I’ve got one last project before winter sets in. I want to build a small shed, but I’m not sure how to frame the standard gable roof. I can handle placing the framing square to make the plumb and heel cuts, but I’m confused about how to arrive at the exact length of the angled roof rafters. This is above my pay grade. Is there a crash course you can teach on how to get the length of the rafter just right?

— Tommy T., Stowe, Vt.

I distinctly remember being in the same situation many years ago as a rookie carpenter. Roof framing was a vast mystery to me, but I was eager to learn and started reading all sorts of books about the subject. Soon I was able to frame very complex roofs and the cuts came out great. I did make a few bonehead mistakes, but I’m not going to let that happen with you on this simple shed roof.

The gable roof, in my opinion, is perhaps the easiest roof to frame outside of a flat roof. To frame a gable roof, all you really need is a framing square that has crisp dimension markings on it as well as all the tables that one normally sees printed on the body of the square.

To get your head around the math that’s involved, let’s just think about a line drawing. After all, the top edge of the two roof rafters really are just two of the three line segments in a triangle. The base of the triangle would be the straight line that connects the two sloped lines where they pass over the outside surface of the exterior walls. In other words, roof framing is just basic trigonometry.

Good framing squares already have done the tough math for you. If you have one of these framing squares, look at the body of the square. This is the part that is almost always 2 inches wide and 24 inches long. On it you’ll see a table. Usually the first line of the table reads: length of common rafters per foot of run. You may have to look at both sides of the square to see this table.

Note there are all sorts of numbers, usually with decimal points, under the inch markings on the square. You should see the number 20.0 under 16 inches, the number 16.97 under 12 inches and 12.65 under the 4-inch mark. This tells you that you are looking at the correct line in the table.

These numbers with the decimal points are the multipliers that will give you the exact length of the rafter along its sloped line. All you need to do is provide the run. The run is one-half of the width of the shed across which the roof covers. If your shed is going to be 20 feet wide, then the run would be 10 feet. I always measure the total width to the outside face of the wall sheathing.

The only other thing you have to decide is the pitch of your roof. That’s what the inch markings on the body of the square represent. Let’s say that you want a 4-12 pitch roof. Using the number from the table on the square, you would multiply 12.65 times 10 to get the length of the common rafter. (I say this assuming your shed is going to be 20 feet wide.)

Doing the math, you will see that the length of the rafter is 126.5 inches. Here’s where it can get a little confusing. This is the true mathematical length of the rafter assuming there is no ridge board. In other words, if you cut two of these rafters exactly the same and set them up on the wall plates, the plumb cut lines at the top would fit perfectly with no gap at all. The same would be true for the heel cut down where the rafter sits on the wall.

In practice, however, there’s almost always a ridge board in common roof framing. It’s usually a 2x piece of lumber. If this is what you’re going to do, then you have to shorten the length of the rafter by half the thickness of the ridge board. It’s half because the ridge board is centered between the two rafters that touch the ridge board.

Now, understand that this doesn’t mean your rafter length is 3 / 4-inch shorter than the 126.5 inches. It’s close to that, but not exactly.

What I always do is make the accurate plumb cut line on the lumber as if there is no ridge board. This is the true length of the rafter. But then I measure out from this plumb cut line perpendicular the 3 / 4-inch shortening dimension. Now draw a second parallel plumb cut line next to your first one. This line needs to be down the rafter making it shorter, not longer. I made that mistake many moons ago!

Tim Carter is a columnist for Tribune Media Services. He can be contacted through his Web site at www.askthebuilder.com.