How do you work out roof area from the floor plan?
Multiply the plan area by the slope factor — 1.118 at 6/12. The factor for every pitch, and why the footprint always understates the roof.
Plan area × the slope factor. At 6/12 that factor is 1.1180, so a 30' × 40' footprint is 1503 ft² of roof.
The footprint is 1200 ft², and the overhang and the slope between them add 303 ft² on top — over a fifth more roof than floor.
How that is worked out
- A sloped roof covers more surface than the ground under it, by exactly the ratio of the rafter's length to its run.
- That ratio is hypot(12, rise) ÷ 12 — the same number as the common rafter per foot of run, divided by twelve. At 6/12 it is 1.1180.
- Take the plan area *including the overhangs*, then multiply. The overhang is flat area that gets sloped along with everything else, and leaving it out is the other half of why footprint estimates come up short.
Slope factor by pitch, and what it does to a 30' × 40' footprint
| Pitch | Angle | Slope factor | Roof area | Over the footprint by |
|---|---|---|---|---|
| 3:12 | 14.0° | 1.0308 | 1385 ft² | 15% |
| 4:12 | 18.4° | 1.0541 | 1417 ft² | 18% |
| 5:12 | 22.6° | 1.0833 | 1456 ft² | 21% |
| 6:12 | 26.6° | 1.1180 | 1503 ft² | 25% |
| 7:12 | 30.3° | 1.1577 | 1556 ft² | 30% |
| 8:12 | 33.7° | 1.2019 | 1615 ft² | 35% |
| 10:12 | 39.8° | 1.3017 | 1749 ft² | 46% |
| 12:12 | 45.0° | 1.4142 | 1901 ft² | 58% |
Worth knowing
- The slope factor is the single most-skipped step in a roofing estimate, and it is always an undercount — never an over. At 12/12 the roof is over 40% larger than the footprint before the overhang is counted.
- Overhangs matter more than they look. A 12" overhang on all four sides of a 30' × 40' house adds 144 ft² of plan area before the slope factor touches it.
- This is for a simple gable. Hips have the same area as a gable over the same footprint, but a roof with dormers, valleys or varying pitches has to be broken into planes and added up.
- The factor is the same number the rafter tables print, divided by twelve — which is why a framing square can be used to check a roofing estimate.
Work out your own numbers
- Roofing calculator
Squares, bundles, starter strip, ridge cap and underlayment from a building footprint and a pitch.
- Rafters
Common, hip and jack rafters for any pitch, with the birdsmouth laid out and the cut angles alongside.
Related questions
- What is the roof pitch multiplier?
- The number you multiply a flat plan area by to get the sloped area over it. It is hypot(12, rise) ÷ 12 — 1.118 at 6/12, 1.202 at 8/12, 1.414 at 12/12. It is the same geometry as a rafter being longer than its run, expressed as a ratio.
- Is roof area the same as the footprint of the house?
- No, and never. It is larger by the slope factor and larger again by the overhangs. A 6/12 roof on a 1,200 ft² footprint with 12" overhangs is around 1,500 ft² of actual roof — a quarter more material than the floor area suggests.
- Does a hip roof have more area than a gable?
- Over the same footprint and at the same pitch, no — the areas are the same. What a hip roof has more of is cuts: every hip is a compound-angled cut on every course, which is why hip roofs cost more in both labour and waste even though the material area matches.