The footprint is not the roof
A roof is longer than the building it sits on, because it slopes. The flat area you measure on the ground, or read off a plan, has to be stretched by the pitch to give the real surface you will be covering.
The pitch multiplier
For a pitch given as a rise over a run, the multiplier is:
multiplier = √(1 + (rise ÷ run)²)
For a pitch in degrees it is 1 ÷ cos(angle). Common values:
- 4:12 (18.4°): 1.054
- 6:12 (26.6°): 1.118
- 9:12 (36.9°): 1.250
- 12:12 (45°): 1.414
- 30°: 1.155
- 45°: 1.414
A worked example
A simple gable roof on a building 10 m by 8 m, at 6:12.
- Footprint: 10 × 8 = 80 m², including the overhang if there is one.
- Roof surface: 80 × 1.118 = 89.4 m² across both slopes.
- Each slope is half of that, 44.7 m².
A hip roof over the same footprint at the same pitch has the same total area, because every part of it is still that footprint tilted by the same amount. What changes is the cutting and the ridge and hip lengths, not the square metres.
Roofs that are not simple
Split the plan into rectangles and triangles, multiply each by the multiplier for its own pitch, and add them up. Dormers, lower extensions and a garage at a different angle each need their own figure. Remember to include the eaves overhang, which can add a surprising amount on a small building.
Turning area into materials
- Shingles are sold by the square, which is 100 ft² or 9.29 m². Add 10% for waste, and more for a cut-up roof.
- Tiles go by the covering area each one gives at the lap you are using, which the maker publishes; it is not the tile's own size.
- Underlay and membrane need the laps counted too, typically 100 to 150 mm horizontally.
- Battens are a length, not an area: divide the slope length by the batten gauge to get the number of rows.
Measuring the pitch without climbing up
From inside the loft, hold a level horizontally against a rafter, measure 12 in or 300 mm along it, and measure straight up to the rafter. That vertical distance is the rise over that run. A phone inclinometer held flat on a rafter gives the angle directly.
Tools
The Roof Area Calculator applies the multiplier for you and takes the pitch as a ratio or an angle. The Roof Pitch Calculator converts between ratio, degrees and percent, Paint Calculator covers coating a flat or metal roof, and the Gravel Calculator handles ballast on a flat roof.