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A mansard roof has two pitches on all four sides: steep lower slopes, usually 60° to 70°, rising to a curb, and a low hip-shaped or flat top. The Mansard Roof Calculator steps the lower slopes in by their height × 12 ÷ their pitch on every side to find the size of the top, then treats each part as planes of a single pitch — sloped area is plan area times √(144 + rise²) ÷ 12. It returns the area of the lower slopes and the top, both rafters, the lower and upper hips, the top ridge, the curb and eave lengths, the total height and the shingle bundles at 3 per square, leaving a top flatter than 2/12 (the IRC R905.2.2 shingle minimum) out as membrane. A 40 × 30 ft building with 8 ft lower slopes at 24/12 and a 4/12 top steps in 4 ft, has 1,109 sq ft of lower slopes and a 742 sq ft top, and needs 64 bundles with 15% waste.
A mansard roof has two pitches on every side: steep lower slopes that rise to a curb and a low hip-shaped or flat top. The lower slopes step in by their height × 12 ÷ their pitch, which fixes the size of the top. Every plane has a single pitch, so its sloped area is its plan area times √(144 + rise²) ÷ 12.
| Lower pitch | Steps in | Top | Lower area | Total area | Bundles |
|---|---|---|---|---|---|
| 18/12 (56.3°) | 5.33 ft | 29.3 × 19.3 ft | 1,141 sq ft | 1,739 sq ft | 60 |
| 21/12 (60.3°) | 4.57 ft | 30.9 × 20.9 ft | 1,121 sq ft | 1,800 sq ft | 63 |
| 24/12 (63.4°) | 4.00 ft | 32.0 × 22.0 ft | 1,109 sq ft | 1,851 sq ft | 64 |
| 30/12 (68.2°) | 3.20 ft | 33.6 × 23.6 ft | 1,096 sq ft | 1,932 sq ft | 67 |
| 36/12 (71.6°) | 2.67 ft | 34.7 × 24.7 ft | 1,091 sq ft | 1,992 sq ft | 69 |
Split it into the steep lower slopes and the low top. Each plane has one pitch, so its sloped area is its plan area times the pitch factor √(144 + rise²) ÷ 12. A 40 × 30 ft mansard with 8 ft lower slopes at 24/12 steps in 4 ft on every side; the lower ring is 496 sq ft of plan × 2.236 = 1,109 sq ft and the 32 × 22 ft top at 4/12 is 742 sq ft, 1,851 sq ft in all.
The lower slopes are usually 60° to 70° — about 21/12 to 33/12 — and the top is low, often 2/12 to 4/12 or flat. Shingles need at least 2/12 (IRC R905.2.2), so a flatter top needs a low-slope membrane.
Squares of shingled area × (1 + waste) × 3 bundles per square. Mansards cut a lot at the corner hips, so 15% waste is a sensible start. The 40 × 30 ft example needs 18.51 squares, 21.29 with waste, so 64 bundles.
Yes, but slopes steeper than 21/12 need the manufacturer's steep-slope application: six nails per shingle and hand-sealing each tab with asphalt cement, because the sun cannot seal the strips on a near-vertical wall. Check the wrapper for the exact instructions.
A gambrel has two pitches on two sides with gable end walls, like a barn. A mansard has two pitches on all four sides, so it is a hip roof with a steep lower storey — the lower slopes form the walls of the top floor.
Need the whole roof at once? The free roofing calculator works out roof area, squares, shingle bundles, underlayment, drip edge, ridge cap and installed cost from one set of measurements.