How to Find the Area of a Sloped Roof (using the slope and the footprint):

(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.

Determine the slope, or pitch, of the roof. 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 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.

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 slope 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.

             

Roof Slope

1) 1/12

2) 2/12

3) 3/12

4) 4/12

5) 5/12

6) 6/12

7) 7/12

8) 8/12

9) 9/12

10) 10/12

11) 11/12

12) 12/12

13) 13/12

14) 14/12

15) 15/12

16) 16/12

17) 17/12

18) 18/12

19) 19/12

20) 20/12

21) 21/12

22) 22/12

23) 23/12

24) 24/12

25) 25/12

26) 26/12

27) 27/12

28) 28/12

29) 29/12

30) 30/12

Roof Slope Multiplier

1) 1.003

2) 1.014

3) 1.031

4) 1.054

5) 1.083

6) 1.118

7) 1.158

8) 1.202

9) 1.250

10) 1.302

11) 1.357

12) 1.414 

13) 1.474

14) 1.537

15) 1.601

16) 1.667

17) 1.734

18) 1.803

19) 1.873

20) 1.944

21) 2.016

22) 2.088

23) 2.162

24) 2.236

25) 2.311

26) 2.386

27) 2.462

28) 2.539

29) 2.615

30) 2.693

(in Degrees)       

1) 4.76°  

2) 9.46°

3) 14.04°

4) 18.43°

5) 22.62°

6) 26.57°

7) 30.26° 

8) 33.69° 

9) 36.87°

10) 39.81°

11) 42.51°

12) 45°

13) 47.29° 

14) 49.4°

15) 51.34°

16) 53.13°

17) 54.78°

18) 56.31°

19) 57.72°

20) 59.04°

21) 60.26°

22) 61.39°

23) 62.45°

24) 63.43°

25) 64.36° 

26) 65.22°

27) 66.04°

28) 66.80° 

29) 67.52°

30) 68.20°