Roof geometry
Roof slope area from plan area and pitch
- where
- pitch factor, sloping ÷ plan
- roof pitch (°)
- sloping roof area (m²)
- plan area including overhangs (m²)
Explain this equation
Converts the plan area of a roof, measured off a drawing or the ground, into the actual sloping area you have to cover. Use it for ordering tiles, battens and underlay.
A_p is the area seen from above, including the overhangs. The slope makes the real surface bigger than its shadow on plan, and k is the factor that scales it up. It depends only on the pitch p.
Any length along a slope is its plan length divided by cos p, and the other direction (along the eaves) is unchanged, so the area grows by the same factor. This works for every plane of a roof with one pitch, including hips.
Sense check: at 35° the factor is about 1.22, so 80 m² on plan is about 97.7 m² of slope. At 45° it is 1.41, and at 22.5° only about 1.08.
Watch out: if different parts of the roof have different pitches, work them out separately and add them up.
True area of the roof covering from the area seen on a plan drawing. Works for any roof where every slope has the same pitch, including hipped and valleyed roofs.
Enter your values to see the result.
Good to know
Take the plan area to the outside of the fascia and verge (that is what gets covered). Because all slopes at one pitch are tilted by the same angle, the whole roof area is just plan area divided by cos θ, however many hips and valleys there are. Typical pitch factors: 1.10 at 25°, 1.15 at 30°, 1.22 at 35°, 1.41 at 45°.
Common mistake
Using the floor area of the building as the plan area, which leaves out the eaves and verge overhangs.
Limits
All slopes must share the same pitch. For mixed pitches, split the plan into areas of each pitch. Dormers and openings change the area: see the dormer calculator.
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.