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Roof Pitch & Area Calculator

Pitch ratio, angle, roof area and shingle squares.

Inputs

Given
in
in
ft
ft
ft

Results

Computed

Roof pitch

6.0:12

26.57° from horizontal · slope factor 1.1180

Slope angle26.57°
Roof footprint1,333 sq ft
Actual roof surface area1,490 sq ft
Shingle squares14.90
Bundles (3 per square)45

Add 10–15% for waste, hip and valley cuts, and starter and ridge courses. Complex roofs with dormers waste considerably more than simple gables.

Pitch 6.0:12 · 1,490 sq ft · 14.9 squares

FIG. 1 — ROOF PITCH: RISE OVER RUN
RUN = 12RISE = 6θPITCH 6:12 · θ = arctan(6/12) ≈ 26.6°

How this is calculated

Roof pitch is expressed as rise over run — how many inches the roof climbs for every 12 inches of horizontal travel. A 6:12 roof rises six inches per foot. Converting that ratio to an angle is straightforward trigonometry:

angle = arctan(rise ÷ run) × 180 ÷ π

Roof area is not the same as the building footprint, because the sloped surface is longer than its horizontal projection. The slope factor accounts for that:

slope factor = √(rise² + run²) ÷ run

roof area = (length + 2 × overhang) × (width + 2 × overhang) × slope factor

Roofing material is sold by the square, where one square covers 100 square feet. Standard three-tab and architectural shingles run about three bundles per square. The figures here cover a simple gable roof; hips, valleys, dormers and ridge caps all add material, so most roofers order 10% extra on a simple roof and up to 15–20% on a cut-up one.

Worked example

Shingle squares for a 6/12 gable

  1. A gable roof covers a 30 ft × 40 ft building with a 6/12 pitch (6 in rise per 12 in run).
  2. Slope factor for 6/12 = √(1 + (6/12)²) = √1.25 ≈ 1.118.
  3. Plan area = 30 × 40 = 1,200 sq ft; true roof area = 1,200 × 1.118 ≈ 1,342 sq ft.
  4. Add 10% waste for hips, valleys and cuts: ≈ 1,476 sq ft.
  5. Shingles are sold by the square (100 sq ft): order 15 squares.

Common mistakes

  • Using plan area instead of slope area

    The steeper the pitch, the more the true surface exceeds the footprint. A 12/12 roof has 41% more surface than its plan area — under-ordering by that margin stops a job cold.

  • Reading pitch as an angle

    A 6/12 pitch is 26.6°, not 30°. Pitch is rise over a 12-unit run; the angle is the arctangent of that ratio.

  • Skipping the waste factor

    Simple gables need about 10% extra; roofs with hips, valleys or dormers can need 15% or more. Ordering the bare area leaves the last ridge unfinished.

What to do with this result

Frequently asked questions