Roof geometry
Gable-fronted dormer: cheeks, front, dormer roof and main roof displaced
- where
- depth of the dormer back into the main roof (m)
- cheek height at the front (m)
- main roof pitch (°)
- area of both cheeks (m²)
- front face including gable triangle (m²)
- dormer width (m)
- dormer roof pitch (°)
- plan area of the dormer roof (m²)
- dormer roof area, both slopes (m²)
- main roof area displaced (m²)
Explain this equation
Takes off a gable-fronted dormer: the two triangular cheeks, the front with its gable, the dormer roof, and the area of main roof it replaces. Use it for pricing cladding, tiling and the main-roof deduction.
The dormer roof runs back level until it meets the main roof. Its eaves sit h above the main slope, so it runs back d = h / tan p. Each cheek is a right triangle h by d, and two halves make h × d. The front is a rectangle w × h plus a gable triangle whose height is (w/2) tan a. The dormer ridge also rises, so it runs further back: that extra is the second part of A_pl. Dividing plan areas by cos of the relevant pitch gives sloping areas.
All of it is right-triangle geometry: plan length over cosine for slopes, rise over tangent for run.
Sense check: a 2 m wide dormer, 1.2 m cheeks, 35° main roof and 45° dormer roof runs about 1.71 m back, with about 2.06 m² of cheeks and 3.4 m² of front.
Watch out: this assumes the cheeks are triangles on a plain slope and the dormer ridge meets the main roof. Flat-roofed or hipped dormers need different shapes.
Areas for a pitched, gable-fronted dormer standing on a main roof: the two triangular cheeks, the front face, the dormer’s own roof and the main roof area it takes away.
Enter your values to see the result.
Good to know
Each cheek is a right triangle: height h at the front and running back until the main roof rises to the dormer eaves level, d = h / tan θ. The dormer roof covers the rectangle over the cheeks plus a triangle behind, where its ridge runs back to meet the main roof between the two valleys. Deduct the displaced area from the main roof and add the dormer roof, cheeks (tile-hanging or cladding) and front. Front face includes the window: deduct it for cladding.
Common mistake
Taking the cheek as a rectangle. Its area is half of height × depth on each side.
Limits
Gable-fronted dormer with a horizontal ridge below the main ridge, front wall standing on the main roof slope, no overhangs. Flat-roofed and hipped dormers differ (the flat-roof covering is in the flat roof calculators).
Sources
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the roof covering manufacturer’s fixing specification, BS 5534, BS 8000-6, BS 6229, the Lead Sheet Training Academy guidance and Building Regulations. Wind uplift and structural design need a competent designer.