Enter the size of the building, the eave overhang and the roof pitch. For a hip roof with the same pitch on all four sides, the calculator gives the roof area, squares and shingle bundles, plus the ridge, hip and common rafter lengths.
How to use the hip roof calculator
- Enter the building length and width wall to wall. The calculator adds the overhang on every side.
- Enter the eave overhang measured level, and the pitch in inches of rise per 12 in of run.
- Keep 15% waste for shingles, since every hip needs angled cuts, and check the bundles per square on the wrapper.
- Read the rafter lengths as line lengths. Allow for the ridge board, the plumb cut and the tail when you cut real rafters.
Hip roof formulas
Plan length A = length + 2 × overhang; plan width B = width + 2 × overhang (B ≤ A) Pitch factor = √(1 + (pitch ÷ 12)²) Roof area = A × B × pitch factor Ridge length = A − B Run = B ÷ 2 Common rafter = run × pitch factor Hip factor = √(2 + (pitch ÷ 12)²); hip rafter = run × hip factor Hip and ridge cap = ridge + 4 × hip rafter; eaves = 2 × (A + B)
When all four slopes have the same pitch, each one rises at the same angle from the same eave line, so the whole roof is the plan area multiplied by the pitch factor, just like a gable roof. The hip rafter runs diagonally across a square of plan, so its run is √2 times the common run, which gives the hip factor.
Worked example: a 40 × 30 ft house, 12 in overhang, 6/12 pitch
- Plan with overhang: 42 × 32 ft = 1,344 ft².
- Pitch factor at 6/12: √(1 + 0.5²) = 1.118. Roof area: 1,344 × 1.118 = 1,503 ft².
- With 15% waste: 17.28 squares, or 52 bundles at 3 per square.
- Ridge: 42 − 32 = 10 ft. Run: 32 ÷ 2 = 16 ft.
- Common rafter: 16 × 1.118 = 17.89 ft. Hip rafter: 16 × √(2 + 0.25) = 16 × 1.5 = 24 ft.
- Hip and ridge cap: 10 + 4 × 24 = 106 ft. Eaves: 2 × (42 + 32) = 148 ft.
Pitch and hip factors
| Pitch | Angle | Pitch factor (area, common rafter) | Hip factor (hip rafter) |
|---|---|---|---|
| 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 |
| 12/12 | 45.0° | 1.414 | 1.732 |
Multiply the plan area by the pitch factor for roof area, and the run (half the plan width) by the hip factor for the length of each hip.
Shingles for a hip roof
GAF, a major shingle maker, defines a roofing square as 100 ft² and notes that most 3-tab and architectural shingles come three bundles to the square, with 10 to 15 percent added for waste. A hip roof sits at the top of that range: every course ends in an angled cut along a hip, so 15% is a sensible starting point. Hip and ridge cap shingles are sold separately by the linear foot of coverage, so use the hip-and-ridge figure above to order them.
Hip roof or gable roof?
For the same building and pitch, a hip roof and a gable roof have the same roof area, because both are the plan area times the pitch factor. The hip roof replaces the two gable walls with roof, so it needs more cap shingles and more cutting, but no siding on the gable ends. Use the roofing calculator for a gable roof and the siding calculator for its gable walls.
Questions
How do you calculate the area of a hip roof?
Add the overhang to the length and width, multiply them, then multiply by the pitch factor √(1 + (pitch ÷ 12)²). A 42 × 32 ft plan at 6/12 is 1,344 × 1.118 = 1,503 ft².
How do you find the length of a hip rafter?
Take half the plan width as the run and multiply by √(2 + (pitch ÷ 12)²). At 6/12 the hip factor is 1.5, so a 16 ft run gives a 24 ft hip.
How long is the ridge on a hip roof?
The plan length minus the plan width, both including the overhang. A square building has no ridge at all: it is a pyramid roof with four hips meeting at a point.
Does a hip roof need more shingles than a gable roof?
The roof area is the same for the same footprint and pitch, but a hip roof wastes more in cuts and needs more cap shingles, so order about 5% more field shingles.
Sources
- How Many Bundles of Shingles Are in a Square?, GAF Roof Views blog.
Used for: 100 ft² per square, three bundles per square for most 3-tab and architectural shingles, 10–15% waste. - NIST Guide to the SI, Appendix B.8: Factors for units listed alphabetically, National Institute of Standards and Technology.
Used for: Exact inch and foot definitions; square metre conversions.