I think I already know the formula, but wanted to check if there are any instances where this may not work. I have been estimating construction costs for 5 years and haven’t found one instance where the following formula doesn’t give the correct answer:
Incline area = flat area (measured on plan)/cos (pitch in degrees)
So far this has worked for:
- Square, rectangular, hexagonal, circular, curved edge roofs
- Roofs of varying pitches eg. 5 degrees one side, 10 degrees the other. Just measure 2 separate areas and use the formula
It wouldn’t work for: - Roofs that are arced or domed vertically
Can anyone prove me wrong because I’ve seen so many people losing their mind over something so simple?
Just combining the comments above as an answer.
$\theta$ is the angle of the roof with the horizontal at the edge
$a$ = plan view radius
Area = $2\pi\cdot a^2\cdot\frac{1-\cos(\theta)}{\cos(\theta)}$
$\theta$ is the angle of the roof with the horizontal at the edge in radians
$a$ = plan view width
$l$ = plan view length
Area = $2\theta\cdot\frac{al}{\cos(\theta)}$