The pitch multiplier
A roof measured from the ground gives you a flat rectangle. The actual surface you have to cover is the hypotenuse of that rectangle and the rise, and it is always larger.
The relationship is one divided by the cosine of the pitch angle. At 30° that is 1.155, so a roof whose footprint is 100 m² actually has about 115 m² of surface. At 45° the multiplier is 1.414, adding over 40%. At 60° it is 2.0 — the surface is double the footprint.
This is the single most common under-order in roofing, and it scales badly: the steeper the roof, the bigger the error and the more expensive the second delivery.
| Pitch | Multiplier | Extra area over footprint |
|---|---|---|
| 15° | 1.035 | +3.5% |
| 22.5° | 1.082 | +8% |
| 30° | 1.155 | +15% |
| 40° | 1.305 | +31% |
| 45° | 1.414 | +41% |
| 60° | 2.000 | +100% |
Squares, and why roofers use them
Roofing in imperial markets is quoted in squares, where one square is 100 square feet. It is a convenient unit because most roofing materials are packaged to cover a fraction of one — three bundles of asphalt shingle typically make a square.
The calculator gives the figure in squares alongside the area, so you can talk to a supplier in the units they price in. Note that the square applies to the sloped area, not the footprint, which is exactly the trap this page exists to avoid.
Waste, and what is not included
Ten per cent is the usual allowance on a simple gable roof. Hips and valleys generate substantially more cutting and 15% is more realistic; a complex roof with dormers can justify 20%.
The calculator covers the field area only. Ridge, hip and valley materials are length-based rather than area-based and are usually priced separately, as are underlay, battens, flashings, vents and fixings. On a real order those items are a meaningful fraction of the total.
Roofing is also the job where working at height changes the arithmetic. Scaffolding is often the largest single line on a domestic roofing quote, and it is not proportional to area at all.
Common questions
How do I work out roof area from the ground?
Measure the footprint, then multiply by the pitch multiplier — 1.155 at 30°, 1.414 at 45°. The calculator applies it for any angle.
What is a roofing square?
One hundred square feet of roof surface. Materials are often packaged and priced by the square.
How much waste should I allow?
10% on a simple gable roof, 15% with hips and valleys, up to 20% on a complex roof with dormers.