 1 in trim = 178.20 in → buy 16 ft boards
  5. Plumb cut 7.25 in × 1.118 = 8.11 in; heel 3.5 in seat × 6/12 = 1.75 in; HAP = 8.11 in − 1.75 in = 6.36 in = 6-3/8 in
  6. Top of ridge board = HAP 6.36 in + run 143.25 in × 6/12 = 78 in (6 ft 6 in) above the plates
  7. Birdsmouth depth = heel 1.75 in × cos 26.6° = 1.57 in — limit ¼ × 7.25 in = 1.81 in → OK

Twenty-four feet is the classic two-car garage width. At 6/12 the rafters come out at about 14 ft 5-9/16 in along the top edge — longer than a 14 ft board before you make a single cut — so this roof is framed from 16 ft stock. With 2×8s the plumb-cut tail and an inch of trim bring the board you need to about 178-3/16 in, comfortably inside 192 in.

Rafters this long need the right size and grade for your snow load, and a 24 ft span usually calls for ceiling ties or a structural ridge — take those from your code’s span tables or an engineer. The 2×8 here is only an example size.

Adjust for your project

ft
Measure across the tops of the walls, outside edge to outside edge.
in 12
Rise in inches for every 12 in of level run (6 = 6/12). A roofer’s pitch gauge or a level and tape will read it.
in
Measured level from the outside of the wall to the end of the tail. Shed roof: the low wall.
The board’s actual depth — a 2×6 is 5½ in deep. It sets the plumb cuts and the birdsmouth.
ft
More options: Ridge · Seat · Tail …
in
Half is deducted from each rafter. A 2× ridge is 1½ in thick.
in
Usually the full width of the top plate: 3½ in on a 2×4 wall, 5½ in on a 2×6 wall. The code minimum is 1½ in of bearing on wood (IRC R802.6).
in
How far the roof runs past the end walls. Adds fly (barge) rafters and lengthens the ridge and sheathing.
Rafter length (top edge, with overhang)173-9/16 in (14 ft 5-9/16 in)
Board length to buy16 ft boards
Rafters needed
38 rafters
Height above plate (HAP) at the wall line
6-3/8 in
Top of ridge board above the wall plates
78 in (6 ft 6 in)
Rise at the building line (measuring line)
72 in (6 ft)
Birdsmouth heel cut (plumb height)
1-3/4 in
Birdsmouth depth, square to the rafter
1-9/16 in
Plumb cut length (ridge and tail)
8-1/8 in
Ridge board depth
2×10 or deeper (plumb cut 8-1/8 in)
Bottom of the tail below the top of the wall (fascia line)
7-3/4 in
Length without overhang
160-3/16 in (13 ft 4-3/16 in)
Rafter length (decimal inches)
173.57 in
Roof angle (plumb-cut angle from square)
26.6 degrees
Pitch
6/12 = 26.57°
Ridge board length (building plus rake overhangs)
288 in (24 ft)
Roof area to sheathe (all slopes)
694 sq ft
  • Rafter length is the line length along the top edge, from the ridge plumb cut (after the ridge deduction) to the end of the tail. Mark the birdsmouth heel cut where the rafter crosses the outside of the wall plate.
  • Birdsmouth depth 1-9/16 in (measured square to the rafter) is within ¼ of the 7-1/4 in depth (1-13/16 in) — the limit IRC Figure R802.7.1.1 shows for the seat notch.
  • Rafter size, spacing and span, ridge support, ties and uplift connections are set by your local building code and span tables (IRC R802) — this calculator only does the geometry.
Check your codeCode limits vary by jurisdiction — confirm with your building department before you cut or build. (IRC R802)

For this job · affiliate link
Speed square (7 in)Pivot a speed square to 6 on the COMMON scale and one line marks the plumb cut, the birdsmouth and the tail — the same setting on every rafter.
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Rafter length for a 24 ft span at 6/12, by eave overhang

Rafter length for a 24 ft span at 6/12, by eave overhang
OverhangRafter length (top edge, with overhang)Board length to buyBottom of the tail below the top of the wall (fascia line)
0 in160-3/16 in (13 ft 4-3/16 in)14 ft boards0 in
6 in166-7/8 in (13 ft 10-7/8 in)16 ft boards4-3/4 in
12 in173-9/16 in (14 ft 5-9/16 in)16 ft boards7-3/4 in
18 in180-5/16 in (15 ft 5/16 in)16 ft boards10-3/4 in
24 in187 in (15 ft 7 in)16 ft boards13-3/4 in

What to know about rafters for a 24 ft wide roof

Each side of the roof covers 12 ft of level run, less ¾ in for half the ridge board, so the line length from ridge to wall is 160.16 in. The 12 in overhang, measured level, adds about 13.4 in along the slope. The rise on the measuring line is 72 in (144 in of run × 6/12), at an angle of about 26.6° — the angle you set on a speed square or saw for the plumb cuts. That 72 in is not the height of the ridge board, though: 2×8 rafters with a 3½ in seat leave a height above plate (HAP) of 6-3/8 in, so the top of the ridge board sits about 78 in above the top plates.

A 2×8 at 6/12 has a plumb cut of 8-1/8 in, and the IRC wants the ridge board at least as deep as that cut end (R802.3) — a 2×10 ridge. The birdsmouth is fine: a full 3½ in seat gives a 1-3/4 in heel and a notch 1-9/16 in deep measured square to the rafter, inside the ¼-depth limit of 1-13/16 in. The same seat on a 2×6 would not pass; its limit is 1-3/8 in.

Rafter size is where this calculator stops. Section R802 of the IRC covers wood roof framing: rafter span tables by species, grade, spacing and snow load, the ridge, and the ties or ceiling joists that stop the walls from spreading. The horizontal span here is about 11 ft 11 in per side; find that span in the table for your species, grade and snow load rather than picking a size by eye. On a garage with no interior walls, the ties matter as much as the rafters.

The count is 19 per side: 288 in of building length ÷ 16 in gives 18 spaces, plus one to close the last. That makes 38 rafters of 16 ft stock. At 24 in on center it drops to 26, a common spacing for trusses but one that needs a bigger or stiffer rafter under the same load.

The long walls under this roof are on How many studs for a 24 ft wall with a door and a window. The same math on a smaller building is Rafter length for a 12 ft shed at 4/12.

What you’ll need

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Frequently asked questions

How long are rafters for a 24 ft wide roof at 4/12 pitch?

About 163-5/8 inches (13 feet 7-5/8 inches) with the same 12 inch overhang — 14 ft boards. The top of the ridge board drops to 54-1/4 inches (4 feet 6-1/4 inches) above the plates.

How long are rafters for a 24 ft span at 8/12 pitch?

About 186-9/16 inches (15 feet 6-9/16 inches) — with the 2×8 plumb-cut tail and trim that needs 18 ft boards. The top of the ridge board climbs to 101-7/8 inches (8 feet 5-7/8 inches) above the plates, at 33.7 degrees. A full 3½ inch seat is too deep at this pitch: the notch would be 1-15/16 inches, over a quarter of the 2×8’s depth, so shorten the seat.

Sources