What is a multiplier in roof design?

The multiplier is a factor used to convert horizontal measurements into actual lengths needed for rafters, taking into account the pitch of the roof.

A plumb cut is the angled cut made at the top of a rafter, allowing it to fit properly against the ridge board of the roof.

Why is snow load important in roof design?

Snow load is crucial for ensuring that a roof can support the weight of accumulated snow, which varies by location and must be considered in the overall design.

4/12 gable rafter on a 16 ft span

Explore the essentials of gable roofs with a 4/12 pitch over a 16 ft span. Learn about the multiplier, plumb cut, and the importance of snow load considerations.

Formula SSC-2026.1

4.00 / 12 · 18.43°

Pitch angle

18.43°

Multiplier 1.0541

Common rafter

9 ft 5 1/16 in

Tail 1 ft 5/8 in

Cuts

18.43° plumb

71.57° seat

Roof area

490 ft²

4.90 squares

Shingle bundles

3 bundles per square + 10% waste

Sheathing / felt

17 sheets

2 underlayment rolls

Delivery weight

2,028 lb

920 kg · 70 lb bundles, 46 lb sheets, 28 lb rolls

Gable truss triangleLive scaled blueprint

Rise and run are scaled from the span, overhang, and pitch. The small triangle is the pitch ratio.

Bill of materials and shopping list
Item	Net	Waste	Order	Unit price	Line total	Source Spec Material / Tool
Architectural shingle bundles	4.90 squares	10%	17 bundles	USD	$714.00	Source Spec Material / Tool
4x8 CDX sheathing	15.3 sheets	10%	17 sheets	USD	$476.00	Source Spec Material / Tool
Underlayment rolls	490 ft²	overlap allowance	2 rolls	USD	$110.00	Source Spec Material / Tool
Ridge cap bundles	26.0 ft ridge	—	2 bundles	25 ft per bundle	—	Source Spec Material / Tool

Source links open a product search on the Amazon storefront for the selected currency. SiteSpecCalc may earn a commission. The link does not change the quantities above.

Side-by-side pitch comparison
Pitch	Degrees	Multiplier	Rafter	Squares	Bundles	Sheets
4.0/12	18.43°	1.054	9 ft 5 1/16 in	4.90	17	17
6.0/12	26.57°	1.118	9 ft 11 15/16 in	5.20	18	18

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: 4/12 gable rafter on a 16 ft span

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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 gable roof with a 4/12 pitch means that for every 12 horizontal units, the roof rises 4 vertical units. This ratio is crucial for determining the roof's slope and overall design. The multiplier is used in calculations to convert the horizontal span into the actual length of the rafters needed to achieve the desired pitch.

The plumb cut refers to the cut made at the top of the rafter, which is angled to fit snugly against the ridge board. Proper plumb cuts are essential for ensuring the structural integrity of the roof. Additionally, while snow load is an important factor in roof design, it is not sized in this context and should be assessed separately based on local building codes and conditions.

Code reference

Consult local building codes for specific requirements related to snow load and roof design.

Field questions

What is a multiplier in roof design?: The multiplier is a factor used to convert horizontal measurements into actual lengths needed for rafters, taking into account the pitch of the roof.
What is a plumb cut?: A plumb cut is the angled cut made at the top of a rafter, allowing it to fit properly against the ridge board of the roof.
Why is snow load important in roof design?: Snow load is crucial for ensuring that a roof can support the weight of accumulated snow, which varies by location and must be considered in the overall design.