Measuring & pitch
Why your roof is bigger than your house
A 2,000 square foot house rarely has a 2,000 square foot roof. Three things make the difference, and each one is easy to measure.
The three differences
A house’s square footage is its heated floor area, measured inside or outside the walls depending on who is counting. A roof’s area is the sloped surface of every roof plane. Three things separate the two.
- Storeys. The roof covers the footprint once, however many floors are under it. A 2,000 square foot two-storey house may sit on a 1,000 square foot footprint.
- Overhangs. The roof extends past the walls on every side, and the overhang is roofed like the rest.
- Pitch. Every plane is tilted, so it is longer than its plan by the pitch factor.
Dormers, porches and bump-outs add their own pieces, and garages are often under the same roof without being in the living area.
Overhangs: the forgotten tenth
On a 50 by 32 foot house a 12-inch overhang on every side gives a 52 by 34 foot footprint: 1,768 square feet against 1,600, an increase of 10.5 percent. A 24-inch overhang makes it 21.5 percent. Small buildings feel it most: a 10 by 12 foot shed with 6-inch overhangs grows 18 percent.
Pitch: the factor that grows with steepness
The pitch factor, √(1 + (rise ÷ 12)²), turns plan area into sloped area. At 4/12 it is 1.054, at 6/12 1.118, at 8/12 1.202, at 12/12 1.414. The pitch factor calculator lists the factor for any pitch, and roof pitch explained shows where it comes from.
The same house, three roofs
A 50 by 32 foot single-storey house (1,600 sq ft) with 12-inch overhangs, so a 1,768 sq ft footprint.
- At 4/12: 1,768 × 1.054 = 1,864 sq ft of roof, 1.17 times the floor
- At 6/12: 1,768 × 1.118 = 1,977 sq ft, 1.24 times the floor
- At 12/12: 1,768 × 1.414 = 2,500 sq ft, 1.56 times the floor
The roof area calculator gives the 6/12 figure as its default example: 19.77 squares before waste.
Gable or hip: the same area, different waste
It is a common belief that a hip roof has more area than a gable roof. For one pitch over one footprint it does not. Each plane of a hip roof is tilted at the same pitch as a gable’s two planes would be, and the sloped area of any plane is its plan area times the same factor. The triangular hip ends cover exactly the plan area that the gable walls would have stood on.
What does change is everything at the edges. A hip roof has no rakes, four hips instead of none, a shorter ridge, more cut shingles along every hip and more cap. Estimators allow about 15 percent waste on a hip roof against 10 on a plain gable, so the order is bigger even though the area is not. The gable roof, meanwhile, has two triangles of wall that need siding or sheathing: on the 32-foot-wide house at 6/12 each gable is 32 × 8 ÷ 2 = 128 square feet, which the gable area calculator computes.
Dormers, porches and second pitches
Dormers add their roof faces and their cheek walls: a small gable dormer is about 40 square feet of roofing and siding, a shed dormer across a bedroom 100 or more. Porches are often a different, shallower pitch and should be run as their own footprint and factor. Garages under the main roof belong in the footprint even though they are not living space.
| House | Floor area | Footprint with overhangs | Pitch | Roof area | Roof ÷ floor |
|---|---|---|---|---|---|
| 50 × 32 ft ranch | 1,600 sq ft | 1,768 sq ft | 6/12 | 1,977 sq ft | 1.24 |
| Same, two storeys | 3,200 sq ft | 1,768 sq ft | 6/12 | 1,977 sq ft | 0.62 |
| Same, 24 in overhangs | 1,600 sq ft | 1,944 sq ft | 6/12 | 2,173 sq ft | 1.36 |
| Same, 8/12 with two dormers | 1,600 sq ft | 1,768 sq ft | 8/12 | 2,205 sq ft | 1.38 |
The last row is 1,768 × 1.202 = 2,125 square feet plus 80 for two small dormers. The arithmetic is the same every time; only the inputs change.
Height follows from the same triangle
The rise that makes the roof bigger also makes the house taller. On a 24-foot span at 6/12 the roof rises 6 feet; with the rafter’s height above the plate and an 8-foot wall, the ridge sits about 14½ feet above the floor, which the ridge height calculator works out. A trussed roof of the same span needs one truss every 2 feet along the building, 21 on a 40-foot length, from the truss count calculator.
Two-storey and split-level houses
On a two-storey house the roof sits over the upper floor’s footprint, which may be smaller than the ground floor if there is a garage, porch or one-storey wing with its own roof. Treat each roof as its own footprint: the main roof over the second floor, the lower roof over the wing, each with its overhangs and its pitch. Where a lower roof meets the upper wall there is no eave, but there is a sidewall or headwall to flash, which the step flashing calculator counts. Split-level houses usually have two or three roof sections at different heights and sometimes different pitches; add them up rather than estimating the whole house from its square footage.
What this means for quotes
Roofers quote in squares of roof area, usually with waste. A quote for 24 squares on the 1,600 square foot ranch is not inflated: it is 19.8 squares of roof plus about 20 percent for waste and rounding. The waste guide explains the allowance, and measuring a roof from the ground gives you your own figure to compare.