How roof area is calculated
Every plane of a gable, hip or shed roof with one pitch is tilted by the same angle, so the roof surface is the flat footprint stretched by one number: the slope factor. You never need the rafter lengths to find the area.
slope factor = √(1 + (pitch ÷ 12)²)
plan area = (length + 2 × rake overhang) × (width + 2 × eave overhang)
roof area = plan area × slope factor
squares = roof area ÷ 100
A hip roof has eaves on all four sides, so it uses the eave overhang on both dimensions: plan area = (length + 2 × eave overhang) × (width + 2 × eave overhang).
A house with a porch, garage or wing is several sections, each with its own type and pitch. Every section's plan area is multiplied by its own slope factor, and the results are added: roof area = sum of (plan area × slope factor) over all sections.
The linear measurements follow from the same overhang-inclusive footprint (L′ × W′):
gable ridge = L′ hip ridge = L′ − W′ (0 if W′ ≥ L′)
hip length = (W′ ÷ 2) × √(2 + (pitch ÷ 12)²), four per hip roof
eaves = 2 × L′ (gable, shed) 2 × L′ + 2 × W′ (hip)
rakes = 2 × W′ × slope factor (gable, shed)
Worked example: 40 × 30 ft gable at 6/12
The calculator opens on a 40 × 30 ft gable roof at 6/12 with 12 in eave and rake overhangs.
- Slope factor: √(1 + (6 ÷ 12)²) = √1.25 = 1.118. The roof angle is 26.6°.
- Footprint with overhangs: 40' + 2 × 12 in = 42' long, and 30' + 2 × 12 in = 32' wide.
- Plan area: 42 × 32 = 1,344 ft².
- Roof area: 1,344 × 1.118 = 1,503 ft², or 15.0 squares.
- Ridge 42.0 ft, eaves 84.0 ft, rakes 2 × 32 × 1.118 = 71.6 ft.
Roof pitch factor table
Multiply the footprint area, overhangs included, by the factor for your pitch. The angle is the roof slope in degrees.
| Pitch | Slope factor | Angle |
|---|---|---|
| 1/12 | 1.003 | 4.8° |
| 2/12 | 1.014 | 9.5° |
| 3/12 | 1.031 | 14.0° |
| 4/12 | 1.054 | 18.4° |
| 5/12 | 1.083 | 22.6° |
| 6/12 | 1.118 | 26.6° |
| 7/12 | 1.158 | 30.3° |
| 8/12 | 1.202 | 33.7° |
| 9/12 | 1.250 | 36.9° |
| 10/12 | 1.302 | 39.8° |
| 11/12 | 1.357 | 42.5° |
| 12/12 | 1.414 | 45.0° |
| 13/12 | 1.474 | 47.3° |
| 14/12 | 1.537 | 49.4° |
| 15/12 | 1.601 | 51.3° |
| 16/12 | 1.667 | 53.1° |
| 17/12 | 1.734 | 54.8° |
| 18/12 | 1.803 | 56.3° |
Measuring tips
- Measure the building along the walls, not the roof. Use the outside of the wall framing or siding and take the length along the ridge direction.
- Measure the overhang horizontally, from the wall face to the outside of the fascia, at one eave and one gable end.
- Find the pitch with a 12 in level and a tape: hold the level against the underside of a rafter tail or on the roof surface and measure the rise over 12 in of run.
- For an L-shaped or T-shaped house, enter the main block as the first section and each wing with “+ Add another section”; each wing adds its own ridge and eaves.
- A porch, garage or wing at a different pitch or roof type is its own section. Add it with “+ Add another section” and set its type and pitch; the calculator applies each section's slope factor before adding up the squares.
When to hire a pro
Get a roofer to measure if the roof is steeper than about 8/12, has several pitches, valleys or dormers, or if you are comparing bids. Many roofers use aerial or drone measurements, which pick up every facet and are a good check on a hand measurement. Never walk a wet, icy or steep roof without fall protection.
Sources
- International Code Council, 2021 International Residential Code, Section R905.2.2 (asphalt shingle slope limits) and R905.1.1 (underlayment)
- Slope factor: Pythagorean theorem on the rise and run of one roof plane, √(1 + (rise/12)²)
- Industry convention: 1 roofing square = 100 ft² of roof surface