Hip Roof Calculator
Calculate total area, hip rafter length, ridge length, and complete material estimates for a four-sided hip roof from building length, width, and pitch.
Hip Roof Dimensions
ft
ft
ft
Total Roof Area
1,503 sq ft
Roofing Squares15.03 sq
Main Slopes (×2)930 sq ft
Hip Slopes (×2)572 sq ft
Footprint1,344 sq ft
Ridge Length10.0 ft
Hip Rafter Length24.0 ft
Common Rafter17.9 ft
Pitch Multiplier1.118×
Area Breakdown
2× Main trapezoidal slopes (42.0' × 17.9' slant avg)930 sq ft
2× Hip triangular slopes (32.0' base × 17.9' slant)572 sq ft
Total roofing area1,503 sq ft
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How to Use This Calculator
A hip roof is more geometrically complex than a gable roof. This calculator handles all the trigonometry automatically:
- Building Length — The longer footprint dimension (parallel to the ridge)
- Building Width — The shorter footprint dimension (perpendicular to the ridge)
- Roof Pitch — The common rafter pitch (rise over 12 inches). Hip roofs use this pitch for all common rafters — hip rafters are automatically computed at a shallower angle.
- Overhang — Eave overhang distance (horizontal)
The output includes: total roof area, ridge length, hip rafter length (each of 4), common rafter length, valley length (if any), roofing squares, and shingle bundles with waste.
The Formula
Ridge Length = Building Length - Building Width
Common Run = Building Width / 2
Common Rafter Length = Common Run × Pitch Multiplier
Hip Run = √(Common Run² + Common Run²) = Common Run × √2
Hip Pitch Multiplier = √(1 + (pitch/12)² / 2)
Hip Rafter Length = Hip Run × Hip Pitch Multiplier
Two Trapezoidal Slopes Area = 2 × ((Ridge + Building Length) / 2) × Common Rafter Length
Two Triangular End Slopes = 2 × (Common Rafter Length × Common Run / 2)
Total Roof Area = Trapezoid Areas + Triangle Areas
Common Run = Building Width / 2
Common Rafter Length = Common Run × Pitch Multiplier
Hip Run = √(Common Run² + Common Run²) = Common Run × √2
Hip Pitch Multiplier = √(1 + (pitch/12)² / 2)
Hip Rafter Length = Hip Run × Hip Pitch Multiplier
Two Trapezoidal Slopes Area = 2 × ((Ridge + Building Length) / 2) × Common Rafter Length
Two Triangular End Slopes = 2 × (Common Rafter Length × Common Run / 2)
Total Roof Area = Trapezoid Areas + Triangle Areas
Example: 40 x 24 ft Hip Roof at 5/12
Example: 40 ft long, 24 ft wide, 5/12 pitch hip roof
Ridge Length40 - 24 = 16 ft
Common Run24 / 2 = 12 ft
Common Rafter12 × 1.083 = 13.0 ft
Hip Run12 × 1.414 = 16.97 ft
Hip Rafter Length~17.7 ft (each)
Long Slope Area (each)(16 + 40) / 2 × 13.0 = 364 sq ft
End Triangle (each)13.0 × 12 / 2 = 78 sq ft
Total Roof Area2(364) + 2(78) = 884 sq ft
With 15% waste for the hip cuts, order 11.3 squares (34 bundles) of shingles. Hip roofs use more material per sq ft of footprint than gable roofs because of the angled cuts along each hip line.
Frequently Asked Questions
A gable roof has two sloped sides and two vertical triangular ends (gables). A hip roof has four sloped sides with no vertical ends. Hip roofs are stronger in wind, look more refined, but cost more and provide less attic space.
Start by installing the ridge board. Install the four hip rafters running from each corner to the ends of the ridge. Fill in common rafters between hips. Install jack rafters — shortened common rafters that run from the top plate to a hip rafter. This calculator gives you all the lengths needed.
Every shingle along a hip line must be cut diagonally, creating waste. Also, hip roofs require ridge cap shingles along all four hip lines plus the ridge, compared to just the ridge on a gable roof. Use a 15–20% waste factor for hip roofs vs. 10% for simple gables.
The hip rafter plumb cut angle = arctan(Rise / (Run × √2)). For a 6/12 common pitch: angle = arctan(6 / (12 × 1.414)) = arctan(0.354) = 19.47°. This is the backing angle needed for proper seating of hip jack rafters.
In most cases, hip roofs cost less to insure than gable roofs in wind-prone areas. Insurance companies in Florida and other hurricane states often offer discounts for hip roofs because they perform better in high winds. Check with your insurer for specific credits.