How to Find the Area of a Sloped Roof
(Using the roof pitch and the footprint of the building):
(Scroll to the bottom if you just want to see the handy chart.)
Determine the area of the roof’s footprint, which is the area covered by the roof regardless of slope (or the apparent area of the roof when you look straight down at it, like from a satellite). Google Earth makes this pretty easy, but you can also simply measure the dimensions of the building on the ground and figure out the area that way. (See here for help using Google Earth.) Don't forget to take into account overhanging eaves or any other areas where the roof extends beyond the exterior walls of the building. You will also need to adjust your total roof area to account for any areas where one roof section overhangs another roof section.
Determine the slope, or pitch, of the roof. (Please note that all of these calculations work the same whether you are using inches or centimeters. You just have to plug the numbers in. A roof that rises 10 cm for every 30 cm of horizontal span, or run, has the same slope as a roof that rises 4 inches for every 12 inches of run). The slope of the roof is typically expressed as the ratio rise/run, which by general agreement in the roofing industry always uses 12 inches as the run, and states how many inches the roof rises for every 12 inches the roof extends horizontally. So pretty standard sloped roofs have slopes like 6/12 or 8/12. A roof that goes up at a 45 degree angle has a slope of 12/12. You can find the slope by getting up there and measuring with a yardstick and a spirit/bubble level, or you can take your measurement in the attic using a rafter, the underside of the roof deck, or even the ceiling, if you’re sure that it follows the slope of the roof. You can also just eyeball the slope and guess, (like "well, it looks like it goes up 6 feet for every 12 feet it goes across"; this gives you a working value of a 6/12 slope). The result you get from guessing like this will probably be close enough for government work, but if it’s a really large roof and you’re a roofer with a 7% profit margin, I wouldn’t recommend it.
(There are also a number of smartphone apps that you can use to find your roof pitch, to a useful degree of accuracy, if you have a clear view of a gable end on the building. You don't have to get up on the roof or go to the attic to use these. Go search your app store for "roof pitch" apps. You'll see.)
Once you have the slope of the roof, you can consider yourself in possession of the lengths of two sides of a right triangle. Now you need to pull out your trusty Pythagorean Theorem and figure out the length of the hypotenuse. (A convenient calculator can be found at http://web2.0calc.com). As I’m sure you remember, A² + B² = C². So, if your slope is 6/12,
6² + 12² = C²
36 + 144 = C²
180 = C²
√180 = C
13.416 = C
Now that you have the length of your hypotenuse, 13.416, you want to think of that as the actual roof surface, and find out how much longer it would be than the roof’s footprint width if it were laid down on top of it. So here, for every 12 inches the roof goes horizontally, while rising 6 inches, there’s actually 13.416 inches of roof. If you divide the 13.416 inches by the 12 inches, that gives you 1.118. And for a roof with a pitch of 6/12, that number, 1.118, is your roof pitch multiplier.
Take the area of the roof’s footprint, say 5,000 square feet, and multiply it by 1.118. That gives you 5,590 square feet, and that’s the number you’ve been looking for.
(Note that if the roof has areas with different slopes, as on a gambrel roof, for instance, you'll have to figure out more than one slope and use the appropriate roof pitch multiplier for the different areas.)