How to Find The Area of a Roof
Using the Roof Slope and the Footprint of the Building
Roof Online Staff
Table of Contents
– click to jump to section –
- Find the Area of a Roof: Short Version
- Find the Area of a Roof: Long Version
- Notes on Calculating Roof Area
- Roof Slope Multiplier Chart
Find the Area of a Roof: Short Version
Determine the square footage of the area covered by your roof.
Figure out the pitch of your roof.
Look up the roof pitch multiplier for that pitch.
Multiply the square footage of the covered area by the roof pitch multiplier.
Find the Area of a Roof: Long Version
Find the Area of the Roof’s Footprint
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 our page 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 increase your total footprint area to include any areas where one roof section overhangs another roof section.
Expressing Slope in Standard Pitch
Note: 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 distance has the same slope as a roof that rises 4 inches for every 12 inches of run.
In the U.S., the slope of the roof is typically given in standard pitch, which is a ratio expressed as “rise-in-run”, “X-in-12″, or “X:12”.
Traditionally, “12″ is always used as the run, because there are twelve inches in a foot, and you are stating how many inches the roof rises vertically for every foot the roof spans horizontally.
Pitched roofs commonly have slopes between 4-in-12 (6:12) and 12-in-12 (12:12). A roof that goes up at a 45-degree angle has a slope of 12:12.
Expressing Roof Slope in Degrees
The rest of the English-speaking world uses degrees, which seems simpler, but it takes a few extra steps to figure it out mathematically.
It also doesn’t immediately convey as much information about the roof on a practical level as the rise-in-run ratio expression.
To express the slope in degrees, you divide the rise by the run and find the inverse tangent of the result.
But you still need to know the rise and the run to find the roof slope in degrees unless you’re using a slope finder that tells you the slope in degrees.
Find the Slope of the Roof
You can find the slope by getting up on a ladder at the rake edge of the roof (the sloping edge) and measuring with a ruler and a spirit level, or you can use a specially-designed slope finder.*
You could also take your measurement in the attic using the underside of a rafter, the underside of the roof sheathing, or even the ceiling, if you’re sure that it follows the slope of the roof.
Eyeballing the slope and guessing (like “well, it looks like it goes up 6 feet for every 12 feet it goes across, so it’s about a 6:12 slope) is probably not a good idea.
The result you get from guessing like this might be close enough for government work, but if it’s a large roof and you’re a roofer with a 10% profit margin, I wouldn’t recommend it.
There are also a number of smartphone apps that you can use to find the slope of your roof, if you have a clear view of a gable end on the building. These can be acceptably accurate sometimes.
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.
Determine the Roof Slope Multiplier
For example, if the roof slope angle is 45°, then sec(45) = 1.414213. That will be your roof slope multiplier.
So, to proceed.
Once you have the slope of the roof expressed in standard pitch, you can consider yourself in possession of the lengths of the a and b sides of a right triangle. Now you need to pull out your trusty Pythagorean Theorem and figure out the length of the hypotenuse.
A good calculator can be found at 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
So 13.416 is the length of the hypotenuse.
Now that you have the length of your hypotenuse, 13.416, you want to think of that as the length of a line on the actual sloped roof surface over a horizontal distance of 12 inches. You want to find out how much longer that line is than the 12 inches it covers.
You will express this difference as a number, called the roof slope factor (also called the roof slope multiplier, roof pitch factor, or roof pitch multiplier).
Once you know the roof slope multiplier for any particular slope, you can use it to find the actual area of any size roof with the same slope.
So in this case, for every 12 inches the roof goes across horizontally (b), while rising 6 inches (a), there’s actually 13.416 inches of roof (c).
If you divide the 13.416 inches by the 12 inches (c/b), that gives you 1.118.
So the actual roof surface, if it were laid down flat on the ground, would be 1.118 times larger than the footprint of the roof. And for a roof with a slope of 6:12, that number, 1.118, is your roof slope multiplier.
Calculate the Surface Area of the Roof
Take the area of the roof’s footprint, say it’s 5,000 square feet, and multiply 5,000 by 1.118.
That gives you 5,590 square feet, which is the actual area of the surface of the roof. And that’s what you were looking for.
This applies to rafter lengths as well as areas. A rafter for a roof with a 6:12 slope will be 1.118 times as long as the horizontal length that it covers.
Notes on Calculating Roof Area
If the roof has areas with different slopes, as on a gambrel roof, you’ll have to figure out more than one slope and use the appropriate roof slope multiplier for the different areas.
As a shortcut, the roof slope multiplier for any slope can be determined by finding the square root of ((rise/run)² + 1).Divide the rise by the run. Square the result. Add 1 to the result of that. Find the square root of that result.
Roof Slope Multiplier Chart
We also have a much more complete roof slope multiplier chart that includes slopes by the half inch and slopes up to 30.5-in-12.
If you’re using the table below, you should consider getting yourself a construction calculator. That way you can instantly calculate the factor for any slope, among many other useful things. This one is very good.*
|Roof Pitch||Slope In Degrees||Roof Slope Multiplier|