10/12 Gable Rafter Length on a 24×40 Building
A 10/12 gable, 24 ft wide and 40 ft long, with a 12 in overhang and a 1.5 in ridge.
Formula SSC-2026.1
10.00 / 12 · 39.81°
Pitch angle
39.81°
Multiplier 1.3017
Common rafter
16 ft 10 1/16 in
Tail 1 ft 3 5/8 in
Cuts
39.81° plumb
50.19° seat
Roof area
1,415 ft²
14.15 squares
Shingle bundles
47
3 bundles per square + 10% waste
Sheathing / felt
49 sheets
4 underlayment rolls
Delivery weight
5,656 lb
2,566 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 | 14.15 squares | 10% | 47 bundles | USD | $1,974.00 |
| 4x8 CDX sheathing | 44.2 sheets | 10% | 49 sheets | USD | $1,372.00 |
| Underlayment rolls | 1,415 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 |
|---|---|---|---|---|---|---|
| 10.0/12 | 39.81° | 1.302 | 16 ft 10 1/16 in | 14.15 | 47 | 49 |
| 12.0/12 | 45.00° | 1.414 | 18 ft 3 9/16 in | 15.37 | 51 | 53 |
| 8.0/12 | 33.69° | 1.202 | 15 ft 6 9/16 in | 13.06 | 44 | 45 |
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.
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Project: 10/12 Gable Rafter Length on a 24×40 Building
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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 10/12 pitch is arctan(10/12). The multiplier is the square root of 1 plus (10/12) 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 10/12 pitch?
- It is the arctangent of 10 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.
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