Explanation
Simple pitched roof area
A pitched surface has more area than its horizontal footprint. The slope factor converts the projected area into surface area for a simple roof with one consistent pitch.
Measure the footprint and the pitch
Measure the horizontal footprint including any overhang you want covered. Enter the pitch as a rise and run in the same units. The ratio is unitless, so a 6-in-12 pitch can be entered as 6 and 12.
S = L × W × √(1 + (r/R)²) × (1 + a/100)
| S | Roof surface area (m²) |
|---|---|
| L | Footprint length |
| W | Footprint width |
| r | Rise |
| R | Run |
| a | Allowance |
Flat footprint without allowance
| Footprint length | 10 |
|---|---|
| Footprint width | 8 |
| Rise | 0 |
| Run | 12 |
| Allowance | 0 |
| Result | 80 m² |
Footprint 10 m × 8 m = 80 m². Slope factor √(1 + (0/12)²) = 1, so the sloped surface is 80 m². Add the 0% allowance = 80 m².
A 3:4 slope on a 10 m × 8 m footprint
| Footprint length | 10 |
|---|---|
| Footprint width | 8 |
| Rise | 3 |
| Run | 4 |
| Allowance | 0 |
| Result | 100 m² |
Footprint 10 m × 8 m = 80 m². Slope factor √(1 + (3/4)²) = 1.25, so the sloped surface is 100 m². Add the 0% allowance = 100 m².
The same slope with a 10% allowance
| Footprint length | 10 |
|---|---|
| Footprint width | 8 |
| Rise | 3 |
| Run | 4 |
| Allowance | 10 |
| Result | 110 m² |
Footprint 10 m × 8 m = 80 m². Slope factor √(1 + (3/4)²) = 1.25, so the sloped surface is 100 m². Add the 10% allowance = 110 m².
Diagram of this result
The section shows one gable end. The sloped edge is longer than the run by the slope factor, and so is the roof area compared with its footprint.
The rise, run, slope factor, footprint, sloped area and area with allowance are stated as numbers in the diagram.
Common mistakes
Do not enter the sloping rafter length as footprint width. Do not apply one pitch factor to sections that have different pitches.
Assumptions and limits
Simple roof with uniform slope and rectangular projected footprint. Dimensions and rise/run are bounded to one million; run is positive, rise may be zero; allowance 0–100%. Valleys, dormers, hips, penetrations and fastening specifications require separate assessment. Material estimates only; verify measurements, product guidance and site requirements before ordering.
Does this size rafters or roof loads?
No. It estimates surface area only. Structural strength, snow and wind loads, access and installation requirements need appropriate professional assessment.
Method and references
By Pythagoras, a slope with rise r over run R is √(1 + (r/R)²) times longer than its run, so a uniform roof’s area is its footprint times that factor. Material allowances must come from the chosen product and installer.