Roofing Calculator (squares, bundles, pitch factor)
Turn a building footprint and roof pitch into the real sloping area, roofing squares, and shingle bundles to order.
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Pitch factors and what they cost you
The same 1500 ft² building footprint at every common pitch. The rightmost columns are what you would actually be buying — a steep roof is a substantially bigger job than the plan view suggests.
| Pitch | Factor | Angle | Grade | Roof area | Squares |
|---|---|---|---|---|---|
| 1/12 | 1.0035 | 4.764° | 8.333% | 1 505.2 ft² | 16 |
| 2/12 | 1.0138 | 9.462° | 16.67% | 1 520.7 ft² | 16 |
| 3/12 | 1.0308 | 14.04° | 25% | 1 546.2 ft² | 16 |
| 4/12 | 1.0541 | 18.43° | 33.33% | 1 581.1 ft² | 16 |
| 5/12 | 1.0833 | 22.62° | 41.67% | 1 625 ft² | 17 |
| 6/12 | 1.118 | 26.57° | 50% | 1 677.1 ft² | 17 |
| 7/12 | 1.1577 | 30.26° | 58.33% | 1 736.6 ft² | 18 |
| 8/12 | 1.2019 | 33.69° | 66.67% | 1 802.8 ft² | 19 |
| 9/12 | 1.25 | 36.87° | 75% | 1 875 ft² | 19 |
| 10/12 | 1.3017 | 39.81° | 83.33% | 1 952.6 ft² | 20 |
| 12/12 | 1.4142 | 45° | 100% | 2 121.3 ft² | 22 |
| 14/12 | 1.5366 | 49.4° | 116.7% | 2 304.9 ft² | 24 |
| 16/12 | 1.6667 | 53.13° | 133.3% | 2 500 ft² | 25 |
| 18/12 | 1.8028 | 56.31° | 150% | 2 704.2 ft² | 28 |
Areas are net of waste. Below about 2/12, asphalt shingles are generally not suitable and a membrane roof is used instead.
Why a roof is bigger than the house
Measure a building from above and you get its footprint. But the roof is sloped, so the surface you are covering is longer than the horizontal distance it spans — and ordering material by the footprint is the single commonest way a roofing estimate comes up short.
Pitch factor = √(rise² + 12²) / 12 · Roof area = footprint × factor
Roof pitch in the US is written as rise per 12 inches of horizontal run — a "6/12" roof climbs 6 inches for every foot across. Pythagoras turns that into the slope length, and the ratio of slope to run is the pitch factor.
Worked example
A 50 × 30 ft house has a 1500 ft² footprint. On a 6/12 roof the pitch factor is √(36 + 144)/12 = 1.118, so the real roof area is 1500 × 1.118 = 1677 ft² — nearly 12% more than the plan view. That is 16.77 squares, and with 10% for waste you would be ordering 19 squares, or 56 bundles.
Squares and bundles
Roofing is sold by the "square", which is 100 ft² of finished roof surface — a unit that exists nowhere else in construction. Asphalt shingles come in bundles, and standard three-tab and architectural shingles run3 bundles to the square. Heavier premium shingles sometimes need four or five, so check the wrapper before ordering.
A 12/12 roof is exactly √2
When the rise equals the run the roof sits at exactly 45°, and the slope is exactly √2 ≈ 1.4142 times the horizontal — a 41% increase in material for the same building. It is a useful anchor for sanity-checking any pitch factor: anything at or below 45° must come out between 1 and 1.414.
What this doesn't include
This is the field area only. It does not add for hips, valleys, ridges, or starter courses, all of which need extra material and generate offcuts — a cut-up roof with several dormers can want 15% waste rather than 10. It also assumes a simple gable or hip where the whole footprint is roofed. For a complex roof, break it into rectangular sections, run each through separately, and add the results.
Related
The pitch factor is a right-triangle problem — theright triangle calculator will give you the rafter length for a given run and rise directly, and thetrigonometry calculator converts freely between angle, grade, and ratio.