3/12 Gable Rafter Length on a 24×40 Building
A 3/12 gable, 24 ft wide and 40 ft long, with a 12 in overhang and a 1.5 in ridge.
Formula SSC-2026.1
3.00 / 12 · 14.04°
Pitch angle
14.04°
Multiplier 1.0308
Common rafter
13 ft 4 in
Tail 1 ft 3/8 in
Cuts
14.04° plumb
75.96° seat
Roof area
1,120 ft²
11.20 squares
Shingle bundles
37
3 bundles per square + 10% waste
Sheathing / felt
39 sheets
4 underlayment rolls
Delivery weight
4,496 lb
2,039 kg · 70 lb bundles, 46 lb sheets, 28 lb rolls
Rise and run are scaled from the span, overhang, and pitch. The small triangle is the pitch ratio.
| Item | Net | Waste | Order | Unit price | Line total |
|---|---|---|---|---|---|
| Architectural shingle bundles | 11.20 squares | 10% | 37 bundles | USD | $1,554.00 |
| 4x8 CDX sheathing | 35.0 sheets | 10% | 39 sheets | USD | $1,092.00 |
| Underlayment rolls | 1,120 ft² | overlap allowance | 4 rolls | USD | $220.00 |
| Ridge cap bundles | 42.0 ft ridge | — | 2 bundles | 25 ft per bundle | — |
| Pitch | Degrees | Multiplier | Rafter | Squares | Bundles | Sheets |
|---|---|---|---|---|---|---|
| 3.0/12 | 14.04° | 1.031 | 13 ft 4 in | 11.20 | 37 | 39 |
| 5.0/12 | 22.62° | 1.083 | 14 ft 3/16 in | 11.77 | 39 | 41 |
| 2.0/12 | 9.46° | 1.014 | 13 ft 1 3/8 in | 11.02 | 37 | 38 |
Show the deterministic formula
Angle = arctan(rise ÷ 12). Multiplier = √(1 + (rise ÷ 12)²). Gable run = span ÷ 2 − ridge thickness ÷ 2. Rafter length = (run + horizontal overhang) × multiplier.
Plumb cut = pitch angle. Seat cut = 90° − pitch angle. Area uses both slopes on a gable and one slope on a shed, and it includes a rake overhang equal to the eave overhang.
Bundles = ceiling of squares × 3 × 1.10. Sheets = ceiling of area × 1.10 ÷ 32. Rolls use 360 ft² effective coverage. Delivery weight plans 70 lb per bundle, 46 lb per sheet, and 28 lb per roll, then the header converts that pound total at 1 lb = 0.45359237 kg.
Contractor sign-off
Project: 3/12 Gable Rafter Length on a 24×40 Building
Prepared by
Date
Verified by (PE / electrician / inspector)
License number
Signature
This sheet is an estimate for ordering and layout discussion. It is not a sealed design. Confirm the quantities with a licensed local professional and the authority having jurisdiction before you buy or build.
Engineering notes
A 3/12 pitch is arctan(3/12). The multiplier is the square root of 1 plus (3/12) squared. On this 24 ft span the common-rafter run is half the span minus half of the 1.5 in ridge, then the 1 ft overhang is added before the multiplier. Bundles are 3 per square plus 10 percent. Sheets are the roof area times 1.10 divided by 32. The page does not size the rafter for snow or wind.
Code reference
IRC R802 covers conventional wood roof framing and R905 covers roof coverings. This page does not size the rafter for snow or wind.
Field questions
- What is the angle of a 3/12 pitch?
- It is the arctangent of 3 divided by 12, in degrees. The plumb cut uses that angle and the seat cut is 90 degrees minus that angle.
- Does the rafter length include the overhang?
- Yes. The reported length includes the body and the tail. The tail is also listed on its own.
- How many bundles is a square?
- The planning count is 3 bundles per 100 square feet, then 10 percent waste, rounded up.
Explore Related Engineering Calculations
- 6/12 Roof Pitch, Rafter Length, and Shingle Bundles
- 4/12 vs 8/12 Gable Roof Material Estimator
- 12/12 Pitch Gable Rafter on a 24 Foot Span
- Shed Roof 3/12 Pitch on a 10 by 12 Foot Building
- 9/12 Pitch Roof on a 30 Foot Span
- Shingle Bundle Delivery Weight for a 6/12 Roof
- 20×20 Garage Slab: 4 Inch vs 6 Inch
- 50 Amp EV Charger Wire Size at 50, 75, and 100 Feet
- Deck Stair Stringer Calculator, 36 to 96 Inch Rise
- 20 ft dry, US 48×40 pallets: Pallet Count, CBM, and Payload