Hip roofs look complicated, so many people try to measure every triangle on the roof. You usually do not need to. If the whole roof has one pitch, there is a one-line formula. Here is that method, a second method to check it and the extra lengths you need for shingles.
Method 1: footprint × pitch multiplier
This works for any roof shape, hip or gable, as long as every plane has the same pitch.
- Measure the footprint along the outside walls: 40 × 30 ft.
- Add the overhang to both ends of each side: with 12 inches, it becomes 42 × 32 ft = 1,344 sq ft.
- Find the multiplier for your pitch: 6/12 = 1.118 (see the pitch angle chart).
- Multiply: 1,344 × 1.118 = 1,503 sq ft of roof surface.
Method 2: triangles and trapezoids
A simple hip roof on a rectangle has two triangle ends and two trapezoid sides. Use this to check Method 1, or when the pitches are different.
Slope height (from eave to ridge, along the roof) = run × multiplier = 16 × 1.118 = 17.89 ft. The run is half the width with overhang: 32 ÷ 2 = 16 ft.
Ridge length = long side − short side = 42 − 32 = 10 ft.
| Plane | Shape | Formula | Area |
|---|---|---|---|
| End 1 | Triangle | 32 × 17.89 ÷ 2 | 286.2 sq ft |
| End 2 | Triangle | 32 × 17.89 ÷ 2 | 286.2 sq ft |
| Side 1 | Trapezoid | (42 + 10) ÷ 2 × 17.89 | 465.1 sq ft |
| Side 2 | Trapezoid | (42 + 10) ÷ 2 × 17.89 | 465.1 sq ft |
| Total | 1,502.7 sq ft |
Both methods match. If one side has a different pitch, use that plane’s own multiplier for its slope height.
The extra lengths you need
Hip length
Each hip runs diagonally from a corner to the end of the ridge:
hip = run × √(2 + (rise ÷ 12)²) = 16 × √(2 + 0.25) = 16 × 1.5 = 24 ft
Four hips = 96 ft. Add the 10 ft ridge for 106 ft of hip and ridge cap. At about 33 linear feet per bundle of cap shingles, that is 4 bundles.
Eaves
All four sides have eaves: 2 × (42 + 32) = 148 ft of drip edge and starter strip.
From area to a shingle order
| Item | Calculation | Order |
|---|---|---|
| Squares | 1,503 × 1.15 ÷ 100 | 17.28 squares |
| Field shingle bundles | 17.28 × 3 | 52 bundles |
| Hip and ridge cap | 106 ft ÷ 33 | 4 bundles |
| Drip edge (10 ft pieces) | 148 ÷ 10 | 15 pieces |
| Synthetic underlayment | 1,503 × 1.1 ÷ 1,000 | 2 rolls |
Why 15% waste? Every course is cut at an angle where it meets a hip. Add more if there are valleys or dormers.
Skip the arithmetic with the calculator’s hip preset. It applies the 15% waste and computes hip and ridge length for you.
Common mistakes
- Measuring along the walls only. The overhang can add 10% or more to the area.
- Using the hip pitch instead of the common pitch. Use the pitch of the roof planes, not the slope of the hip line.
- Forgetting cap shingles. Hip roofs need two to three times more cap than a gable roof of the same size. See hip roof vs gable roof.