A sloped roof is larger than the ground it covers. If every slope has the same pitch, the roof area is the footprint – with the overhangs – divided by the cosine of the roof angle, which is the same as multiplying by √(1 + (rise ÷ 12)²). That factor is all you need, and it works for gable and hip roofs alike.
Example: a house 40 × 30 ft including the eaves, with a 6/12 roof. The footprint is 1,200 ft²; the slope factor for 6/12 is 1.118, so the roof is 1,342 ft², or 13.4 squares. With 10% extra: 14.8 squares, 45 bundles of three-to-a-square shingles. In metric: a 12 × 9 m footprint under a 30° roof is 108 ÷ cos 30° = 124.7 m², 137.2 m² with 10% extra.
Pitch, angle and slope factor
Multiply the footprint by the factor to get the roof area.
| Pitch (rise in 12) | Angle | Slope % | Factor |
|---|---|---|---|
| 2/12 | 9.5° | 17% | 1.014 |
| 3/12 | 14.0° | 25% | 1.031 |
| 4/12 | 18.4° | 33% | 1.054 |
| 5/12 | 22.6° | 42% | 1.083 |
| 6/12 | 26.6° | 50% | 1.118 |
| 7/12 | 30.3° | 58% | 1.158 |
| 8/12 | 33.7° | 67% | 1.202 |
| 9/12 | 36.9° | 75% | 1.250 |
| 10/12 | 39.8° | 83% | 1.302 |
| 12/12 | 45.0° | 100% | 1.414 |
| 14/12 | 49.4° | 117% | 1.537 |
| 18/12 | 56.3° | 150% | 1.803 |
Outside North America roofs are described by their angle in degrees; tile makers state a minimum angle for each tile, often somewhere between 15° and 35°. The same table in degrees:
| Angle | Factor | Same as |
|---|---|---|
| 15° | 1.035 | 3.2/12 |
| 20° | 1.064 | 4.4/12 |
| 25° | 1.103 | 5.6/12 |
| 30° | 1.155 | 6.9/12 |
| 35° | 1.221 | 8.4/12 |
| 40° | 1.305 | 10.1/12 |
| 45° | 1.414 | 12/12 |
| 50° | 1.556 | 14.3/12 |
What to measure
- The footprint with the overhangs: measure the house walls and add the eaves on each side (often 1–2 ft, 30–60 cm), or measure the roof edge from the ground with a long tape and a helper.
- The pitch: see the FAQ; or count siding courses or bricks up a gable to estimate the rise.
- The ridge: on a gable roof it runs the full length of the house; on a hip roof with one pitch it is the length minus the width. The calculator gives both, for ridge caps.
Roofing materials by area
Shingles are sold by the square; metal sheets, membranes and underlayment by the roll or sheet with a stated coverage; roof tiles by the number per m² or per square, which the maker gives for each tile (it changes with the overlap, which in turn depends on the pitch). Divide the roof area with extra by the coverage on the label. Valleys, dormers and skylights add cutting: allow 15% or more for complicated roofs.
Working on a roof is dangerous: use fall protection, and have a roofer measure anything steep or high. Once zet4u is saved on your phone, the calculator works offline, up a ladder or in a lumber yard.
Frequently asked questions
How many squares is my roof?
A roofing square is 100 ft² of roof surface. A 40 × 30 ft house with a 6/12 pitch has a footprint of 1,200 ft² and a roof of 1,342 ft², or 13.4 squares; with 10% extra for cuts and the ridge, order 14.8 squares (about 45 bundles of shingles).
How do I find my roof pitch without climbing on the roof?
Measure it from a gable end or in the attic: hold a level horizontally against a rafter, mark 12 in along it, and measure straight up to the rafter. That rise in inches is the pitch (6 in up = 6/12). A phone level app on a rafter gives the angle in degrees, which the calculator also takes.
Does a hip roof have more area than a gable roof?
Not if the pitch is the same. Every slope of a roof with one pitch is tilted by the same angle, so the total is always the footprint ÷ cos(angle), whatever the shape. A hip roof needs more waste allowance, because of the cuts along the hips.
How many bundles of shingles in a square?
Usually three for the common asphalt shingles (3-tab and most architectural ones); some heavy designer shingles come four or five to the square. The coverage is printed on the bundle wrapper, so check it before you order.
Sources
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