The roof pitch factor (also called the pitch multiplier or slope factor) converts a flat, footprint-measured roof area into the actual sloped surface area. The formula: pitch factor = √(rise² + 144) / 12. A 6/12 roof has a factor of 1.118, so a 2,000 sq ft footprint is really 2,236 sq ft of roof surface. Hips and valleys run diagonally, so they use a steeper factor: hip/valley factor = √(rise² + 288) / 12. The full chart below covers every pitch from 1/12 to 18/12 — or use the free interactive calculator on this page to convert any rise/run to degrees and adjust your roof area instantly.
| Pitch | Angle (degrees) | Pitch Factor | Hip/Valley Factor |
|---|---|---|---|
| 1/12 | 4.8° | 1.003 | 1.417 |
| 2/12 | 9.5° | 1.014 | 1.424 |
| 3/12 | 14.0° | 1.031 | 1.436 |
| 4/12 | 18.4° | 1.054 | 1.453 |
| 5/12 | 22.6° | 1.083 | 1.474 |
| 6/12 | 26.6° | 1.118 | 1.500 |
| 7/12 | 30.3° | 1.158 | 1.530 |
| 8/12 | 33.7° | 1.202 | 1.563 |
| 9/12 | 36.9° | 1.250 | 1.601 |
| 10/12 | 39.8° | 1.302 | 1.641 |
| 11/12 | 42.5° | 1.357 | 1.685 |
| 12/12 | 45.0° | 1.414 | 1.732 |
| 13/12 | 47.3° | 1.474 | 1.781 |
| 14/12 | 49.4° | 1.537 | 1.833 |
| 15/12 | 51.3° | 1.601 | 1.887 |
| 16/12 | 53.1° | 1.667 | 1.944 |
| 17/12 | 54.8° | 1.734 | 2.002 |
| 18/12 | 56.3° | 1.803 | 2.062 |
Actual roof area = flat (footprint) area × pitch factor. Example: a 2,000 sq ft footprint at 8/12 pitch = 2,000 × 1.202 = 2,404 sq ft, or 24.04 roofing squares. Use the hip/valley factor the same way for diagonal hip and valley lengths measured off a plan view.
A roof pitch factor is a multiplier that converts flat, footprint-measured roof area into the actual sloped surface area. A 6/12 pitch has a factor of 1.118, so a 2,000 sq ft footprint has 2,236 sq ft of actual roof surface.
Pitch factor = √(rise² + 144) / 12 for standard X/12 pitches. For a 6/12 pitch: √(36 + 144) / 12 = √180 / 12 = 1.118. The hip/valley factor uses √(rise² + 288) / 12 — for 6/12 that is 1.500.
A 6/12 roof has a pitch factor of 1.118 and an angle of 26.6° — the roof surface is 11.8% larger than its footprint. Its hip/valley factor is 1.500.
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