Roofing Calculator

A 6/12 roof has 11.8% more surface than the floor beneath it

Roof area is not the same as the footprint it covers, because a pitched roof is a slope and a slope is longer than its horizontal run. A 6/12 pitch multiplies the area by 1.1180, so a 100 m² footprint carries 111.8 m² of roof. Order materials from the floor plan and you are short before you start.

How it works

• Converts a footprint and a pitch into actual roof surface area.
• Applies the pitch multiplier, which is where estimates from a floor plan go wrong.
• Adds waste allowance and converts to the bundles or sheets you actually buy.

multiplier = √(1 + (rise ÷ run)²)

roof area = footprint × multiplier

3/12 → 1.0308    6/12 → 1.1180    12/12 → 1.4142

the multiplier is the hypotenuse of the pitch triangle

Worked example

A 100 m² footprint at each common pitch.

1. 3/12 → 103.1 m² of roof
2. 4/12 → 105.4 m²
3. 6/12 → 111.8 m²
4. 9/12 → 125.0 m²
5. 12/12 → 141.4 m²

The same building needs anywhere from 3% to 41% more material than its floor area, depending only on pitch. A 45-degree roof — 12/12 — needs √2 times the footprint, which is the steepest common case and the one most often underestimated.

Reading the result

• Add waste on top of the corrected area, not instead of it. A simple gable roof wastes around 10%; a roof with valleys, hips and dormers runs to 15% or more because every cut line creates offcuts that cannot be used elsewhere.
• Overhangs are not in the footprint. Eaves and gable overhangs add area beyond the walls, and on a small building a 50 cm overhang on all sides is a surprisingly large fraction of the total.
• Pitch is expressed as rise over run, and the run is always 12 in imperial notation. A roof described as 6/12 rises 6 units for every 12 horizontal — it is not 6 units of anything absolute, which is why the multiplier is a ratio and dimensionless.
• Steeper roofs shed water and snow better and cost more in material and labour at the same footprint. The 41% extra at 12/12 is the material part of that trade; access and safety requirements add the rest.

Common questions

Can I just order materials for the floor area?

No, and the shortfall scales with pitch. At 6/12 you would be 11.8% short; at 12/12 you would be 41.4% short. Multiply the footprint by the pitch multiplier first, then add waste.

How much waste should I allow?

Around 10% for a straightforward gable, 15% or more once valleys, hips and dormers are involved. Complex roofs generate offcuts that cannot be reused, so the allowance rises with the number of cut lines rather than with the area.