How the roofing calculator works
A sloped roof has more surface than the flat area it covers. The steeper the pitch, the bigger the difference. The calculator starts from the building’s footprint, adds the overhang on every side, then scales it up with a pitch multiplier.
Pitch is written as rise over 12: a 6/12 roof climbs 6 inches for every 12 inches across. The multiplier is the length of the sloping rafter compared with its flat run, from Pythagoras’ theorem. If you know the angle instead, the multiplier is 1 ÷ cos(angle).
This works for gable roofs, hip roofs and most combinations, as long as every slope has the same pitch. A hip roof and a gable roof over the same footprint at the same pitch have the same surface area.
Worked examples
A simple gable roof. The house is 40 ft × 30 ft with a 12 in overhang, and the pitch is 6/12.
- Plan area: (40 + 2) × (30 + 2) = 42 × 32 = 1,344 sq ft.
- Multiplier: √(1 + 0.5²) = √1.25 = 1.1180.
- Roof area: 1,344 × 1.118 = 1,503 sq ft.
- With 10% waste: 1,653 sq ft = 16.53 squares.
- Shingles: 16.53 × 3 = 49.6, so buy 50 bundles. #15 felt at about 4 squares a roll: 15.03 ÷ 4 = 3.8, so 4 rolls.
A hip roof. The footprint including overhangs is 2,000 sq ft and the pitch is 8/12.
- Multiplier: √(1 + 0.667²) = 1.2019. Roof area: 2,000 × 1.2019 = 2,404 sq ft.
- With 15% waste for the hips: 2,764 sq ft = 27.64 squares, or 83 bundles.
- If a roofer quotes $450 per square installed, that is about 27.64 × 450 = $12,440. Real prices vary widely by region and material, so use your own quotes.
A metric roof. A 12 m × 9 m house with a 50 cm overhang and a 30° roof.
- Plan area: 13 × 10 = 130 m². Multiplier: 1 ÷ cos 30° = 1.1547.
- Roof area: 130 × 1.1547 = 150.1 m². With 10% waste: 165.1 m².
- In squares: 165.1 ÷ 9.29 = 17.77 squares, or 54 bundles.
Roof pitch table
| Pitch | Angle | Multiplier | Extra area over flat |
|---|---|---|---|
| 3/12 | 14.0° | 1.0308 | 3% |
| 4/12 | 18.4° | 1.0541 | 5% |
| 5/12 | 22.6° | 1.0833 | 8% |
| 6/12 | 26.6° | 1.1180 | 12% |
| 7/12 | 30.3° | 1.1577 | 16% |
| 8/12 | 33.7° | 1.2019 | 20% |
| 9/12 | 36.9° | 1.2500 | 25% |
| 10/12 | 39.8° | 1.3017 | 30% |
| 12/12 | 45.0° | 1.4142 | 41% |
The full table, up to 24/12, is under the calculator. Pitches below 4/12 are called low slope. In the US the International Residential Code allows asphalt shingles only on slopes of 2/12 or steeper, with extra underlayment between 2/12 and 4/12. Flatter roofs need membrane systems instead.
Squares, bundles and waste
- One square is 100 sq ft (9.29 m²) of roof. It is the standard unit for pricing shingles and labour in North America.
- Bundles: standard 3-tab and most architectural shingles come 3 bundles to a square. Some heavy designer shingles need 4 or 5. The wrapper always states the coverage.
- Waste: allow about 10% on a plain gable roof and 15% on hip roofs or roofs with valleys, dormers and skylights. The allowance covers trimming at edges, starter courses and ridge caps. Very cut-up roofs can need 20%.
- Underlayment: typical rolls cover about 4 squares (#15 felt), 2 squares (#30 felt) or 10 squares (synthetic). These are worked out on the roof area before waste.
Measuring tips
- Measure from the ground. Measure the outside walls, then add the overhang on each side. The eaves usually stick out 12 to 24 inches.
- Find the pitch safely. From a ladder at the gable end, hold a level horizontally against the trim, mark 12 inches along it and measure straight up to the roof edge. That number is the rise.
- Split complex roofs. If different parts of the roof have different pitches, work each part out separately and add the squares.
- Add ridge and hip caps. Ridge cap shingles are often sold separately by length. Measure the total length of ridges and hips.
Related calculators
To turn a rise and run into a slope or angle, use the slope calculator. The square footage calculator adds up the floor area of the rooms below, and the area calculator handles triangles and other shapes such as gable ends. For percentage sums such as waste, try the percentage calculator.