Roof area and squares calculator
A pitched roof covers more area than its footprint, so the tool multiplies the footprint by a factor for the roof's slope, then turns the roof area into roofing squares, with an allowance for waste if you add one. A roofing square is 100 square feet of roof.1
Result
- Footprint
- 1,302 sq ft
- Pitch factor
- 1.2500
- Pitch angle
- 36.9°
- Roof area
- 1,628 sq ft
- Squares
- 16.28
- Area with 10% waste
- 1,790 sq ft
- Squares with 10% waste
- 17.90
A square is 100 square feet of roof.
Estimate from the numbers you enter, not a roof measurement or a bid.
How the math works
Roof slope is the inches of vertical rise for every 12 inches of horizontal run, written like 4:12, or an angle in degrees.1
- Footprint: length × width, or an area already measured. This is the roof's horizontal projection, the surface it covers seen from above.2
- Pitch factor: the slope's length over 12 inches of run, divided by 12. By the Pythagorean theorem that is √(12² + rise²) ÷ 12, or √(1 + (rise ÷ 12)²). It matches the area factors in a shingle manufacturer's estimating guide: 1.118 at 6 in 12, 1.250 at 9 in 12, 1.414 at 12 in 12.3,2
- Roof area: footprint × pitch factor.2
- Squares: roof area ÷ 100.1
- Pitch angle: arctan(rise ÷ 12). A roof that rises 4 for every 12 of run is about 18.4 degrees.3
- With waste: roof area × (1 + waste percent). The guide's worked example allows 10%.2
Sections with different slopes are figured separately and added only after each is converted to roof area.2
Example
The guide's worked example has two sections: 1,302 square feet of footprint at 9 in 12 and 643 square feet at 6 in 12, with a 10% waste allowance. It rounds each section's roof area to the nearest square foot (1,627.5 to 1,628) before adding.2
| 9 in 12 | 6 in 12 | Total | |
|---|---|---|---|
| Footprint | 1,302 | 643 | 1,945 |
| Pitch factor | 1.250 | 1.118 | |
| Roof area | 1,628 | 719 | 2,347 |
| With 10% waste | 2,582 | ||
| Squares with waste | 25.82 |
The tool opens on the 9 in 12 section. Enter each section in turn and add the results.2
Where the numbers come from
- Footprint: the building plans, or measurements taken from the ground or from inside the attic.
- Pitch: the plans, or a reading taken from the ground with a pitch card or a carpenter's folding rule.
- Low-slope roofs: NRCA's low-slope category covers membrane roofs at 3:12 or less. The 2006 International Residential Code (Section R905.2.2) allows asphalt shingles only from 2:12, with double underlayment from 2:12 up to 4:12. Below 2:12 the tool still computes and notes it.1,4
Questions
- How many square feet are in a roofing square?
- 100. NRCA defines a square as a unit of roof area equal to 100 square feet, or enough material to cover 100 square feet of roof deck.1
- How do you calculate roof area from the footprint?
- Multiply the projected horizontal area by the factor for the roof's slope. The guide's factor for 6 in 12 is 1.118, so its 643 square foot section becomes about 719 square feet of roof.2
- What is a 4/12 pitch in degrees?
- About 18.4 degrees, the arctangent of 4 ÷ 12.3
- What is the minimum slope for asphalt shingles?
- 2:12 under Section R905.2.2 of the 2006 International Residential Code, with double underlayment from 2:12 up to 4:12.4
Terms used here
Cloudbreak
Cloudbreak records every roof section and rooftop unit before a storm, in photos, drone video and notes, so each roof's condition on a given date is on file.
Sources
The tool does arithmetic only and sends nothing anywhere. The rules it follows are from the published sources below.
- 1. National Roofing Contractors Association: Glossary of Roofing Terms
- 2. IKO: Estimating How Much Roofing Is Required
- 3. Richard Wright, Andrews University: Precalculus, 4-10: Applications of Right Triangle Trigonometry
- 4. LSU AgCenter: Consumer's Guide to Code-Compliant Roofing Installations, Pub. 3104 (March 2009)