Real area of a sloped roof

How it is calculated

A sloped roof has more real area than its shadow on the ground (the "plan area"): slope factor = 1 ÷ cos(angle). Real area = plan area × slope factor.

If you give the slope as a percentage, the angle is the arctangent of (slope/100); for example, 30% is equivalent to 16.7°. If you already know it in degrees, it is used directly.

Number of tiles = real area × tiles per m² × (1 + waste allowance), rounded up.

Example: 100 m² plan area, 30% slope. Angle = arctan(0.30) ≈ 16.7°. Factor = 1/cos(16.7°) ≈ 1.044. Real area = 100 × 1.044 = 104.4 m². With 28 tiles/m² and 5% waste: 104.4 × 28 × 1.05 ≈ 3069.4 → 3070 tiles.

Keep in mind

• This real area is that of the finished sloped roof, which is what has to be covered with tiles, waterproofing or sheet metal; do not confuse it with the plan area, which is usually what you know from the drawings.
• The number of tiles is indicative: actual consumption depends on the exact format, the overlap between pieces, and cuts at eaves, hips, ridges and chimney junctions; always ask for the manufacturer's coverage figure or use a sample tile if you can.
• Below about 30% slope, overlapping clay tile may not stay watertight against wind and heavy rain; for very low slopes, other systems are used (sheet metal with sealed joints, waterproof membranes under tile, flat roofs with a membrane).