To find the area of a sloped roof, multiply the area of its footprint (overhangs included) by the pitch multiplier: √(1 + (rise ÷ 12)²). A 6/12 roof has a multiplier of 1.118, so a 1,176 sq ft footprint carries 1,315 sq ft of roof.
Pitch multiplier chart
| Pitch | Angle | Multiplier | Hip / valley factor | Rafter length per 10 ft of run |
|---|---|---|---|---|
| 1/12 | 4.8° | 1.003 | 1.417 | 10.03 ft |
| 2/12 | 9.5° | 1.014 | 1.424 | 10.14 ft |
| 3/12 | 14° | 1.031 | 1.436 | 10.31 ft |
| 4/12 | 18.4° | 1.054 | 1.453 | 10.54 ft |
| 5/12 | 22.6° | 1.083 | 1.474 | 10.83 ft |
| 6/12 | 26.6° | 1.118 | 1.5 | 11.18 ft |
| 7/12 | 30.3° | 1.158 | 1.53 | 11.58 ft |
| 8/12 | 33.7° | 1.202 | 1.563 | 12.02 ft |
| 9/12 | 36.9° | 1.25 | 1.601 | 12.5 ft |
| 10/12 | 39.8° | 1.302 | 1.641 | 13.02 ft |
| 11/12 | 42.5° | 1.357 | 1.685 | 13.57 ft |
| 12/12 | 45° | 1.414 | 1.732 | 14.14 ft |
| 14/12 | 49.4° | 1.537 | 1.833 | 15.37 ft |
| 16/12 | 53.1° | 1.667 | 1.944 | 16.67 ft |
| 18/12 | 56.3° | 1.803 | 2.062 | 18.03 ft |
Why one multiplier works for the whole roof
It seems too simple, but it’s exact: every plane of a roof with one pitch is tilted by the same angle, and tilting a surface stretches it in one direction by the same factor. So whether the roof is a gable, a hip or a complicated mix of both, if every slope has the same pitch, roof area = footprint × multiplier. Valleys and hips don’t change the area; they only change where the cuts and the waste are.
When planes have different pitches, such as a 12/12 main roof with a 4/12 porch, split the footprint into the parts under each pitch and apply each multiplier separately.
Worked example
A house measures 40 × 26 ft with 12 in overhangs on all sides, and the roof is a 7/12 hip.
- Footprint with overhangs: 42 × 28 = 1,176 sq ft.
- Multiplier at 7/12: 1.158.
- Roof area: 1,176 × 1.158 = 1,361 sq ft, or 13.6 squares.
- Hips: the common rafter run is half the width, 14 ft. Each hip is 14 × 1.53 = 21.4 ft, so four hips need 86 ft of hip cap.
The roofing calculator turns that area into shingle bundles, ridge cap, starter strip and drip edge.
How to find your pitch without climbing
- From the attic: hold a level horizontally against the underside of a rafter, mark 12 in along the level, and measure straight up from that mark to the rafter. That’s the rise.
- From a ladder at the gable end: the same measurement works on the rake board.
- From a photo: a photo taken square to the gable end lets you measure the angle; then match it to the angle column above.
- From plans: the pitch is usually printed on the elevations as a small triangle, like 6 over 12.
Pitch and your choice of roofing
Low slopes shed water slowly. Asphalt shingle makers set a minimum slope, and below about 4/12 they typically require extra underlayment, while very low slopes need a different roofing system altogether. Steep roofs, from about 8/12 up, are dangerous to walk and usually need roof jacks or harness systems, which matters if you’re comparing a DIY quote with a contractor’s.