A gambrel roof has two slopes on each side, a steep lower slope and a shallow upper slope, which gives far more headroom in the loft than a simple gable. A popular layout uses four rafters of equal length, with the lower ones at about 60° and the upper ones at about 30°.
How to use the Gambrel Roof Calculator
- Building width
- Building length
- Lower slope angle
- Upper slope angle
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the building width and length and the angles of the lower and upper slopes. The calculator finds the common rafter length that closes the roof, the height, pitches in x/12, roof area, gable end area and attic volume.
Inputs explained
| Field | What to enter |
|---|---|
| Building width | Units: ft, m, in, yd, cm |
| Building length | Units: ft, m, in, yd, cm |
| Lower slope angle | Units: °, rad |
| Upper slope angle | Units: °, rad |
What each result means
- Rafter length (each of 4) = [Building width]÷(2×(cos(rad([Lower slope angle])) + cos(rad([Upper slope angle]))))
- Height of lower slope = [Rafter length (each of 4)]×sin(rad([Lower slope angle]))
- Total roof height = [Rafter length (each of 4)]×(sin(rad([Lower slope angle])) + sin(rad([Upper slope angle])))
- Lower pitch = 12×tan(rad([Lower slope angle]))
- Upper pitch = 12×tan(rad([Upper slope angle]))
- Roof surface area = 4×[Rafter length (each of 4)]×[Building length]
- Gable cross-section area = 2×([Rafter length (each of 4)]^2×cos(rad([Lower slope angle]))×sin(rad([Lower slope angle]))÷2 + [Rafter length (each of 4)]×cos(rad([Upper slope angle]))×([Height of lower slope] + [Total roof height])÷2)
- Both gable ends = 2×[Gable cross-section area]
- Attic volume = [Gable cross-section area]×[Building length]
Example values
How the main result changes when Building width changes and everything else stays at the example values above:
| Building width (ft) | Rafter length (each of 4) (ft) |
|---|---|
| 12 | 4.392 |
| 18 | 6.588 |
| 24 | 8.785 |
| 30 | 10.981 |
| 36 | 13.177 |
| 48 | 17.569 |
Formula
Rafter length r = W ÷ (2 × (cos α₁ + cos α₂))
Height = r × (sin α₁ + sin α₂)
Roof area = 4 × r × L
Cross-section = 2 × [½ r² cos α₁ sin α₁ + ½ r cos α₂ (r sin α₁ + height)]
Worked example
Inputs: Building width: 24 ft; Building length: 32 ft; Lower slope angle: 60 °; Upper slope angle: 30 °.
Results: Rafter length (each of 4) = 8.785 ft; Height of lower slope = 7.608 ft; Total roof height = 12 ft; Lower pitch = 20.78 /12; Upper pitch = 6.93 /12; Roof surface area = 1,124 ft²; Gable cross-section area = 182.6 ft²; Both gable ends = 365.2 ft²; Attic volume = 5,843 ft³.
Frequently asked questions
What angles are used for a gambrel roof?
Commonly 60° (about 21/12) for the lower slopes and 30° (about 7/12) for the upper slopes, with equal rafter lengths.
Why build a gambrel roof?
It creates a nearly full-height loft or second storey within the roof.
Are gambrel roofs good in snow?
The shallow upper slope holds snow, so it must be designed for your snow load.