Hip Roof Shingle Calculator
Calculate shingle bundles, underlayment, and rafter lengths for 4-slope hip roofs. Includes waste factor and ridge cap estimation.
About
A hip roof differs from a standard gable roof as it has four sloping sides that meet at the top, creating a more aerodynamic and stable structure, though significantly more complex to frame and sheath. Accurate material estimation is critical here because the triangular geometry of the hip ends increases the amount of cutting and waste required compared to simple rectangular roofs. Underestimating materials on a hip roof is a common error that leads to expensive project delays.
This calculator determines the true surface area of the roof based on the pitch (slope) and the building's footprint. It accounts for the Multiplication Factor derived from trigonometry to convert the flat plan area into the sloped area. Crucially, it calculates the linear footage for Ridge Caps (where planes meet) and Hip Rafters, which require specific capping shingles often sold separately from standard field shingles.
Formulas
The core logic uses the Pythagorean theorem extended to 3D roof planes. Given a pitch P (rise over 12 run):
Rafter Length Multiplier (Common):
M = √1 + P2144
Total Roof Area:
Area = (Length × Width + Overhangs) × M
Hip Rafter Length (Corner):
Lhip = Run × √2 + (P/12)2
Reference Data
| Roof Pitch | Angle (°) | Multiplier | Approx Area Increase |
|---|---|---|---|
| 3/12 | 14.0° | 1.0308 | +3.1% |
| 4/12 | 18.4° | 1.0541 | +5.4% |
| 5/12 | 22.6° | 1.0833 | +8.3% |
| 6/12 | 26.6° | 1.1180 | +11.8% |
| 8/12 | 33.7° | 1.2019 | +20.2% |
| 12/12 | 45.0° | 1.4142 | +41.4% |